Ensemble prediction experiments using conditional nonlinear optimal perturbation
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Two methods for initialization of ensemble forecasts are compared, namely, singular vector (SV) and conditional nonlinear optimal perturbation (CNOP). The comparison is done for forecast lengths of up to 10 days with a three-level quasi-geostrophic (QG) atmospheric model in a perfect model scenario. Ten cases are randomly selected from 1982/1983 winter to 1993/1994 winter (from December to the following February). Anomaly correlation coefficient (ACC) is adopted as a tool to measure the quality of the predicted ensembles on the Northern Hemisphere 500 hPa geopotential height. The results show that the forecast quality of ensemble samples in which the first SV is replaced by CNOP is higher than that of samples composed of only SVs in the medium range, based on the occurrence of weather re-gime transitions in Northern Hemisphere after about four days. Besides, the reliability of ensemble forecasts is evaluated by the Rank Histograms. The above conclusions confirm and extend those reached earlier by the authors, which stated that the introduction of CNOP improves the forecast skill under the condition that the analysis error belongs to a kind of fast-growing error by using a barotropic QG model.
Ensemble prediction experiments using conditional nonlinear optimal perturbation
Institute of Scientific and Technical Information of China (English)
JIANG ZhiNa; MU Mu; WANG DongHai
2009-01-01
Two methods for initialization of ensemble forecasts are compared, namely, singular vector (SV) and conditional nonlinear optimal perturbation (CNOP). The comparison is done for forecast lengths of up to 10 days with a three-level quasi-geostrophic (QG) atmospheric model in a perfect model scenario. Ten cases are randomly selected from 1982/1983 winter to 1993/1994 winter (from 12 to the following February). Anomaly correlation coefficient (ACC) is adopted as a tool to measure the quality of the predicted ensembles on the Northern Hemisphere 500 hPa geopotential height. The results show that the forecast quality of ensemble samples in which the first SV is replaced by CNOP is higher than that of samples composed of only SVs in the medium range, based on the occurrence of weather re-gime transitions in Northern Hemisphere after about four days. Besides, the reliability of ensemble forecasts is evaluated by the Rank Histograms. The above conclusions confirm .and extend those reached earlier by the authors, which stated that the introduction of CNOP improves the forecast skill under the condition that the analysis error belongs to a kind of fast-growing error by using a barotropic QG model.
Conditional nonlinear optimal perturbations of the double-gyre ocean circulation
Terwisscha van Scheltinga, A.D.; Dijkstra, H.A.
2008-01-01
In this paper, we study the development of finite amplitude perturbations on linearly stable steady barotropic double-gyre flows in a rectangular basin using the concept of Conditional Nonlinear Optimal Perturbation (CNOP). The CNOPs depend on a time scale of evolution te and an initial perturbation
Farano, Mirko; Cherubini, Stefania; Robinet, Jean-Christophe; De Palma, Pietro
2016-12-01
Subcritical transition in plane Poiseuille flow is investigated by means of a Lagrange-multiplier direct-adjoint optimization procedure with the aim of finding localized three-dimensional perturbations optimally growing in a given time interval (target time). Space localization of these optimal perturbations (OPs) is achieved by choosing as objective function either a p-norm (with p\\gg 1) of the perturbation energy density in a linear framework; or the classical (1-norm) perturbation energy, including nonlinear effects. This work aims at analyzing the structure of linear and nonlinear localized OPs for Poiseuille flow, and comparing their transition thresholds and scenarios. The nonlinear optimization approach provides three types of solutions: a weakly nonlinear, a hairpin-like and a highly nonlinear optimal perturbation, depending on the value of the initial energy and the target time. The former shows localization only in the wall-normal direction, whereas the latter appears much more localized and breaks the spanwise symmetry found at lower target times. Both solutions show spanwise inclined vortices and large values of the streamwise component of velocity already at the initial time. On the other hand, p-norm optimal perturbations, although being strongly localized in space, keep a shape similar to linear 1-norm optimal perturbations, showing streamwise-aligned vortices characterized by low values of the streamwise velocity component. When used for initializing direct numerical simulations, in most of the cases nonlinear OPs provide the most efficient route to transition in terms of time to transition and initial energy, even when they are less localized in space than the p-norm OP. The p-norm OP follows a transition path similar to the oblique transition scenario, with slightly oscillating streaks which saturate and eventually experience secondary instability. On the other hand, the nonlinear OP rapidly forms large-amplitude bent streaks and skips the phases
Zhang, Xing; Mu, Mu; Wang, Qiang; Pierini, Stefano
2017-06-01
In this study, the initial perturbations that are the easiest to trigger the Kuroshio Extension (KE) transition connecting a basic weak jet state and a strong, fairly stable meandering state, are investigated using a reduced-gravity shallow water ocean model and the CNOP (Conditional Nonlinear Optimal Perturbation) approach. This kind of initial perturbation is called an optimal precursor (OPR). The spatial structures and evolutionary processes of the OPRs are analyzed in detail. The results show that most of the OPRs are in the form of negative sea surface height (SSH) anomalies mainly located in a narrow band region south of the KE jet, in basic agreement with altimetric observations. These negative SSH anomalies reduce the meridional SSH gradient within the KE, thus weakening the strength of the jet. The KE jet then becomes more convoluted, with a high-frequency and large-amplitude variability corresponding to a high eddy kinetic energy level; this gradually strengthens the KE jet through an inverse energy cascade. Eventually, the KE reaches a high-energy state characterized by two well defined and fairly stable anticyclonic meanders. Moreover, sensitivity experiments indicate that the spatial structures of the OPRs are not sensitive to the model parameters and to the optimization times used in the analysis.
Pavarini, C.
1974-01-01
Work in two somewhat distinct areas is presented. First, the optimal system design problem for a Mars-roving vehicle is attacked by creating static system models and a system evaluation function and optimizing via nonlinear programming techniques. The second area concerns the problem of perturbed-optimal solutions. Given an initial perturbation in an element of the solution to a nonlinear programming problem, a linear method is determined to approximate the optimal readjustments of the other elements of the solution. Then, the sensitivity of the Mars rover designs is described by application of this method.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Considering the limitation of the linear theory of singular vector (SV), the authors and their collaborators proposed conditional nonlinear optimal perturbation (CNOP) and then applied it in the predictability study and the sensitivity analysis of weather and climate system. To celebrate the 20th anniversary of Chinese National Committee for World Climate Research Programme (WCRP), this paper is devoted to reviewing the main results of these studies. First, CNOP represents the initial perturbation that has largest nonlinear evolution at prediction time, which is different from linear singular vector (LSV) for the large magnitude of initial perturbation or/and the long optimization time interval. Second, CNOP,rather than linear singular vector (LSV), represents the initial anomaly that evolves into ENSO events most probably. It is also the CNOP that induces the most prominent seasonal variation of error growth for ENSO predictability; furthermore, CNOP was applied to investigate the decadal variability of ENSO asymmetry. It is demonstrated that the changing nonlinearity causes the change of ENSO asymmetry.Third, in the studies of the sensitivity and stability of ocean's thermohaline circulation (THC), the non-linear asymmetric response of THC to finite amplitude of initial perturbations was revealed by CNOP.Through this approach the passive mechanism of decadal variation of THC was demonstrated; Also the authors studies the instability and sensitivity analysis of grassland ecosystem by using CNOP and show the mechanism of the transitions between the grassland and desert states. Finally, a detailed discussion on the results obtained by CNOP suggests the applicability of CNOP in predictability studies and sensitivity analysis.
Institute of Scientific and Technical Information of China (English)
WANG Bo; HUO Zhenhua
2013-01-01
An extension of the conditional nonlinear optimal parameter perturbation (CNOP-P) method is applied to the parameter optimization of the Common Land Model (CoLM) for the North China Plain with the differential evolution (DE) method.Using National Meteorological Center (NMC) Reanalysis 6-hourly surface flux data and National Center for Environmental Prediction/Department of Energy (NCEP/DOE)Atmospheric Model Intercomparison Project II (AMIP-II) 6-hourly Reanalysis Gaussian Grid data,two experiments (I and II) were designed to investigate the impact of the percentages of sand and clay in the shallow soil in CoLM on its ability to simulate shallow soil moisture.A third experiment (III) was designed to study the shallow soil moisture and latent heat flux simultaneously.In all the three experiments,after the optimization stage,the percentages of sand and clay of the shallow soil were used to predict the shallow soil moisture in the following month.The results show that the optimal parameters can enable CoLM to better simulate shallow soil moisture,with the simulation results of CoLM after the double-parameter optimal experiment being better than the single-parameter optimal experiment in the optimization slot.Furthermore,the optimal parameters were able to significantly improve the prediction results of CoLM at the prediction stage.In addition,whether or not the atmospheric forcing and observational data are accurate can seriously affect the results of optimization,and the more accurate the data are,the more significant the results of optimization may be.
Zheng, Qin; Yang, Zubin; Sha, Jianxin; Yan, Jun
2017-02-01
In predictability problem research, the conditional nonlinear optimal perturbation (CNOP) describes the initial perturbation that satisfies a certain constraint condition and causes the largest prediction error at the prediction time. The CNOP has been successfully applied in estimation of the lower bound of maximum predictable time (LBMPT). Generally, CNOPs are calculated by a gradient descent algorithm based on the adjoint model, which is called ADJ-CNOP. This study, through the two-dimensional Ikeda model, investigates the impacts of the nonlinearity on ADJ-CNOP and the corresponding precision problems when using ADJ-CNOP to estimate the LBMPT. Our conclusions are that (1) when the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model in the prediction variable will lead to failure of the ADJ-CNOP method, and (2) when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making a false estimation of the LBMPT. Furthermore, the particle swarm optimization (PSO) algorithm, one kind of intelligent algorithm, is introduced to solve this problem. The method using PSO to compute CNOP is called PSO-CNOP. The results of numerical experiments show that even with a large initial perturbation and long prediction time, or when the objective function has multiple extreme values, PSO-CNOP can always obtain the global CNOP. Since the PSO algorithm is a heuristic search algorithm based on the population, it can overcome the impact of nonlinearity and the disturbance from multiple extremes of the objective function. In addition, to check the estimation accuracy of the LBMPT presented by PSO-CNOP and ADJ-CNOP, we partition the constraint domain of initial perturbations into sufficiently fine grid meshes and take the LBMPT obtained by the filtering method as a benchmark. The result shows that the estimation presented by PSO-CNOP is closer to the true value than the
Institute of Scientific and Technical Information of China (English)
JIANG Zhina; MU Mu
2009-01-01
The authors apply the technique of conditional nonlinear optimal perturbations (CNOPs) as a means of providing initial perturbations for ensemble forecasting by using a barotropic quasi-gcostrophic (QG) model in a perfect-model scenario. Ensemble forecasts for the medium range (14 days) are made from the initial states perturbed by CNOPs and singular vectors (SVs). 13 different cases have been chosen when analysis error is a kind of fast growing error. Our experiments show that the introduction of CNOP provides better forecast skill than the SV method. Moreover, the spread-skill relationship reveals that the ensemble samples in which the first SV is replaced by CNOP appear supcrior to those obtained by SVs from day 6 to day 14. Rank diagrams are adopted to compare the new method with the SV approach. The results illustrate that the introduction of CNOP has higher reliability for medium-range ensemble forecasts.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on small-scale vortices in Jupiter's atmosphere. Conditional nonlinear optimal perturbations (CNOPs) and linear singular vectors (LSVs) are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter's atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found.The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter's atmosphere and to compare the stability of motions in Jupiter's atmosphere and Earth's atmosphere further.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Wang, Qiang; Mu, Mu; Dijkstra, Henk A.
2012-01-01
A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander (KLM) state using the conditional nonlinear optimal parameter perturbation (CNOP-P) method. Because of their relatively large uncertainties, three model parameters were considered: the interfacial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 (SPG2) algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation (CNOP-I) method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.
Institute of Scientific and Technical Information of China (English)
WANG Qiang; MU Mu; Henk A. DIJKSTRA
2012-01-01
A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations.The results show that the model was able to capture the essential features of these path variations.We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander (KLM) state using the conditional nonlinear optimal parameter perturbation (CNOP-P) method.Because of their relatively large uncertainties,three model parameters were considcred:the interfacial friction coefficient,the wind-stress amplitude,and the lateral friction coefficient.We determined the CNOP-Ps optimized for each of these three parameters independently,and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 (SPG2) algorithm.Similarly,the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation (CNOP-I) method.Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days.But the prediction error caused by CNOP-I is greater than that caused by CNOP-P.The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored.Hence,to enhance the forecast skill of the KLM in this model,the initial conditions should first be improved,the model parameters should use the best possible estimates.
2010-07-01
Henson, M. 1998. "Nonlinear model predictive control: current status and future directions." Computers and Chemical Engineering , 23: 187-202. Ikhouane...Eichhorn2, Ralph Smith3 1Florida Center for Advanced Aero Propulsion (FCAAP), Department of Mechanical Engineering , Florida State University...collected using (AE Techron 7780 linear amplifier, DS1003 dSpace processor board, Matlab V5.2/ Simulink V2.2.1, Schaevitz 025MHR LVDT). The experimental
Ardema, M. D.
1979-01-01
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
Directory of Open Access Journals (Sweden)
Xudong Yin
2014-02-01
Full Text Available The authors propose to implement conditional non-linear optimal perturbation related to model parameters (CNOP-P through an ensemble-based approach. The approach was first used in our earlier study and is improved to be suitable for calculating CNOP-P. Idealised experiments using the Lorenz-63 model are conducted to evaluate the performance of the improved ensemble-based approach. The results show that the maximum prediction error after optimisation has been multiplied manifold compared with the initial-guess prediction error, and is extremely close to, or greater than, the maximum value of the exhaustive attack method (a million random samples. The calculation of CNOP-P by the ensemble-based approach is capable of maintaining a high accuracy over a long prediction time under different constraints and initial conditions. Further, the CNOP-P obtained by the approach is applied to sensitivity analysis of the Lorenz-63 model. The sensitivity analysis indicates that when the prediction time is set to 0.2 time units, the Lorenz-63 model becomes extremely insensitive to one parameter, which leaves the other two parameters to affect the uncertainty of the model. Finally, a serial of parameter estimation experiments are performed to verify sensitivity analysis. It is found that when the three parameters are estimated simultaneously, the insensitive parameter is estimated much worse, but the Lorenz-63 model can still generate a very good simulation thanks to the relatively accurate values of the other two parameters. When only two sensitive parameters are estimated simultaneously and the insensitive parameter is left to be non-optimised, the outcome is better than the case when the three parameters are estimated simultaneously. With the increase of prediction time and observation, however, the model sensitivity to the insensitive parameter increases accordingly and the insensitive parameter can also be estimated successfully.
Perturbations of normally solvable nonlinear operators, I
Directory of Open Access Journals (Sweden)
William O. Ray
1985-01-01
Full Text Available Let X and Y be Banach spaces and let ℱ and be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+ is surjective for sufficiently small perturbations of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.
Coupled Oscillator Model for Nonlinear Gravitational Perturbations
Yang, Huan; Green, Stephen R; Lehner, Luis
2015-01-01
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although borne out of the gravity/fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, w...
SOLVABILITY FOR NONLINEAR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The solvability of nonlinear elliptic equation with boundary perturbation is considered. The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.
Strongly Nonlinear Transverse Perturbations in Phononic Crystals
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S. Nikitenkova
2014-01-01
Full Text Available The dynamics of the surface heterogeneities formation in low-dimensional phononic crystals is studied. It is shown that phononic transverse perturbations in this medium are highly nonlinear. They can be described with the help of the Riemann wave and may form stable wave structures of the finite amplitude. The Riemann wave deformation is described analytically. The Riemann wave time existence up to the beginning of the gradient catastrophe is calculated.
Nonlinear Acoustics -- Perturbation Theory and Webster's Equation
Jorge, Rogério
2013-01-01
Webster's horn equation (1919) offers a one-dimensional approximation for low-frequency sound waves along a rigid tube with a variable cross-sectional area. It can be thought as a wave equation with a source term that takes into account the nonlinear geometry of the tube. In this document we derive this equation using a simplified fluid model of an ideal gas. By a simple change of variables, we convert it to a Schr\\"odinger equation and use the well-known variational and perturbative methods to seek perturbative solutions. As an example, we apply these methods to the Gabriel's Horn geometry, deriving the first order corrections to the linear frequency. An algorithm to the harmonic modes in any order for a general horn geometry is derived.
Perturbation analysis of nonlinear matrix population models
Directory of Open Access Journals (Sweden)
Hal Caswell
2008-03-01
Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.
Nonlinearly perturbed semi-Markov processes
Silvestrov, Dmitrii
2017-01-01
The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will cont...
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong
2015-08-19
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.
A Unified Approach for Solving Nonlinear Regular Perturbation Problems
Khuri, S. A.
2008-01-01
This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…
Direct Perturbation Method for Derivative Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
CHENG Xue-Ping; LIN Ji; HAN Ping
2008-01-01
We extend Lou's direct perturbation method for solving the nonlinear SchrSdinger equation to the case of the derivative nonlinear Schrodinger equation (DNLSE). By applying this method, different types of perturbation solutions axe obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.
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Constantin Bota
2014-01-01
Full Text Available The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results.
Directory of Open Access Journals (Sweden)
G. Sun
2011-11-01
Full Text Available Human activities and climate change are important factors that affect grassland ecosystems. A new optimization approach, the approach of conditional nonlinear optimal perturbation (CNOP related to initial and parameter perturbations, is employed to explore the nonlinearly combined impacts of human activities and climate change on a grassland ecosystem using a theoretical grassland model. In our study, it is assumed that the initial perturbations and parameter perturbations are regarded as human activities and climate change, respectively. Numerical results indicate that the climate changes causing the maximum effect in the grassland ecosystem are different under disparate intensities of human activities. This implies the pattern of climate change is very critical to the maintenance or degradation of grassland ecosystem in light of high intensity of human activities and that the grassland ecosystem should be rationally managed when the moisture index decreases. The grassland ecosystem influenced by the nonlinear combination of human activities and climate change undergoes abrupt change, while the grassland ecosystem affected by other types of human activities and climate change fails to show the abrupt change under a certain range of perturbations with the theoretical model. The further numerical analyses also indicate that the growth of living biomass and the evaporation from soil surface shaded by the wilted biomass may be crucial factors contributing to the abrupt change of the grassland equilibrium state within the theoretical model.
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
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Boglaev Igor
2009-01-01
Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
de Sitter limit of inflation and nonlinear perturbation theory
Jarnhus, Philip R
2007-01-01
We study the fourth order action of comoving curvature perturbations in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbations to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of comoving curvature perturbations and discuss the slow-roll order of the n-point correlation function.
Optimization under Nonlinear Constraints
1982-01-01
In this paper a timesaving method is proposed for maximizing likelihood functions when the parameter space is subject to nonlinear constraints, expressible as second order polynomials. The suggested approach is especially attractive when dealing with systems with many parameters.
Intelligent perturbation algorithms for space scheduling optimization
Kurtzman, Clifford R.
1990-01-01
The optimization of space operations is examined in the light of optimization heuristics for computer algorithms and iterative search techniques. Specific attention is given to the search concepts known collectively as intelligent perturbation algorithms (IPAs) and their application to crew/resource allocation problems. IPAs iteratively examine successive schedules which become progressively more efficient, and the characteristics of good perturbation operators are listed. IPAs can be applied to aerospace systems to efficiently utilize crews, payloads, and resources in the context of systems such as Space-Station scheduling. A program is presented called the MFIVE Space Station Scheduling Worksheet which generates task assignments and resource usage structures. The IPAs can be used to develop flexible manifesting and scheduling for the Industrial Space Facility.
THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
王国灿; 金丽
2002-01-01
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established.Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained.The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
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Jinmyoung Seok
2015-07-01
Full Text Available In this article, we are interested in singularly perturbed nonlinear elliptic problems involving a fractional Laplacian. Under a class of nonlinearity which is believed to be almost optimal, we construct a positive solution which exhibits multiple spikes near any given local minimum components of an exterior potential of the problem.
A numerical-perturbation method for the nonlinear analysis of structural vibrations
Nayfeh, A. H.; Mook, D. T.; Lobitz, D. W.
1974-01-01
A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.
Random perturbations of nonlinear parabolic systems
Beck, Lisa
2011-01-01
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed, presents both classes of systems where all weak solutions are in fact more regular, and examples of systems with weak solutions which develop singularities in finite time. Our main result is the extension of a regularity result due to Kalita to the stochastic case. Concerning the examples with singular solutions (outside the setting of Kalita's regularity result), we do not know whether stochastic noise may prevent the emergence of singularities, as it happens for easier PDEs. We can only prove that, for a linear stochastic parabolic system with coefficients outside the previous regularity theory, the expected value of the solution is not singular.
Comparison of alternative improved perturbative methods for nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico)]. E-mail: paolo@ucol.mx; Raya, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2005-06-06
We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt-Poincare technique. As illustrative examples we choose one-dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.
ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION
Institute of Scientific and Technical Information of China (English)
JIA Xinchun; ZHENG Nanning; LIU Yuehu
2005-01-01
The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.
Fully nonlinear and exact perturbations of the Friedmann world model
Hwang, Jai-chan
2012-01-01
In 1988 Bardeen has suggested a pragmatic formulation of cosmological perturbation theory which is powerful in practice to employ various fundamental gauge conditions easily depending on the character of the problem. The perturbation equations are presented without fixing the temporal gauge condition and are arranged so that one can easily impose fundamental gauge conditions by simply setting one of the perturbation variables in the equations equal to zero. In this way one can use the gauge degrees of freedom as an advantage in handling problems. Except for the synchronous gauge condition, all the other fundamental gauge conditions completely fix the gauge mode, and consequently, each variable in such a gauge has a unique gauge invariant counterpart, so that we can identify the variable as the gauge-invariant one. Here, we extend Bardeen's linear formulation to fully nonlinear order in perturbations, with the gauge advantage kept intact. Derived equations are exact, and from these we can easily expand to high...
Linear and non-linear perturbations in dark energy models
Escamilla-Rivera, Celia; Fabris, Julio C; Alcaniz, Jailson S
2016-01-01
In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state $w(z)$. In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected $w(z)$ parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard $\\Lambda$CDM model.
Application of the homotopy perturbation method to the nonlinear pendulum
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Hernandez, A; Belendez, T; Neipp, C; Marquez, A [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-01-15
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as high as 130{sup 0}. Another important point is that this method provides an analytical expression for the angular displacement as a function of time as the sum of an infinite number of harmonics; although for practical purposes it is sufficient to consider only a finite number of harmonics. We believe that the present study may be a suitable and fruitful exercise for teaching and better understanding perturbation techniques in advanced undergraduate courses on classical mechanics.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
Pietroni, Massimo
2008-01-01
Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum and the bispectrum are obtained -at any redshift and for any momentum scale- by integrating a coupled system of differential equations. The solution of the equations corresponds, in perturbation theory, to the summation of an infinite class of corrections. Compared to other resummation frameworks, the scheme discussed here is particularly suited to cosmologies other than LambdaCDM, such as those based on modifications of gravity and those containing massive neutrinos. As a first application, we compute the Baryonic Acoustic Oscillation feature of the power spectrum, and compare the results with perturbation theory, the halo model, and N-body simulations. The density-velocity and velocity-velocity power spectra are also computed, showing that they are much less contaminated by nonlinearities than the densit...
Institute of Scientific and Technical Information of China (English)
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Nonlinear Optimization with Financial Applications
Bartholomew-Biggs, Michael
2005-01-01
The book introduces the key ideas behind practical nonlinear optimization. Computational finance - an increasingly popular area of mathematics degree programs - is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material - which occupies about one-third of the text - is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performan
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Passive Control and ε-Bound Estimation of Singularly Perturbed Systems with Nonlinear Nonlinearities
Directory of Open Access Journals (Sweden)
Linna Zhou
2013-01-01
Full Text Available This paper considers the problems of passivity analysis and synthesis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameter ε, a new method is proposed to estimate the ε-bound, such that the system is passive when the singular perturbation parameter is lower than the ε-bound. Furthermore, a controller design method is proposed to achieve a predefined ε-bound. The proposed results are shown to be less conservative than the existing ones because the adopted storage function is more general. Finally, an RLC circuit is presented to illustrate the advantages and effectiveness of the proposed methods.
Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.
Nagarale, Ravindrakumar M; Patre, B M
2014-05-01
This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.
Non-Gaussianity vs. non-linearity of cosmological perturbations
Verde, L
2001-01-01
Following the discovery of the CMB, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us towards a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, non-linear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but these might not be faithful tr...
Geometric scaling in ultrahigh energy neutrinos and nonlinear perturbative QCD
Machado, M V T
2011-01-01
The ultrahigh energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes. Currently there are several approaches which predict different behaviors for its magnitude for ultrahigh energies. In this contribution is presented a summary of current predictions based on the non-linear QCD evolution equations, the so-called perturbative saturation physics. In particular, predictions are shown based on the parton saturation approaches and the consequences of geometric scaling property at high energies are discussed. The scaling property allows an analytical computation of the neutrino scattering on nucleon/nucleus at high energies, providing a theoretical parameterization.
Perturbation and harmonic balance methods for nonlinear panel flutter.
Kuo, C.-C.; Morino, L.; Dugundji, J.
1972-01-01
A systematic way of applying both perturbation methods and harmonic balance methods to nonlinear panel flutter problems is developed here. Results obtained by both these methods for two-dimensional simply supported and three-dimensional clamped-clamped plates with six modes agree well with those obtained by the straightforward direct integration method, yet require less computer time and provide better insight into the solutions. Effects of viscoelastic structural damping on the flutter stability boundary are generally found to be destabilizing and the postflutter behavior becomes more explosive. The methods developed here may be of interest in related vibration problems.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Fully localised nonlinear energy growth optimals in pipe flow
Pringle, Chris C T; Kerswell, Rich R
2014-01-01
A new, fully-localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known (streamwise-independent) linear optimal (Schmid \\& Henningson 1994) is selected, and appears to remain the optimal up until the critical energy at which transition is triggered. The form of this optimal is similar to that found in short pipes (Pringle et al.\\ 2012) albeit now with full localisation in the streamwise direction. This fully-localised optimal perturbation represents the best approximation yet of the {\\em minimal seed} (the smallest perturbation capable of triggering a turbulent episode) for `real' (laboratory) pipe flows.
Formal Proofs for Nonlinear Optimization
Directory of Open Access Journals (Sweden)
Victor Magron
2015-01-01
Full Text Available We present a formally verified global optimization framework. Given a semialgebraic or transcendental function f and a compact semialgebraic domain K, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of f over K.This method allows to bound in a modular way some of the constituents of f by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by sums of squares relaxations. Our implementation tool interleaves semialgebraic approximations with sums of squares witnesses to form certificates. It is interfaced with Coq and thus benefits from the trusted arithmetic available inside the proof assistant. This feature is used to produce, from the certificates, both valid underestimators and lower bounds for each approximated constituent.The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of multivariate transcendental inequalities. We illustrate the performance of our formal framework on some of these inequalities as well as on examples from the global optimization literature.
Stability analysis for nonlinear multi－variable delay perturbation problems
Institute of Scientific and Technical Information of China (English)
WangHongshan; ZhangChengjian
2003-01-01
This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems(MVDPP) of the form x′(t) = f(x(t),x(t - τ1(t)),…,x(t -τm(t)),y(t),y(t - τ1(t)),…,y(t - τm(t))), and gy′(t) = g(x(t),x(t- τ1(t)),…,x(t- τm(t)),y(t),y(t- τ1(t)),…,y(t- τm(t))), where 0 < ε <<1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1998-01-01
The simultaneous perturbation stochastic approximation (SPSA) algorithm has attracted considerable attention for challenging optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient...... simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1997-01-01
The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient...... simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...
Optimal design for nonlinear response models
Fedorov, Valerii V
2013-01-01
Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss ada
Global Optimization Using Diffusion Perturbations with Large Noise Intensity
Institute of Scientific and Technical Information of China (English)
G. Yin; K. Yin
2006-01-01
This work develops an algorithm for global optimization. The algorithm is of gradient ascent type and uses random perturbations. In contrast to the annealing type procedures, the perturbation noise intensity is large. We demonstrate that by properly varying the noise intensity, approximations to the global maximum can be achieved. We also show that the expected time to reach the domain of attraction of the global maximum,which can be approximated by the solution of a boundary value problem, is finite. Discrete-time algorithms are proposed; recursive algorithms with occasional perturbations involving large noise intensity are developed.Numerical examples are provided for illustration.
Introduction to Nonlinear and Global Optimization
Hendrix, E.M.T.; Tóth, B.
2010-01-01
This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization
Rahman, T.
2009-01-01
In this thesis, a finite element based perturbation approach is presented for geometrically nonlinear analysis of thin-walled structures. Geometrically nonlinear static and dynamic analyses are essential for this class of structures. Nowadays nonlinear analysis of thin-walled shell structures is oft
Parallel Nonlinear Optimization for Astrodynamic Navigation Project
National Aeronautics and Space Administration — CU Aerospace proposes the development of a new parallel nonlinear program (NLP) solver software package. NLPs allow the solution of complex optimization problems,...
Two-parameter non-linear spacetime perturbations gauge transformations and gauge invariance
Bruni, M; Sopuerta, C F; Bruni, Marco; Gualtieri, Leonardo; Sopuerta, Carlos F.
2003-01-01
An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity Omega), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by lambda) are then built on top of the axisymmetric perturbations in Omega. Clearly, any interesting physics requires non-linear perturbations, as at least terms lambda Omega need to be considered. In this paper we analyse the gauge dependence of non-linear perturbations depending on two parameters, derive explicit higher order gauge transformation rules, and define gaug...
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.
Nonlinear Generation of Fluting Perturbations by Kink Mode
Ruderman, M. S.
2017-08-01
We study the excitation of fluting perturbations in a magnetic tube by an initially imposed kink mode. We use the ideal magnetohydrodynamic (MHD) equations in the cold-plasma approximation. We also use the thin-tube approximation and scale the dependent and independent variables accordingly. Then we assume that the dimensionless amplitude of the kink mode is small and use it as an expansion parameter in the regular perturbation method. We obtain the expression for the tube boundary perturbation in the second-order approximation. This perturbation is a superposition of sausage and fluting perturbations. The amplitude of the fluting perturbation takes its maximum at the middle of the tube, and it monotonically decreases with the distance from the middle of the tube.
Performance optimization of queueing systems with perturbation realization
Xia, Li
2012-04-01
After the intensive studies of queueing theory in the past decades, many excellent results in performance analysis have been obtained, and successful examples abound. However, exploring special features of queueing systems directly in performance optimization still seems to be a territory not very well cultivated. Recent progresses of perturbation analysis (PA) and sensitivity-based optimization provide a new perspective of performance optimization of queueing systems. PA utilizes the structural information of queueing systems to efficiently extract the performance sensitivity information from a sample path of system. This paper gives a brief review of PA and performance optimization of queueing systems, focusing on a fundamental concept called perturbation realization factors, which captures the special dynamic feature of a queueing system. With the perturbation realization factors as building blocks, the performance derivative formula and performance difference formula can be obtained. With performance derivatives, gradient-based optimization can be derived, while with performance difference, policy iteration and optimality equations can be derived. These two fundamental formulas provide a foundation for performance optimization of queueing systems from a sensitivity-based point of view. We hope this survey may provide some inspirations on this promising research topic. © 2011 Elsevier B.V. All rights reserved.
Nonlinear Vibration of Rotor Rubbing Stator Caused by Initial Perturbation
Institute of Scientific and Technical Information of China (English)
张小章; 隆锦胜; 李正光
2001-01-01
The vibration of a rotor rubbing a stator caused by an initial perturbation was studied analytically.The analytical model consists of a simple disc shaft rotor and a fixed stator. The perturbation is aninstantaneous change of the radial velocity when the rotor is operating in its normal steady state. The analysisshowed that the rotor may continue rubbing the stator for small clearance, even if the initial perturbation nolonger exists. For the interest of engineering applications, we investigated various rotating speeds,perturbation amplitudes and clearances between the rotor and the stator. Various friction coefficients on thecontact surface were also considered. The graphical results can be used for the design of rotating machines.``
Steepest-Ascent Constrained Simultaneous Perturbation for Multiobjective Optimization
DEFF Research Database (Denmark)
McClary, Dan; Syrotiuk, Violet; Kulahci, Murat
2011-01-01
that leverages information about the known gradient to constrain the perturbations used to approximate the others. We apply SP(SA)(2) to the cross-layer optimization of throughput, packet loss, and end-to-end delay in a mobile ad hoc network (MANET), a self-organizing wireless network. The results show that SP...
A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators
Smith, Ralph C.
1998-01-01
This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
Institute of Scientific and Technical Information of China (English)
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
NONLINEAR PERTURBATION METHOD FOR CALCULATING AXISYMMETRIC CAVITATIONAL FLOWS
Directory of Open Access Journals (Sweden)
Vasyl Buivol
2013-12-01
Full Text Available A mathematical model of a cavity under the influence of perturbations of various origins is evaluated. The model is based on hydrodynamics of flows with free boundaries and the theory of small perturbations. Specific analysis is provided for cavitational flows behind cones
Perturbed dynamics of discrete-time switched nonlinear systems with delays and uncertainties.
Liu, Xingwen; Cheng, Jun
2016-05-01
This paper addresses the dynamics of a class of discrete-time switched nonlinear systems with time-varying delays and uncertainties and subject to perturbations. It is assumed that the nominal switched nonlinear system is robustly uniformly exponentially stable. It is revealed that there exists a maximal Lipschitz constant, if perturbation satisfies a Lipschitz condition with any Lipschitz constant less than the maximum, then the perturbed system can preserve the stability property of the nominal system. In situations where the perturbations are known, it is proved that there exists an upper bound of coefficient such that the perturbed system remains exponentially stable provided that the perturbation is scaled by any coefficient bounded by the upper bound. A numerical example is provided to illustrate the proposed theoretical results.
PERSISTENT HOMOCLINIC ORBITS FOR A PERTURBED CUBIC-QUINTIC NONLINEAR SCHRODINGER EQUATION
Institute of Scientific and Technical Information of China (English)
郭柏灵; 陈翰林
2002-01-01
In this paper, the existence of homoclinic orbits, for a perturbed cubicquintic nonlinear Schrodinger equation with even periodic boundary conditions, under the generalized parameters conditions is established. More specifically, we combine geometric singular perturbation theory with Melnikov analysis and integrable theory to prove the persistence of homoclinic orbits.
Indian Academy of Sciences (India)
J B ZHOU; J XU; J D WEI; X Q YANG
2017-04-01
This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.
Improving Convergence of Iterative Feedback Tuning using Optimal External Perturbations
DEFF Research Database (Denmark)
Huusom, Jakob Kjøbsted; Hjalmarsson, Håkon; Poulsen, Niels Kjølstad
2008-01-01
Iterative feedback tuning constitutes an attractive control loop tuning method for processes in the absence of sufficient process insight. It is a purely data driven approach to optimization of the loop performance. The standard formulation ensures an unbiased estimate of the loop performance cost...... function gradient, which is used in a search algorithm. A slow rate of convergence of the tuning method is often experienced when tuning for disturbance rejection. This is due to a poor signal to noise ratio in the process data. A method is proposed for increasing the information content in data...... by introducing an optimal perturbation signal in the tuning algorithm. For minimum variance control design the optimal design of an external perturbation signal is derived in terms of the asymptotic accuracy of the iterative feedback tuning method....
Structural optimization for nonlinear dynamic response
DEFF Research Database (Denmark)
Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.
2015-01-01
condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped–clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...... by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance...
Mode matching for optimal plasmonic nonlinear generation
O'Brien, Kevin; Suchowski, Haim; Rho, Jun Suk; Kante, Boubacar; Yin, Xiaobo; Zhang, Xiang
2013-03-01
Nanostructures and metamaterials have attracted interest in the nonlinear optics community due to the possibility of engineering their nonlinear responses; however, the underlying physics to describe nonlinear light generation in nanostructures and the design rules to maximize the emission are still under debate. We study the geometry dependence of the second harmonic and third harmonic emission from gold nanostructures, by designing arrays of nanostructures whose geometry varies from bars to split ring resonators. We fix the length (and volume) of the nanostructure on one axis, and change the morphology from a split ring resonator on the other axis. We observed that the optimal second harmonic generation does not occur at the morphology indicated by a nonlinear oscillator model with parameters derived from the far field transmission and is not maximized by a spectral overlap of the plasmonic modes; however, we find a near field overlap integral and mode matching considerations accurately predict the optimal geometry.
Optimized Perturbation Theory at Finite Temperature Two-Loop Analysis
Chiku, S
2000-01-01
We study the optimized perturbation theory (OPT) at finite temperature, which is a self-consistent resummation method. Firstly, we generalize the idea of the OPT to optimize the coupling constant in lambda phi^4 theory, and give a proof of the renormalizability of this generalized OPT. Secondly, the principle of minimal sensitivity and the criterion of the fastest apparent convergence, which are conditions to determine the optimal parameter values, are examined in lambda phi^4 theory. Both conditions exhibit a second-order transition at finite temperature with critical exponent beta = 0.5 in the two-loop approximation.
Application of homotopy-perturbation method to nonlinear population dynamics models
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, M.S.H. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia); Hashim, I. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)], E-mail: ishak_h@ukm.my; Abdulaziz, O. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)
2007-08-20
In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)
Fully nonlinear and exact perturbations of the Friedmann world model: non-flat background
Energy Technology Data Exchange (ETDEWEB)
Noh, Hyerim, E-mail: hr@kasi.ac.kr [Korea Astronomy and Space Science Institute, Daejeon, 305-348 (Korea, Republic of)
2014-07-01
We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge condition can be adopted freely depending on the problem to be solved. We consider the scalar, and vector perturbations without anisotropic stress. As an application, we analyze the equations in the special case of irrotational zero-pressure fluid in the comoving gauge condition. We also present the fully nonlinear formulation for a minimally coupled scalar field.
Fully nonlinear and exact perturbations of the Friedmann world model: Non-flat background
Noh, Hyerim
2014-01-01
We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge condition can be adopted freely depending on the problem to be solved. %The background curvature term explicitly appears only in the energy and momentum constraint equations. We consider the scalar, and vector perturbations without anisotropic stress. As an application, we analyze the equations in the special case of irrotational zero-pressure fluid in the comoving gauge condition. We also present the fully nonlinear formulation for a minimally coupled scalar field.
Renormalization Group Optimized Perturbation Theory at Finite Temperatures
Kneur, J -L
2015-01-01
A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar $ \\lambda\\phi^4$ field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-$N$ results of the $O(N)$ model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard therm...
Nonlinear and Perturbative Evolution of Distorted Black Holes; 2, Odd-parity Modes
Baker, J; Campanelli, M; Loustó, C O; Seidel, E; Takahashi, R
2000-01-01
We compare the fully nonlinear and perturbative evolution of nonrotating black holes with odd-parity distortions utilizing the perturbative results to interpret the nonlinear results. This introduction of the second polarization (odd-parity) mode of the system, and the systematic use of combined techniques brings us closer to the goal of studying more complicated systems like distorted, rotating black holes, such as those formed in the final inspiral stage of two black holes. The nonlinear evolutions are performed with the 3D parallel code for Numerical Relativity, {Cactus}, and an independent axisymmetric code, {Magor}. The linearized calculation is performed in two ways: (a) We treat the system as a metric perturbation on Schwarzschild, using the Regge-Wheeler equation to obtain the waveforms produced. (b) We treat the system as a curvature perturbation of a Kerr black hole (but here restricted to the case of vanishing rotation parameter a) and evolve it with the Teukolsky equation The comparisons of the wa...
Nonlinear Circuit Analysis via Perturbation Methods and Hardware Prototyping
Directory of Open Access Journals (Sweden)
K. Odame
2010-01-01
Full Text Available Nonlinear signal processing is necessary in many emerging applications where form factor and power are at a premium. In order to make such complex computation feasible under these constraints, it is necessary to implement the signal processors as analog circuits. Since analog circuit design is largely based on a linear systems perspective, new tools are being introduced to circuit designers that allow them to understand and exploit circuit nonlinearity for useful processing. This paper discusses two such tools, which represent nonlinear circuit behavior in a graphical way, making it easy to develop a qualitative appreciation for the circuits under study.
Optimizing controllability of complex networks by minimum structural perturbations.
Wang, Wen-Xu; Ni, Xuan; Lai, Ying-Cheng; Grebogi, Celso
2012-02-01
To drive a large, complex, networked dynamical system toward some desired state using as few external signals as possible is a fundamental issue in the emerging field of controlling complex networks. Optimal control is referred to the situation where such a network can be fully controlled using only one driving signal. We propose a general approach to optimizing the controllability of complex networks by judiciously perturbing the network structure. The principle of our perturbation method is validated theoretically and demonstrated numerically for homogeneous and heterogeneous random networks and for different types of real networks as well. The applicability of our method is discussed in terms of the relative costs of establishing links and imposing external controllers. Besides the practical usage of our approach, its implementation elucidates, interestingly, the intricate relationship between certain structural properties of the network and its controllability.
Stochastic Recursive Algorithms for Optimization Simultaneous Perturbation Methods
Bhatnagar, S; Prashanth, L A
2013-01-01
Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from sim...
The de Sitter limit of inflation and non-linear perturbation theory
DEFF Research Database (Denmark)
Jarnhus, Philip; Sloth, Martin Snoager
2008-01-01
We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug......, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function....
INITIAL LAYER PHENOMENA FOR A CLASS OF SINGULAR PERTURBED NONLINEAR SYSTEM WITH SLOW VARIABLES
Institute of Scientific and Technical Information of China (English)
黄蔚章; 陈育森
2004-01-01
The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different "thickness", the Norder approximate expansion of perturbed solution concerning small parameter is obtained,and the "multiple layer" phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well.
The de Sitter limit of inflation and non-linear perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Jarnhus, Philip R; Sloth, Martin S, E-mail: pjarn@phys.au.dk, E-mail: sloth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)
2008-02-15
We study the fourth-order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in non-linear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the nth-order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function.
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
Institute of Scientific and Technical Information of China (English)
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
Nonlinear optimization of beam lines
Tomás Garcia, Rogelio
2006-01-01
The current final focus systems of linear colliders have been designed based on the local compensation scheme proposed by P. Raimondi and A. Seryi [1]. However, there exist remaining aberrations that deteriorate the performance of the system. This paper develops a general algorithm for the optimization of beam lines based on the computation of the high orders of the transfer map using MAD-X [2] and PTC [3]. The algorithm is applied to the CLIC [4] Beam Delivery System (BDS).
Optimality conditions in smooth nonlinear programming
Still, G.; Streng, M.
1996-01-01
This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualif
Observer-Based Nonlinear Control of A Torque Motor with Perturbation Estimation
Institute of Scientific and Technical Information of China (English)
J Chen; E Prempain; Q H Wu
2006-01-01
This paper presents an observer-based nonlinear control method that was developed and implemented to provide accurate tracking control of a limited angle torque motor following a 50Hz reference waveform. The method is based on a robust nonlinear observer, which is used to estimate system states and perturbations and then employ input-output feedback linearization to compensate for the system nonlinearities and uncertainties. The estimation of system states and perturbations allows input-output linearization of the nonlinear system without an accurate mathematical model of nominal plant. The simulation results show that the observer-based nonlinear control method is superior in comparison with the conventional model-based state feedback linearizing controller.
Parabolic Perturbation of a Nonlinear Hyperbolic Problem Arising in Physiology
Colli, P.; Grasselli, M.
We study a transport-diffusion initial value problem where the diffusion codlicient is "small" and the transport coefficient is a time function depending on the solution in a nonlinear and nonlocal way. We show the existence and the uniqueness of a weak solution of this problem. Moreover we discuss its asymptotic behaviour as the diffusion coefficient goes to zero, obtaining a well-posed first-order nonlinear hyperbolic problem. These problems arise from mathematical models of muscle contraction in the framework of the sliding filament theory.
Nonlinear analysis approximation theory, optimization and applications
2014-01-01
Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.
Akbarzade, M.; Langari, J.
2011-02-01
In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, comparisons with other results are presented to show the effectiveness of this method. The validity of the method is independent of whether or not there exist small or large parameters in the considered nonlinear equations; the obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. At the end we compare our procedure with the optimal homotopy perturbation method.
Optimized spectral estimation for nonlinear synchronizing systems.
Sommerlade, Linda; Mader, Malenka; Mader, Wolfgang; Timmer, Jens; Thiel, Marco; Grebogi, Celso; Schelter, Björn
2014-03-01
In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.
Optimal Parametric Feedback Excitation of Nonlinear Oscillators
Braun, David J.
2016-01-01
An optimal parametric feedback excitation principle is sought, found, and investigated. The principle is shown to provide an adaptive resonance condition that enables unprecedentedly robust movement generation in a large class of oscillatory dynamical systems. Experimental demonstration of the theory is provided by a nonlinear electronic circuit that realizes self-adaptive parametric excitation without model information, signal processing, and control computation. The observed behavior dramatically differs from the one achievable using classical parametric modulation, which is fundamentally limited by uncertainties in model information and nonlinear effects inevitably present in real world applications.
Delay-dependent passive control of linear systems with nonlinear perturbation
Institute of Scientific and Technical Information of China (English)
Li Caina; Cui Baotong
2008-01-01
The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such that for a time-varying delay in states, the linear system with nonlinear perturbation remains robustly stable and passive.In the system, the delay is time-varying. And the derivation of delay has the maximum and minimum value. The time-varying nonlinear perturbation is allowed to be norm-bounded. Using the effective linear matrix inequality methodology, the sufficient condition is primarily obtained for the system to have robust stability and passivity.Subsequently the existent condition of a state feedback controller is given, and the explicit expression of the controller is obtained by means of the solution of linear matrix inequalities (LMIs). In the end, a numerical example is given to demonstrate the validity and applicability of the proposed approach.
Perturbing engine performance measurements to determine optimal engine control settings
Jiang, Li; Lee, Donghoon; Yilmaz, Hakan; Stefanopoulou, Anna
2014-12-30
Methods and systems for optimizing a performance of a vehicle engine are provided. The method includes determining an initial value for a first engine control parameter based on one or more detected operating conditions of the vehicle engine, determining a value of an engine performance variable, and artificially perturbing the determined value of the engine performance variable. The initial value for the first engine control parameter is then adjusted based on the perturbed engine performance variable causing the engine performance variable to approach a target engine performance variable. Operation of the vehicle engine is controlled based on the adjusted initial value for the first engine control parameter. These acts are repeated until the engine performance variable approaches the target engine performance variable.
Excitation of turbulence in accretion disks of binary stars by non-linear perturbations
Kurbatov, E. P.; Bisikalo, D. V.
2017-06-01
Accretion disks in binary systems can experience hydrodynamical influences at both their inner and outer edges. The former is typical for protoplanetary disks around young T Tauri stars, while the latter is typical for circumstellar disks in close binaries. This influence excites perturbations with various scales and amplitudes in the disk. The nonlinear evolution of perturbations with a finite, but small amplitude against the background of a sub-Keplerian flow is investigated. Nonlinear effects at the fronts of perturbation waves lead to the formation of discontinuities in the density and radial velocity; i.e., to formation of shocks. The tangential flow in the neighborhood of the shock becomes equivalent to a flow in a boundary layer. Due to an instability of the tangential flow, the disk becomes turbulent. The characteristics of the turbulence depend on the parameters of the perturbations, but the Shakura-Syunyaev α parameter does not exceed 0.1.
Desoer, C. A.; Kabuli, M. G.
1989-01-01
The authors consider a linear (not necessarily time-invariant) stable unity-feedback system, where the plant and the compensator have normalized right-coprime factorizations. They study two cases of nonlinear plant perturbations (additive and feedback), with four subcases resulting from: (1) allowing exogenous input to Delta P or not; 2) allowing the observation of the output of Delta P or not. The plant perturbation Delta P is not required to be stable. Using the factorization approach, the authors obtain necessary and sufficient conditions for all cases in terms of two pairs of nonlinear pseudostate maps. Simple physical considerations explain the form of these necessary and sufficient conditions. Finally, the authors obtain the characterization of all perturbations Delta P for which the perturbed system remains stable.
Adaptive Stabilization for a Class of Dynamical Systems with Nonlinear Delayed State Perturbations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the Lyapunov- Karasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.
Singular perturbation methods for nonlinear dynamic systems with time delays
Energy Technology Data Exchange (ETDEWEB)
Hu, H.Y. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)], E-mail: hhyae@nuaa.edu.cn; Wang, Z.H. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)
2009-04-15
This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
Institute of Scientific and Technical Information of China (English)
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
Directory of Open Access Journals (Sweden)
Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
Extending the perturbation technique to the modal representation of nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Soltani, S. [Department of Electrical Engineering, Science and Research Branch, Islamic Azad University (IAU), 1477893855-14515775, Tehran (Iran); Pariz, N.; Ghazi, R. [Department of Electrical Engineering, ferdowsi University, 9177948944-1111, Mashhad (Iran)
2009-08-15
After a brief review of perturbation technique, using this method an approach is developed to represent and study the behavior of nonlinear dynamic power systems. For the first time in this field, perturbation technique is applied to obtain an approximate closed form expression for the zero input response of stressed power systems. In order to show the superiority of the proposed method, it has been applied to a typical nonlinear system which is a single machine infinite bus (SMIB) power system with unified power flow controller (UPFC). The accuracy and competency of this method in comparison with Modal Series method will also be validated. (author)
A filter algorithm for multi-measurement nonlinear system with parameter perturbation
Institute of Scientific and Technical Information of China (English)
GUO Yun-fei; WEI Wei; XUE An-ke; MAO Dong-cai
2006-01-01
An improved interacting multiple models particle filter (IMM-PF) algorithm is proposed for multi-measurement nonlinear system with parameter perturbation. It divides the perturbation region into sub-regions and assigns each of them a particle filter. Hence the perturbation problem is converted into a multi-model filters problem. It combines the multiple measurements into a fusion value according to their likelihood function. In the simulation study, we compared it with the IMM-KF and the H-infinite filter; the results testify to its advantage over the other two methods.
Large-scale weakly nonlinear perturbations of convective magnetic dynamos in a rotating layer
Chertovskih, Roman
2015-01-01
We present a new mechanism for generation of large-scale magnetic field by thermal convection which does not involve the alpha-effect. We consider weakly nonlinear perturbations of space-periodic steady convective magnetic dynamos in a rotating layer that were identified in our previous work. The perturbations have a spatial scale in the horizontal direction that is much larger than the period of the perturbed convective magnetohydrodynamic state. Following the formalism of the multiscale stability theory, we have derived the system of amplitude equations governing the evolution of the leading terms in expansion of the perturbations in power series in the scale ratio. This asymptotic analysis is more involved than in the cases considered earlier, because the kernel of the operator of linearisation has zero-mean neutral modes whose origin lies in the spatial invariance of the perturbed regime, the operator reduced on the generalised kernel has two Jordan normal form blocks of size two, and simplifying symmetri...
Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations.
Piscureanu, M; Manaila-Maximean, D
2000-01-01
We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.
Topology optimization with geometric uncertainties by perturbation techniques
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Schevenels, M.; Sigmund, Ole
2012-01-01
the above assumptions, the proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling. The method is demonstrated on the design of a minimum compliance cantilever beam and a compliant mechanism. Copyright © 2012 John......The aim of this paper was to present a topology optimization methodology for obtaining robust designs insensitive to small uncertainties in the geometry. The variations are modeled using a stochastic field. The model can represent spatially varying geometry imperfections in devices produced...... by etching techniques. Because of under‐etching or over‐etching parts of the structure may become thinner or thicker than a reference design supplied to the manufacturer. The uncertainties are assumed to be small and their influence on the system response is evaluated using perturbation techniques. Under...
Gorbach, Andrey V
2016-01-01
We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived models are applied for analysis of third harmonic generation in a graphene coated dielectric micro-fibre. The efficiency of up to few percent is predicted when using sub-picosecond pump pulses with energies of the order of $0.1$nJ in a sub-millimeter long fibre, when operating near the resonance of the graphene nonlinear conductivity $\\hbar\\omega=(2/3)E_F$.
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
Institute of Scientific and Technical Information of China (English)
Igor Boglaev; Matthew Hardy
2008-01-01
This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type.To solve the nonlinear weighted average finite difference scheme for the partial differential equation,we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition.This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated.Numerical experiments are presented.
A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations
Institute of Scientific and Technical Information of China (English)
Zhang Zhi-Yong; Yong Xue-Lin; Chen Yu-Fu
2009-01-01
A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.
Application of homotopy-perturbation to non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cveticanin, L. [Faculty of Technical Sciences, 21000 Novi Sad, Trg D. Obradovica 6 (Serbia)], E-mail: cveticanin@uns.ns.ac.yu
2009-04-15
In this paper He's homotopy perturbation method has been adopted for solving non-linear partial differential equations. An approximate solution of the differential equation which describes the longitudinal vibration of a beam is obtained. The solution is compared with that found using the variational iteration method introduced by He. The difference between the two solutions is negligible.
Directory of Open Access Journals (Sweden)
Abaker. A. Hassaballa.
2015-10-01
Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation an
SINGULARLY PERTURBED SOLUTION FOR THIRD ORDER NONLINEAR EQUATIONS WITH TWO PARAMETERS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A class of singularly perturbed boundary value problems for nonlinear equation of the third order with two parameters is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the solution for boundary value problem are studied.
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation
Fully non-linear cosmological perturbations of multicomponent fluid and field systems
Hwang, Jai-chan; Noh, Hyerim; Park, Chan-Gyung
2016-09-01
We present fully non-linear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. We include the anisotropic stress. Even in the absence of anisotropic stress of individual component, the multiple component nature introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully non-linear equations and the third-order perturbation equations of the non-relativistic pressure fluids in the CDM-comoving gauge.
Numerical solving for nonlinear using higher order homotopy Taylor-perturbation
Directory of Open Access Journals (Sweden)
Nor Hanim Abd Rahman
2013-03-01
Full Text Available Rootfinding is a classical problem that still remains an interest to many researchers. A series of hybrid methods called Higher Order Homotopy Taylor-perturbation method via start-system functions (HTTPss are implemented to give approximate solutions for nonlinear equations, . The techniques serve as alternative methods for obtaining approximate solutions for different types of nonlinear equations. Thus, this paper presents an analysis on numerical comparison between the classical Newton Raphson (CNR, Homotopy Perturbation method (HTPss and Higher Order Homotopy Taylor-perturbation via start-system (HHTPss. A computational system Maple14 is used for this paper. Numerical and Illustrative results reveal that HHTPss methods are acceptably accurate and applicable.
Optimal non-linear health insurance.
Blomqvist, A
1997-06-01
Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.
Nonlinear fastest growing perturbation and the first kind of predictability
Institute of Scientific and Technical Information of China (English)
MU; Mu
2001-01-01
［1］Jiao Jiujiu, Grey hydrogeologic system analysis and time series model, Survey Science and Technology (in Chinese), 1987,(10): 39-43.［2］Li Shuwen, Wang Baolai, Xiao Guoqiang, A compound model of grey and periodic scrape and its application in groundwater prediction, Journal of Hebei Institute of Architectural Science & Technology (in Chinese), 1992, (3): 246-251.［3］Wang Qingyin, Li Shuwen, Grey distributed parameter model and groundwater analog, Journal of Hebei Institute of Architectural Science & Technology (in Chinese), 1992, (3): 66-70.［4］Guo Chunqing, Xia Riyuan, Liu Zhenglin, Gray Systematic Theory and Methodological Study of Krast Groundwater Resources Evaluation (in Chinese), Beijing: Geological Publishing House, 1993, 3-60.［5］Wang Qingyin, Liu Kaidi, The Mathematical Method of Grey Systematic Theory and Its Application (in Chinese), Chengdu: Publishing House of Southwestern China University of Communication, 1990, 23-27.［6］Wang Qingyin, Wu Heqing, The concept of grey number and its property, in Proceedings of NAFIPS98, USA, 1998,45-49.［7］Givoli, D., Doukhovni, I., Finite element programming approach for contact problems with geometrical nonlinearity, Computers and Structures, 1996, (8): 31-41.［8］Li Shuwen, Wang Zhiqiang, Wu Qiang, The superiority of storage-centered finite element method in solving seepage problem, Coal Geology and Exploration (in Chinese), 1999, (5): 46-49.
Nonlinear evolution of density and flow perturbations on a Bjorken background
Brouzakis, Nikolaos; Tetradis, Nikolaos; Wiedemann, Urs Achim
2015-01-01
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and bispectrum of these perturbations around a longitudinally expanding fireball after a heavy-ion collision. The time-evolution equations couple the spectrum and bispectrum to each other, as well as to higher-order correlation functions through nonlinear terms. A non-trivial bispectrum is thus always generated, even if absent initially. For initial conditions corresponding to a model of independent sources, we discuss the linear and nonlinear evolution is detail. We show that, if the initial conditions are sufficiently smooth for fluid dynamics to be applicable, the nonlinear effects are relatively small.
Nonlinear evolution of density and flow perturbations on a Bjorken background
Brouzakis, Nikolaos; Floerchinger, Stefan; Tetradis, Nikolaos; Wiedemann, Urs Achim
2015-03-01
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and bispectrum of these perturbations around a longitudinally expanding fireball after a heavy-ion collision. The time-evolution equations couple the spectrum and bispectrum to each other, as well as to higher-order correlation functions through nonlinear terms. A nontrivial bispectrum is thus always generated, even if absent initially. For initial conditions corresponding to a model of independent sources, we discuss the linear and nonlinear evolution in detail. We show that, if the initial conditions are sufficiently smooth for fluid dynamics to be applicable, the nonlinear effects are relatively small.
Gnutzmann, Sven; Waltner, Daniel
2016-12-01
We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016), 10.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.
Institute of Scientific and Technical Information of China (English)
DUAN Wan-suo; MU Mu
2005-01-01
Linear singular vector and linear singular value can only describe the evolution of sufficiently small perturbations during the period in which the tangent linear model is valid.With this in mind, the applications of nonlinear optimization methods to the atmospheric and oceanic sciences are introduced, which include nonlinear singular vector (NSV) and nonlinear singular value (NSVA), conditional nonlinear optimal perturbation (CNOP), and their applications to the studies of predictability in numerical weather and climate prediction.The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be explored by NSV and CNOP. Also attentions are paid to the introduction of the classification of predictability problems, which are related to the maximum predictable time,the maximum prediction error, and the maximum allowing error of initial value and the parameters. All the information has the background of application to the evaluation of products of numerical weather and climate prediction. Furthermore the nonlinear optimization methods of the sensitivity analysis with numerical model are also introduced, which can give a quantitative assessment whether a numerical model is able to simulate the observations and find the initial field that yield the optimal simulation. Finally, the difficulties in the lack of ripe algorithms are also discussed, which leave future work to both computational mathematics and scientists in geophysics.
Optimal Variational Method for Truly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Vasile Marinca
2013-01-01
Full Text Available The Optimal Variational Method (OVM is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”. The main advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. This approach does not depend upon any small or large parameters. A very good agreement was found between approximate and numerical solution, which proves that OVM is very efficient and accurate.
Nonlinear optimization in electrical engineering with applications in Matlab
Bakr, Mohamed
2013-01-01
Nonlinear Optimization in Electrical Engineering with Applications in MATLAB® provides an introductory course on nonlinear optimization in electrical engineering, with a focus on applications such as the design of electric, microwave, and photonic circuits, wireless communications, and digital filter design. Basic concepts are introduced using a step-by-step approach and illustrated with MATLAB® codes that the reader can use and adapt. Topics covered include: classical optimization methods; one dimensional optimization; unconstrained and constrained optimization; global optimization; space map
Nonlinear Dynamics and Optimization of Spur Gears
Pellicano, Francesco; Bonori, Giorgio; Faggioni, Marcello; Scagliarini, Giorgio
In the present study a single degree of freedom oscillator with clearance type non-linearity is considered. Such oscillator represents the simplest model able to analyze a single teeth gear pair, neglecting: bearings and shafts stiffness and multi mesh interactions. One of the test cases considered in the present work represents an actual gear pair that is part of a gear box of an agricultural vehicle; such gear pair gave rise to noise problems. The main gear pair characteristics (mesh stiffness and inertia) are evaluated after an accurate geometrical modelling. The meshing stiffness of the gear pair is piecewise linear and time varying (in particular periodic); it is evaluated numerically using nonlinear finite element analysis (with contact mechanics) for different positions along one mesh cycle, then it is expanded in Fourier series. A direct numerical integration approach and a smoothing technique have been considered to obtain the dynamic scenario. Bifurcation diagrams of Poincaré maps are plotted according to some sample case study from literature. Optimization procedures are proposed, in order to find optimal involute modifications that reduce gears vibration.
A discrete homotopy perturbation method for non-linear Schrodinger equation
Directory of Open Access Journals (Sweden)
H. A. Wahab
2015-12-01
Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.
Sharma, Dinkar; Singh, Prince; Chauhan, Shubha
2016-01-01
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers' equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He's polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.
Beyond the perturbative description of the nonlinear optical response of low-index materials.
Reshef, Orad; Giese, Enno; Zahirul Alam, M; De Leon, Israel; Upham, Jeremy; Boyd, Robert W
2017-08-15
We show that standard approximations in nonlinear optics are violated for situations involving a small value of the linear refractive index. Consequently, the conventional equation for the intensity-dependent refractive index, n(I)=n0+n2I, becomes inapplicable in epsilon-near-zero and low-index media, even in the presence of only third-order effects. For the particular case of indium tin oxide, we find that the χ((3)), χ((5)), and χ((7)) contributions to refraction eclipse the linear term; thus, the nonlinear response can no longer be interpreted as a perturbation in these materials. Although the response is non-perturbative, we find no evidence that the power series expansion of the material polarization diverges.
Cosmological perturbations of self-accelerating universe in nonlinear massive gravity
Gumrukcuoglu, A Emir; Mukohyama, Shinji
2011-01-01
We study cosmological perturbations of self-accelerating universe solutions in the recently proposed nonlinear theory of massive gravity, with general matter content. While the broken diffeomorphism invariance implies that there generically are 2 tensor, 2 vector and 2 scalar degrees of freedom in the gravity sector, we find that the scalar and vector degrees have vanishing kinetic terms and nonzero mass terms. Depending on their nonlinear behavior, this indicates either nondynamical nature of these degrees or strong couplings. Assuming the former, we integrate out the 2 vector and 2 scalar degrees of freedom. We then find that in the scalar and vector sectors, gauge-invariant variables constructed from metric and matter perturbations have exactly the same quadratic action as in general relativity. The difference from general relativity arises only in the tensor sector, where the graviton mass modifies the dispersion relation of gravitational waves, with a time-dependent effective mass. This may lead to modif...
ASYMPTOTIC THEORY OF INITIAL VALUE PROBLEMS FOR NONLINEAR PERTURBED KLEIN-GORDON EQUATIONS
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2005-01-01
The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori estimates and the convergence of Bessel function, the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein-Gordon equations. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got. Finally, an application of the asymptotic theory was given, the asymptotic approximation degree of solutions for the initial value problem of a specific nonlinear Klein-Gordon equation was analyzed by using the asymptotic approximation theorem.
Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations.A new stabilization/stability scheme is presented.Using improved Lyapunov functionals.less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities(LMI).Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.
Homotopy perturbation method for nonlinear partial differential equations of fractional order
Energy Technology Data Exchange (ETDEWEB)
Momani, Shaher [Department of Mathematics and Physics, Qatar University (Qatar)]. E-mail: shahermm@yahoo.com; Odibat, Zaid [Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt (Jordan)]. E-mail: odibat@bau.edu.jo
2007-06-11
The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative. The fractional derivative is described in the Caputo sense. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.
Adaptive Third-Order Leader-Following Consensus of Nonlinear Multi-agent Systems with Perturbations
Institute of Scientific and Technical Information of China (English)
SUN Mei; CHEN Ying; CAO Long; WANG Xiao-Fang
2012-01-01
We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies. Based on graph theory and Lyapunov stability theory, the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations. Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.%We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies.Based on graph theory and Lyapunov stability theory,the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations.Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.
Zhang, Tian-Ping; Zhu, Qing; Yang, Yue-Quan
2012-04-01
In this article, two robust adaptive control schemes are investigated for a class of completely non-affine pure-feedback non-linear systems with input non-linearity and perturbed uncertainties using radial basis function neural networks (RBFNNs). Based on the dynamic surface control (DSC) technique and using the quadratic Lyapunov function, the explosion of complexity in the traditional backstepping design is avoided when the gain signs are known. In addition, the unknown virtual gain signs are dealt with using the Nussbaum functions. Using the mean value theorem and Young's inequality, only one learning parameter needs to be tuned online at each step of recursion. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results verify the effectiveness of the proposed approach.
On optimal performance of nonlinear energy sinks in multiple-degree-of-freedom systems
Tripathi, Astitva; Grover, Piyush; Kalmár-Nagy, Tamás
2017-02-01
We study the problem of optimizing the performance of a nonlinear spring-mass-damper attached to a class of multiple-degree-of-freedom systems. We aim to maximize the rate of one-way energy transfer from primary system to the attachment, and focus on impulsive excitation of a two-degree-of-freedom primary system with an essentially nonlinear attachment. The nonlinear attachment is shown to be able to perform as a 'nonlinear energy sink' (NES) by taking away energy from the primary system irreversibly for some types of impulsive excitations. Using perturbation analysis and exploiting separation of time scales, we perform dimensionality reduction of this strongly nonlinear system. Our analysis shows that efficient energy transfer to nonlinear attachment in this system occurs for initial conditions close to homoclinic orbit of the slow time-scale undamped system, a phenomenon that has been previously observed for the case of single-degree-of-freedom primary systems. Analytical formulae for optimal parameters for given impulsive excitation input are derived. Generalization of this framework to systems with arbitrary number of degrees-of-freedom of the primary system is also discussed. The performance of both linear and nonlinear optimally tuned attachments is compared. While NES performance is sensitive to magnitude of the initial impulse, our results show that NES performance is more robust than linear tuned mass damper to several parametric perturbations. Hence, our work provides evidence that homoclinic orbits of the underlying Hamiltonian system play a crucial role in efficient nonlinear energy transfers, even in high dimensional systems, and gives new insight into robustness of systems with essential nonlinearity.
Analytical solitons for Langmuir waves in plasma physics with cubic nonlinearity and perturbations
Energy Technology Data Exchange (ETDEWEB)
Zhou, Qin [Wuhan Donghu Univ. (China). School of Electronics and Information Engineering; Mirzazadeh, M. [Guilan Univ. (Iran, Islamic Republic of). Dept. of Engineering Sciences
2016-07-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schroedinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
Analytical Solitons for Langmuir Waves in Plasma Physics with Cubic Nonlinearity and Perturbations
Zhou, Qin; Mirzazadeh, M.
2016-09-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schrödinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
Zhang, Huayong; Huang, Tousheng; Dai, Liming
2015-05-01
Predator-prey interaction widely exists in nature and the research on predator-prey systems is an important field in ecology. The nonlinear dynamic characteristics of a seasonally perturbed predator-prey system are studied in this research. To study the nonlinear characteristics affected by a wide variety of system parameters, the PR approach is employed and periodic, quasiperiodic, chaotic behaviors and the behaviors between period and quasiperiod are found in the system. Periodic-quasiperiodic-chaotic region diagrams are generated for analyzing the global characteristics of the predator-prey system with desired ranges of system parameters. The ecological significances of the dynamical characteristics are discussed and compared with the theoretical research results existing in the literature. The approach of this research demonstrates effectiveness and efficiency of PR method in analyzing the complex dynamical characteristics of nonlinear ecological systems.
Zhao, Zhao; Zhang, Jin; Li, Hai-yang; Zhou, Jian-yong
2017-01-01
The optimization of an LEO cooperative multi-spacecraft refueling mission considering the J2 perturbation and target's surplus propellant constraint is studied in the paper. First, a mission scenario is introduced. One service spacecraft and several target spacecraft run on an LEO near-circular orbit, the service spacecraft rendezvouses with some service positions one by one, and target spacecraft transfer to corresponding service positions respectively. Each target spacecraft returns to its original position after obtaining required propellant and the service spacecraft returns to its original position after refueling all target spacecraft. Next, an optimization model of this mission is built. The service sequence, orbital transfer time, and service position are used as deign variables, whereas the propellant cost is used as the design objective. The J2 perturbation, time constraint and the target spacecraft's surplus propellant capability constraint are taken into account. Then, a hybrid two-level optimization approach is presented to solve the formulated mixed integer nonlinear programming (MINLP) problem. A hybrid-encoding genetic algorithm is adopted to seek the near optimal solution in the up-level optimization, while a linear relative dynamic equation considering the J2 perturbation is used to obtain the impulses of orbital transfer in the low-level optimization. Finally, the effectiveness of the proposed model and method is validated by numerical examples.
COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U
Energy Technology Data Exchange (ETDEWEB)
Sun, Y.; Borland, Michael
2017-06-25
Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.
Constrained optimization for image restoration using nonlinear programming
Yeh, C.-L.; Chin, R. T.
1985-01-01
The constrained optimization problem for image restoration, utilizing incomplete information and partial constraints, is formulated using nonlinear proramming techniques. This method restores a distorted image by optimizing a chosen object function subject to available constraints. The penalty function method of nonlinear programming is used. Both linear or nonlinear object function, and linear or nonlinear constraint functions can be incorporated in the formulation. This formulation provides a generalized approach to solve constrained optimization problems for image restoration. Experiments using this scheme have been performed. The results are compared with those obtained from other restoration methods and the comparative study is presented.
Topology optimization of nonlinear optical devices
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2011-01-01
This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
Nonlinear Galerkin Optimal Truncated Low—dimensional Dynamical Systems
Institute of Scientific and Technical Information of China (English)
ChuijieWU
1996-01-01
In this paper,a new theory of constructing nonlinear Galerkin optimal truncated Low-Dimensional Dynamical Systems(LDDSs) directly from partial differential equations has been developed.Applying the new theory to the nonlinear Burgers' equation,it is shown that a nearly perfect LDDS can be gotten,and the initial-boundary conditions are automatically included in the optimal bases.The nonlinear Galerkin method does not have advantages within the optimization process,but it can significantly improve the results,after the Galerkin optimal bases have been gotten.
Variational principle and a perturbative solution of non-linear string equations in curved space
Roshchupkin, S N
1999-01-01
String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension constant. A rescaled slow worldsheet time $T=\\epsilon\\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\\epsilon $-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H
Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory
Harada, Koji; Kubo, Hirofumi; Yamamoto, Yuki
2009-01-01
Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.
Indian Academy of Sciences (India)
Zaiyun Zhang; Jianhua Huang; Juan Zhong; Sha-Sha Dou; Jiao Liu; Dan Peng; Ting Gao
2014-06-01
In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger’s equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbations
Energy Technology Data Exchange (ETDEWEB)
Turnbull, A. D.; Ferraro, N. M.; Lao, L. L.; Lanctot, M. J. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Izzo, V. A. [University of California-San Diego, 9500 Gilman Dr., La Jolla, California 92093-0417 (United States); Lazarus, E. A.; Hirshman, S. P. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (United States); Park, J.-K.; Lazerson, S.; Reiman, A. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States); Cooper, W. A. [Association Euratom-Confederation Suisse, Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Federale de Lausanne, Lausanne (Switzerland); Liu, Y. Q. [Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB (United Kingdom); Turco, F. [Columbia University, 116th St and Broadway, New York, New York 10027 (United States)
2013-05-15
With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10{sup −3} relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated nonlinear steady state, appropriate damping mechanisms need to be provided for each normal mode comprising the response. Other issues arise in the technical construction of perturbed flux surfaces from a displacement and from the presence of near nullspace normal modes. For the nearby equilibrium approach, in the absence of a full 3D equilibrium reconstruction with a controlled comparison, constraints relating the 2D system profiles to the final profiles in the 3D system also need to be imposed to assure accessibility. The magnetic helicity profile has been proposed as an appropriate input to a 3D equilibrium calculation and tests of this show the anticipated qualitative behavior.
Energy Technology Data Exchange (ETDEWEB)
Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)
2011-01-15
The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.
Robust adaptive fuzzy control for a class of perturbed pure-feedback nonlinear systems
Institute of Scientific and Technical Information of China (English)
Jianjiang YU; Tianping ZHANG; Haijun GU
2004-01-01
A new design scheme of direct adaptive fuzzy controller for a class of perturbed pure-feedback nonlinear systems is proposed. The design is based on backstepping and the approximation capability of the first type fuzzy systems. A continuous robust term is adopted to minif-y the influence of modeling errors or disturbances. By introducing the modified integral-type Lyapunov function, the approach is able to avoid the requirement of the upper bound of the first time derivation of the high frequency control gain. Through theoretical analysis, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, with tracking error converging to a residual set.
Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems.
Wang, Min; Chen, Bing; Shi, Peng
2008-06-01
This paper proposes a novel adaptive neural control scheme for a class of perturbed strict-feedback nonlinear time-delay systems with unknown virtual control coefficients. Based on the radial basis function neural network online approximation capability, an adaptive neural controller is presented by combining the backstepping approach and Lyapunov-Krasovskii functionals. The proposed controller guarantees the semiglobal boundedness of all the signals in the closed-loop system and contains minimal learning parameters. Finally, three simulation examples are given to demonstrate the effectiveness and applicability of the proposed scheme.
Directory of Open Access Journals (Sweden)
Kanit Mukdasai
2012-01-01
Full Text Available This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
Directory of Open Access Journals (Sweden)
Xia Zhou
2013-01-01
Full Text Available The problem of bounded-input bounded-output (BIBO stabilization in mean square for a class of discrete-time stochastic control systems with mixed time-varying delays and nonlinear perturbations is investigated. Some novel delay-dependent stability conditions for the previously mentioned system are established by constructing a novel Lyapunov-Krasovskii function. These conditions are expressed in the forms of linear matrix inequalities (LMIs, whose feasibility can be easily checked by using MATLAB LMI Toolbox. Finally, a numerical example is given to illustrate the validity of the obtained results.
On properties of nonlinear second order systems under nonlinear impulse perturbations
Directory of Open Access Journals (Sweden)
John R. Graef
1998-11-01
Full Text Available In this paper, we consider the impulsive second order system [ ddot{x}+f(x=0quad (teq t_{n};quad dot{x}(t_{n}+0=b_{n}dot{x}(t_{n} quad (t=t_{n} ] where $t_n=t_0+n,p$ $(p>0, n=1,2dots $. In a previous paper, the authors proved that if $f(x$ is strictly nonlinear, then this system has infinitely many periodic solutions. The impulses account for the main differences in the attractivity properties of the zero solution. Here, we prove that these periodic solutions are attractive in some sense, and we give good estimates for the attractivity region.
Orain, François; Bécoulet, M.; Morales, J.; Huijsmans, G. T. A.; Dif-Pradalier, G.; Hoelzl, M.; Garbet, X.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Fil, A.; Cahyna, P.
2015-01-01
The dynamics of a multi-edge localized mode (ELM) cycle as well as the ELM mitigation by resonant magnetic perturbations (RMPs) are modeled in realistic tokamak X-point geometry with the non-linear reduced MHD code JOREK. The diamagnetic rotation is found to be a key parameter enabling us to reproduce the cyclical dynamics of the plasma relaxations and to model the near-symmetric ELM power deposition on the inner and outer divertor target plates consistently with experimental measurements. Moreover, the non-linear coupling of the RMPs with unstable modes are found to modify the edge magnetic topology and induce a continuous MHD activity in place of a large ELM crash, resulting in the mitigation of the ELMs. At larger diamagnetic rotation, a bifurcation from unmitigated ELMs—at low RMP current—towards fully suppressed ELMs—at large RMP current—is obtained.
Directory of Open Access Journals (Sweden)
Hong Qin
2000-08-01
Full Text Available Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST code is used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment. Detailed simulations in a parameter regime characteristic of the PSR experiment show that the dipole-mode two-stream instability is stabilized by a modest spread (about 0.1% in axial momentum of the beam particles.
Chang, Wen-Jer; Huang, Bo-Jyun
2014-11-01
The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi-Sugeno fuzzy model with perturbations and state multiplicative noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with multiplicative noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method.
Tailoring the nonlinear response of MEMS resonators using shape optimization
DEFF Research Database (Denmark)
Li, Lily L.; Polunin, Pavel M.; Dou, Suguang
2017-01-01
We demonstrate systematic control of mechanical nonlinearities in micro-electromechanical (MEMS) resonators using shape optimization methods. This approach generates beams with non-uniform profiles, which have nonlinearities and frequencies that differ from uniform beams. A set of bridge-type mic......We demonstrate systematic control of mechanical nonlinearities in micro-electromechanical (MEMS) resonators using shape optimization methods. This approach generates beams with non-uniform profiles, which have nonlinearities and frequencies that differ from uniform beams. A set of bridge...
A new topology optimization scheme for nonlinear structures
Energy Technology Data Exchange (ETDEWEB)
Eim, Young Sup; Han, Seog Young [Hanyang University, Seoul (Korea, Republic of)
2014-07-15
A new topology optimization algorithm based on artificial bee colony algorithm (ABCA) was developed and applied to geometrically nonlinear structures. A finite element method and the Newton-Raphson technique were adopted for the nonlinear topology optimization. The distribution of material is expressed by the density of each element and a filter scheme was implemented to prevent a checkerboard pattern in the optimized layouts. In the application of ABCA for long structures or structures with small volume constraints, optimized topologies may be obtained differently for the same problem at each trial. The calculation speed is also very slow since topology optimization based on the roulette-wheel method requires many finite element analyses. To improve the calculation speed and stability of ABCA, a rank-based method was used. By optimizing several examples, it was verified that the developed topology scheme based on ABCA is very effective and applicable in geometrically nonlinear topology optimization problems.
Optimal RG-Improvement of Perturbative Calculations in QCD
Elias, V
2003-01-01
Using renormalization-group methods, differential equations can be obtained for the all-orders summation of leading and subsequent non-leading logarithmic corrections to QCD perturbative series for a number of processes and correlation functions. For a QCD perturbative series known to four orders, such as the e+ e- annihilation cross-section, explicit solutions to these equations are obtained for the summation to all orders in alpha_s of the leading set and the subsequent two non-leading sets of logarithms. Such summations are shown for a number of processes to lead to a substantial reduction in sensitivity to the renormalization scale parameter. Surprisingly, such summations are also shown to lower the infrared singularity within the perturbative expression for the e+ e- annihilation cross-section to coincide with the Landau pole of the naive one-loop running QCD couplant.
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
田保锋; 戴云仙; 孟泽红; 张建军
2003-01-01
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Energy Technology Data Exchange (ETDEWEB)
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
Energy Technology Data Exchange (ETDEWEB)
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato.minamitsuji@ist.utl.pt, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled 'spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
Lyapunov optimal feedback control of a nonlinear inverted pendulum
Grantham, W. J.; Anderson, M. J.
1989-01-01
Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.
Lyapunov optimal feedback control of a nonlinear inverted pendulum
Grantham, W. J.; Anderson, M. J.
1989-01-01
Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.
DEFF Research Database (Denmark)
Sadegh, Payman
1997-01-01
This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...
Single-Dimension Perturbation Glowworm Swarm Optimization Algorithm for Block Motion Estimation
Xiangpin Liu; Shibin Xuan; Feng Liu
2013-01-01
In view of the fact that the classical fast motion estimation methods are easy to fall into local optimum and suffer the high computational cost, the convergence of the motion estimation method based on the swarm intelligence algorithm is very slow. A new block motion estimation method based on single-dimension perturbation glowworm swarm optimization algorithm is proposed. Single-dimension perturbation is a local search strategy which can improve the ability of local optimization. The propos...
Remarks on a benchmark nonlinear constrained optimization problem
Institute of Scientific and Technical Information of China (English)
Luo Yazhong; Lei Yongjun; Tang Guojin
2006-01-01
Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulated annealing using simplex method is employed in our study to solve the benchmark nonlinear constrained problem with mistaken formula and the best-known solution is obtained, whose optimality is testified by the Kuhn-Tucker conditions.
Optimization of nonlinear controller with an enhanced biogeography approach
Directory of Open Access Journals (Sweden)
Mohammed Salem
2014-07-01
Full Text Available This paper is dedicated to the optimization of nonlinear controllers basing of an enhanced Biogeography Based Optimization (BBO approach. Indeed, The BBO is combined to a predator and prey model where several predators are used with introduction of a modified migration operator to increase the diversification along the optimization process so as to avoid local optima and reach the optimal solution quickly. The proposed approach is used in tuning the gains of PID controller for nonlinear systems. Simulations are carried out over a Mass spring damper and an inverted pendulum and has given remarkable results when compared to genetic algorithm and BBO.
Nourazar, S. S.; Nazari-Golshan, A.
2015-01-01
A hybrid of Fourier transform and new modified homotopy perturbation method based on the Adomian method is developed to solve linear and nonlinear partial differential equations. The Taylor series expansion is used to expand nonlinear term of partial differential equation and the Adomian polynomial incorporated into homotopy perturbation method combined with Fourier transform, is used to solve partial differential equations. Three case study problems, partial differential equations, are handled using homotopy perturbation method and Fourier transform modified homotopy perturbation method (FTMHPM). Results obtained are compared with exact solution. The comparison reveals that for same components of recursive sequences, errors associated with Fourier transform modified method are much less than the other and are valid for a large range of x-axis coordinates.
Nonlinear Optimal Trajectories Using Successive Linearization
1977-06-28
integral sign represents a penalty for the local vertical and passing through the vehicle deviations of the perturbed trajectory from the at time equals... integral sign represents the penalty for control variations about the nominal, and needs z s - sin y (14) to be weighted to ensure that the control does
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Aircraft nonlinear optimal control using fuzzy gain scheduling
Nusyirwan, I. F.; Kung, Z. Y.
2016-10-01
Fuzzy gain scheduling is a common solution for nonlinear flight control. The highly nonlinear region of flight dynamics is determined throughout the examination of eigenvalues and the irregular pattern of root locus plots that show the nonlinear characteristic. By using the optimal control for command tracking, the pitch rate stability augmented system is constructed and the longitudinal flight control system is established. The outputs of optimal control for 21 linear systems are fed into the fuzzy gain scheduler. This research explores the capability in using both optimal control and fuzzy gain scheduling to improve the efficiency in finding the optimal control gains and to achieve Level 1 flying qualities. The numerical simulation work is carried out to determine the effectiveness and performance of the entire flight control system. The simulation results show that the fuzzy gain scheduling technique is able to perform in real time to find near optimal control law in various flying conditions.
Optimal Transmission Power in a Nonlinear VLC System
Institute of Scientific and Technical Information of China (English)
ZHAO Shuang; CAI Sunzeng; KANG Kai; QIAN Hua
2016-01-01
In a visible light communication (VLC) system, the light emitting diode (LED) is nonlinear for large signals, which limits the trans⁃mission power or equivalently the coverage of the VLC system. When the input signal amplitude is large, the nonlinear distortion creates harmonic and intermodulation distortion, which degrades the transmission error vector magnitude (EVM). To evaluate the impact of nonlinearity on system performance, the signal to noise and distortion ratio (SNDR) is applied, defined as the linear sig⁃nal power over the thermal noise plus the front end nonlinear distortion. At a given noise level, the optimal system performance can be achieved by maximizing the SNDR, which results in high transmission rate or long transmission range for the VLC system. In this paper, we provide theoretical analysis on the optimization of SNDR with a nonlinear Hammerstein model of LED. Simula⁃tion results and lab experiments validate the theoretical analysis.
Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf -> 16.5
Stevenson, P M
2016-01-01
Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf -> 16.5, where the leading beta-function coefficient vanishes. The Banks-Zaks (BZ) expansion in a0=(8/321)(16.5-nf) is straightforward to obtain from perturbative results in MSbar or any renormalization scheme (RS) whose nf dependence is `regular.' However, `irregular' RS's are perfectly permissible and should ultimately lead to the same BZ results. We show here that the `optimal' RS determined by the Principle of Minimal Sensitivity does yield the same BZ-expansion results when all orders of perturbation theory are taken into account. The BZ limit provides an arena for exploring optimized perturbation theory at arbitrarily high orders. These explorations are facilitated by a `master equation' expressing the optimization conditions in the fixed-point limit. We find an intriguing strong/weak coupling duality a -> a*^2/a about the fixed point a*.
New results on stability analysis for time-varying delay systems with non-linear perturbations.
Liu, Pin-Lin
2013-05-01
The problem of stability for linear time-varying delay systems under nonlinear perturbation is discussed, with delay assumed as time-varying. Delay decomposition approach allows information of the delayed plant states to be fully considered. A less conservative delay-dependent robust stability condition is derived, using integral inequality approach to express the relationship of Leibniz-Newton formula terms in the within the framework of linear matrix inequalities (LMIs). Merits of the proposed results lie in lesser conservatism, which are realized by choosing different Lyapunov matrices in the decomposed integral intervals and estimating the upper bound of some cross term more exactly. Numerical examples are given to illustrate the effectiveness and lesser conservatism of the proposed method.
Georgievskii, D. V.
2007-06-01
Material functions are necessary element of the constitutive relations determining any model of continuum. These functions can be defined as a collection of objects from which the operator of constitutive relations can be reconstructed completely. The material functions are found in test experiments and show the differences between a given medium and other media in the framework of the same model [1]. The "test experiment theory" is an important part of modern experimental mechanics. Just as in any experiment, from determining the viscosity coefficient by using the rotational viscosimeters to constructing the yield surface by using machines combined loading, the material functions are determined with an unavoidable error. For example, experimenters know that, in experiments with arbitrary accuracy, the moduli of elasticity can only be measured with an unimprovable tolerance of about 7%. Starting already from [2], the investigators' attention has been repeatedly drawn to the fact that it is necessary to take into account this tolerance in determining the material constants, functions, and functionals in problems of mechanics and especially in analyzing the stability of deformation processes. Mathematically, this means that problems of stability under perturbations of the initial data, external constantly acting forces, domain boundaries, etc. should be supplemented with the assumption that the material functions have unknown perturbations of a certain class [3]. The variations of material functions in the framework of the linearized stability theory were considered in [2, 4, 5]. In what follows, we study isotropic tensor functions in the most general case of scalar and tensor nonlinearity. These functions are assigned the meaning of constitutive relations between the stress and strain rate tensors in continuum. These constitutive relations contain scalar material functions of invariants on which, as follows from the above, some variations proportional to a small
Köllner, Thomas; Rossi, Maurice; Broer, Frauke; Boeck, Thomas
2014-11-01
A case of convection driven by chemical reactions is studied by linear stability theory and direct numerical simulations. In a plane aqueous layer of glucose, the methylene-blue-enabled catalytic oxidation of glucose produces heavier gluconic acid. As the oxygen is supplied through the top surface, the production of gluconic acid leads to an overturning instability. Our results complement earlier experimental and numerical work by Pons et al. First, we extend the model by including the top air layer with diffusive transport and Henry's law for the oxygen concentration at the interface to provide a more realistic oxygen boundary condition. Second, a linear stability analysis of the diffusive basic state in the layers is performed using an optimal perturbation approach. This method is appropriate for the unsteady basic state and determines the onset time of convection and the associated wavelength. Third, the nonlinear evolution is studied by the use of three-dimensional numerical simulations. Three typical parameters sets are explored in detail showing significant differences in pattern formation. One parameter set for which the flow is dominated by viscous forces, displays persistently growing convection cells. The other set with increased reaction rate displays a different flow regime marked by local chaotic plume emission. The simulated patterns are then compared to experimental observations.
Sopuerta, C F; Gualtieri, L; Sopuerta, Carlos F.; Bruni, Marco; Gualtieri, Leonardo
2003-01-01
We present a new way of deriving gauge transformations in non--linear relativistic perturbation theory. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated formal machinery allows us to generalize one-parameter perturbation theory to an arbitrary number of parameters, and to prove the main results concerning the consistency of the scheme to any order in the perturbations. Gauge transformations at any required order can then be directly derived from a generating exponential formula via a simple Taylor expansion. We outline the relation between our novel formulation and previous results.
Moen, Erick K.; Beier, Hope T.; Thompson, Gary L.; Roth, Caleb C.; Ibey, Bennett L.
2014-03-01
Nonlinear optical probes, especially those involving second harmonic generation (SHG), have proven useful as sensors for near-instantaneous detection of alterations to orientation or energetics within a substance. This has been exploited to some success for observing conformational changes in proteins. SHG probes, therefore, hold promise for reporting rapid and minute changes in lipid membranes. In this report, one of these probes is employed in this regard, using nanosecond electric pulses (nsEPs) as a vehicle for instigating subtle membrane perturbations. The result provides a useful tool and methodology for the observation of minute membrane perturbation, while also providing meaningful information on the phenomenon of electropermeabilization due to nsEP. The SHG probe Di- 4-ANEPPDHQ is used in conjunction with a tuned optical setup to demonstrate nanoporation preferential to one hemisphere, or pole, of the cell given a single square shaped pulse. The results also confirm a correlation of pulse width to the amount of poration. Furthermore, the polarity of this event and the membrane physics of both hemispheres, the poles facing either electrode, were tested using bipolar pulses consisting of two pulses of opposite polarity. The experiment corroborates findings by other researchers that these types of pulses are less effective in causing repairable damage to the lipid membrane of cells.
RF Circuit linearity optimization using a general weak nonlinearity model
Cheng, W.; Oude Alink, M.S.; Annema, Anne J.; Croon, Jeroen A.; Nauta, Bram
2012-01-01
This paper focuses on optimizing the linearity in known RF circuits, by exploring the circuit design space that is usually available in today’s deep submicron CMOS technologies. Instead of using brute force numerical optimizers we apply a generalized weak nonlinearity model that only involves AC
Reliability-based design optimization for nonlinear energy harvesters
Seong, Sumin; Lee, Soobum; Hu, Chao
2015-03-01
The power output of a vibration energy harvesting device is highly sensitive to uncertainties in materials, manufacturing, and operating conditions. Although the use of a nonlinear spring (e.g., snap-through mechanism) in energy harvesting device has been reported to reduce the sensitivity of power output with respect to the excitation frequency, the nonlinear spring characteristic remains significantly sensitive and it causes unreliable power generation. In this paper, we present a reliability-based design optimization (RBDO) study of vibration energy harvesters. For a nonlinear harvester, a purely mechanical nonlinear spring design implemented in the middle of cantilever beam harvester is considered in the study. This design has the curved section in the center of beam that causes bi-stable configuration. When vibrating, the inertia of the tip mass activates the curved shell to cause snap-through buckling and make the nature of vibration nonlinear. In this paper, deterministic optimization (DO) is performed to obtain deterministic optimum of linear and nonlinear energy harvester configuration. As a result of the deterministic optimization, an optimum bi-stable vibration configuration of nonlinear harvester can be obtained for reliable power generation despite uncertainty on input vibration condition. For the linear harvester, RBDO is additionally performed to find the optimum design that satisfies a target reliability on power generation, while accounting for uncertainty in material properties and geometric parameters.
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems
Vázquez, Luis
2013-01-01
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton's equation for the motion of one particle in classical mechanics combined with finite difference methods allows creation of a mechanical scenario to solve basic problems in linear algebra and programming. The authors present a novel, unified numerical and mechanical approach and an important analysis method of optimization. This book also: Presents mechanical method for determining matrix singularity or non-independence of dimension and complexity Illustrates novel mathematical applications of classical Newton’s law Offers a new approach and insight to basic, standard problems Includes numerous examples and applications Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems is an ideal book for undergraduate and graduate students as well as researchers interested in linear problems and optimization, and nonlinear dynamics.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
A Quadratic precision generalized nonlinear global optimization migration velocity inversion method
Institute of Scientific and Technical Information of China (English)
Zhao Taiyin; Hu Guangmin; He Zhenhua; Huang Deji
2009-01-01
An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Marmousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis (MVA) in complex areas.
Optimal Nonlinear Filter for INS Alignment
Institute of Scientific and Technical Information of China (English)
赵瑞; 顾启泰
2002-01-01
All the methods to handle the inertial navigation system (INS) alignment were sub-optimal in the past. In this paper, particle filtering (PF) as an optimal method is used for solving the problem of INS alignment. A sub-optimal two-step filtering algorithm is presented to improve the real-time performance of PF. The approach combines particle filtering with Kalman filtering (KF). Simulation results illustrate the superior performance of these approaches when compared with extended Kalman filtering (EKF).
Application of He's homotopy perturbation method to conservative truly nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Belendez, T.; Marquez, A.; Neipp, C. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-08-15
We apply He's homotopy perturbation method to find improved approximate solutions to conservative truly nonlinear oscillators. This approach gives us not only a truly periodic solution but also the period of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters in the case of the cubic oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second order approximation we have shown that the relative error in the analytical approximate frequency is approximately 0.03% for any parameter values involved. We also compared the analytical approximate solutions and the Fourier series expansion of the exact solution. This has allowed us to compare the coefficients for the different harmonic terms in these solutions. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems.
Introduction to the theory of nonlinear optimization
Jahn, Johannes
2007-01-01
This book serves as an introductory text to optimization theory in normed spaces. The topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a ba
Luo, Biao; Wu, Huai-Ning; Li, Han-Xiong
2015-04-01
Highly dissipative nonlinear partial differential equations (PDEs) are widely employed to describe the system dynamics of industrial spatially distributed processes (SDPs). In this paper, we consider the optimal control problem of the general highly dissipative SDPs, and propose an adaptive optimal control approach based on neuro-dynamic programming (NDP). Initially, Karhunen-Loève decomposition is employed to compute empirical eigenfunctions (EEFs) of the SDP based on the method of snapshots. These EEFs together with singular perturbation technique are then used to obtain a finite-dimensional slow subsystem of ordinary differential equations that accurately describes the dominant dynamics of the PDE system. Subsequently, the optimal control problem is reformulated on the basis of the slow subsystem, which is further converted to solve a Hamilton-Jacobi-Bellman (HJB) equation. HJB equation is a nonlinear PDE that has proven to be impossible to solve analytically. Thus, an adaptive optimal control method is developed via NDP that solves the HJB equation online using neural network (NN) for approximating the value function; and an online NN weight tuning law is proposed without requiring an initial stabilizing control policy. Moreover, by involving the NN estimation error, we prove that the original closed-loop PDE system with the adaptive optimal control policy is semiglobally uniformly ultimately bounded. Finally, the developed method is tested on a nonlinear diffusion-convection-reaction process and applied to a temperature cooling fin of high-speed aerospace vehicle, and the achieved results show its effectiveness.
Optimization-Based Robust Nonlinear Control
2006-08-01
IEEE Transactions on Automatic Control , vol. 51, no. 4, pp. 661...systems with two time scales", A.R. Teel, L. Moreau and D. Nesic, IEEE Transactions on Automatic Control , vol. 48, no. 9, pp. 1526-1544, September 2003...Turner, L. Zaccarian, IEEE Transactions on Automatic Control , vol. 48, no. 9, pp. 1509- 1525, September 2003. 5. "Nonlinear Scheduled anti-windup
A new optimization algotithm with application to nonlinear MPC
Directory of Open Access Journals (Sweden)
Frode Martinsen
2005-01-01
Full Text Available This paper investigates application of SQP optimization algorithm to nonlinear model predictive control. It considers feasible vs. infeasible path methods, sequential vs. simultaneous methods and reduced vs full space methods. A new optimization algorithm coined rFOPT which remains feasibile with respect to inequality constraints is introduced. The suitable choices between these various strategies are assessed informally through a small CSTR case study. The case study also considers the effect various discretization methods have on the optimization problem.
Optimal beamforming in MIMO systems with HPA nonlinearity
Qi, Jian
2010-09-01
In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.
Nonlinear model predictive control based on collective neurodynamic optimization.
Yan, Zheng; Wang, Jun
2015-04-01
In general, nonlinear model predictive control (NMPC) entails solving a sequential global optimization problem with a nonconvex cost function or constraints. This paper presents a novel collective neurodynamic optimization approach to NMPC without linearization. Utilizing a group of recurrent neural networks (RNNs), the proposed collective neurodynamic optimization approach searches for optimal solutions to global optimization problems by emulating brainstorming. Each RNN is guaranteed to converge to a candidate solution by performing constrained local search. By exchanging information and iteratively improving the starting and restarting points of each RNN using the information of local and global best known solutions in a framework of particle swarm optimization, the group of RNNs is able to reach global optimal solutions to global optimization problems. The essence of the proposed collective neurodynamic optimization approach lies in the integration of capabilities of global search and precise local search. The simulation results of many cases are discussed to substantiate the effectiveness and the characteristics of the proposed approach.
奇摄动非线性边值问题%THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2000-01-01
The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities.
Kim, Joonhoon; Reed, Jennifer L
2012-07-05
Predicting cellular responses to perturbations is an important task in systems biology. We report a new approach, RELATCH, which uses flux and gene expression data from a reference state to predict metabolic responses in a genetically or environmentally perturbed state. Using the concept of relative optimality, which considers relative flux changes from a reference state, we hypothesize a relative metabolic flux pattern is maintained from one state to another, and that cells adapt to perturbations using metabolic and regulatory reprogramming to preserve this relative flux pattern. This constraint-based approach will have broad utility where predictions of metabolic responses are needed.
A TRUST-REGION ALGORITHM FOR NONLINEAR INEQUALITY CONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Xiaojiao Tong; Shuzi Zhou
2003-01-01
This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived,which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach.
Multiple optimal solutions to a sort of nonlinear optimization problem
Institute of Scientific and Technical Information of China (English)
Xue Shengjia
2007-01-01
The optimization problem is considered in which the objective function is pseudolinear(both pseudoconvex and pseudoconcave) and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions ( ifthe uniqueness condition is not satisfied ) are provided. Finally, an illustrative example is also given.
Conference on High Performance Software for Nonlinear Optimization
Murli, Almerico; Pardalos, Panos; Toraldo, Gerardo
1998-01-01
This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical...
Nonlinear optimization of load allocation in a manufacturing system
Institute of Scientific and Technical Information of China (English)
GUO Cai-fen; WANG Ning-sheng
2006-01-01
Based on the queuing theory, a nonlinear optimization model is proposed in this paper. A novel transformation of optimization variables is devised and the constraints are properly combined so as to make this model into a convex one, from which the Lagrangian function and the KKT conditions are derived. The interiorpoint method for convex optimization is presented here as a computationally efficient tool. Finally, this model is evaluated on a real example, from which such conclusions are drawn that the optimum result can ensure the full utilization of machines and the least amount of WIP in manufacturing systems; the interior-point method for convex optimization needs fewer iterations with significant computational savings. It appears that many non-linear optimization problems in the industrial engineering field would be amenable to this method of solution.
Novel Approach to Nonlinear PID Parameter Optimization Using Ant Colony Optimization Algorithm
Institute of Scientific and Technical Information of China (English)
Duan Hai-bin; Wang Dao-bo; Yu Xiu-fen
2006-01-01
This paper presents an application of an Ant Colony Optimization (ACO) algorithm to optimize the parameters in the design of a type of nonlinear PID controller. The ACO algorithm is a novel heuristic bionic algorithm, which is based on the behaviour of real ants in nature searching for food. In order to optimize the parameters of the nonlinear PID controller using ACO algorithm,an objective function based on position tracing error was constructed, and elitist strategy was adopted in the improved ACO algorithm. Detailed simulation steps are presented. This nonlinear PID controller using the ACO algorithm has high precision of control and quick response.
Institute of Scientific and Technical Information of China (English)
AI Yuan-fang; MEI Chi; JIANG Shao-jian; HUANG Guo-dong; CHEN Hong-rong
2006-01-01
The heat transfer characteristic of honeycomb ceramic regenerator was optimized by the perturbation analytical-numerical method. The results show that there is a temperature efficiency peak and the corresponding optimal switch time. The decrease of air oxygen concentration leads to the decrease of maximum temperature efficiency. Optimal switch time is directly proportional to the matrix thickness. The solid heat conduction along the flow direction and the regenerator heat storage capacity of the unit volume have no impact on maximum temperature efficiency and optimal switch time. The temperature efficiency tendency based on the semi-analysis is the same as dispersion combustion tests with low oxygen concentration, and optimal switch time of 2 - 4 s agrees well with that of 4 s in high-temperature gasification tests. The possibility of design, operate and control a thin-walled regenerator with high efficiency by means of the perturbation method is proved.
Nonlinear Non-convex Optimization of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef
2013-01-01
Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...... in pumps and also to regulate the pressure at the end-user valves to a desired value. The optimization problem which is solved is a nonlinear and non-convex optimization. The barrier method is used to solve this problem. The modeling framework and the optimization technique which are used are general...
Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong
2014-02-01
Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects.
Asynchronous parallel pattern search for nonlinear optimization
Energy Technology Data Exchange (ETDEWEB)
P. D. Hough; T. G. Kolda; V. J. Torczon
2000-01-01
Parallel pattern search (PPS) can be quite useful for engineering optimization problems characterized by a small number of variables (say 10--50) and by expensive objective function evaluations such as complex simulations that take from minutes to hours to run. However, PPS, which was originally designed for execution on homogeneous and tightly-coupled parallel machine, is not well suited to the more heterogeneous, loosely-coupled, and even fault-prone parallel systems available today. Specifically, PPS is hindered by synchronization penalties and cannot recover in the event of a failure. The authors introduce a new asynchronous and fault tolerant parallel pattern search (AAPS) method and demonstrate its effectiveness on both simple test problems as well as some engineering optimization problems
Modified constrained differential evolution for solving nonlinear global optimization problems
2013-01-01
Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolut...
Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger
2017-01-01
Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods. PMID:28166542
Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations
Energy Technology Data Exchange (ETDEWEB)
Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Huijsmans, G. [ITER Organization, Route de Vinon, F-13115 Saint-Paul-Lez-Durance (France); Pamela, S. [IIFS-PIIM. Aix Marseille Université - CNRS, 13397 Marseille Cedex20 (France); Chapman, I.; Kirk, A.; Thornton, A. [EURATOM/CCFE Fusion Association, Culham Science Centre, Oxon OX14 3DB (United Kingdom); Hoelzl, M. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching (Germany); Cahyna, P. [Association EURATOM/IPP.CR, Prague (Czech Republic)
2013-10-15
The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.
Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations
Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Huijsmans, G.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A.; Chapman, I.; Kirk, A.; Thornton, A.; Hoelzl, M.; Cahyna, P.
2013-10-01
The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.
Optimal state discrimination and unstructured search in nonlinear quantum mechanics
Childs, Andrew M.; Young, Joshua
2016-02-01
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
The optimal antenna for nonlinear spectroscopy of weakly and strongly scattering nanoobjects
Schumacher, Thorsten; Brandstetter, Matthias; Wolf, Daniela; Kratzer, Kai; Hentschel, Mario; Giessen, Harald; Lippitz, Markus
2016-04-01
Optical nanoantennas, i.e., arrangements of plasmonic nanostructures, promise to enhance the light-matter interaction on the nanoscale. In particular, nonlinear optical spectroscopy of single nanoobjects would profit from such an antenna, as nonlinear optical effects are already weak for bulk material, and become almost undetectable for single nanoobjects. We investigate the design of optical nanoantennas for transient absorption spectroscopy in two different cases: the mechanical breathing mode of a metal nanodisk and the quantum-confined carrier dynamics in a single CdSe nanowire. In the latter case, an antenna with a resonance at the desired wavelength optimally increases the light intensity at the nanoobject. In the first case, the perturbation of the antenna by the investigated nanosystem cannot be neglected and off-resonant antennas become most efficient.
Special section on analysis, design and optimization of nonlinear circuits
Okumura, Kohshi
Nonlinear theory plays an indispensable role in analysis, design and optimization of electric/electronic circuits because almost all circuits in the real world are modeled by nonlinear systems. Also, as the scale and complexity of circuits increase, more effective and systematic methods for the analysis, design and optimization are desired. The goal of this special section is to bring together research results from a variety of perspectives and academic disciplines related to nonlinear electric/electronic circuits.This special section includes three invited papers and six regular papers. The first invited paper by Kennedy entitled “Recent advances in the analysis, design and optimization of digital delta-sigma modulators” gives an overview of digital delta-sigma modulators and some techniques for improving their efficiency. The second invited paper by Trajkovic entitled “DC operating points of transistor circuits” surveys main theoretical results on the analysis of DC operating points of transistor circuits and discusses numerical methods for calculating them. The third invited paper by Nishi et al. entitled “Some properties of solution curves of a class of nonlinear equations and the number of solutions” gives several new theorems concerning solution curves of a class of nonlinear equations which is closely related to DC operating point analysis of nonlinear circuits. The six regular papers cover a wide range of areas such as memristors, chaos circuits, filters, sigma-delta modulators, energy harvesting systems and analog circuits for solving optimization problems.The guest editor would like to express his sincere thanks to the authors who submitted their papers to this special section. He also thanks the reviewers and the editorial committee members of this special section for their support during the review process. Last, but not least, he would also like to acknowledge the editorial staff of the NOLTA journal for their continuous support of this
Squire's transformation and 3D Optimal Perturbations in Bounded Parallel Shear Flows
Chomaz, Jean-Marc; Soundar Jerome, J. John
2011-11-01
The aim of this short communication is to present the implication of Squire's transformation on the optimal transient growth of arbitrary 3D disturbances in parallel shear flow bounded in the cross-stream direction. To our best knowledge this simple property has never been discussed before. In particular it allows to express the long-time optimal growth for perturbations of arbitrary wavenumbers as the product of the gains from the 2D optimal at a lower Reynolds number itself due to the Orr-mechanism by a term that may be identified as due to the lift-up mechanism. This property predict scalings for the 3D optimal perturbation well verified by direct computation. It may be extended to take into account buoyancy effect.
Directory of Open Access Journals (Sweden)
Musa Danjuma SHEHU
2008-06-01
Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.
Route Monopolie and Optimal Nonlinear Pricing
Tournut, Jacques
2003-01-01
To cope with air traffic growth and congested airports, two solutions are apparent on the supply side: 1) use larger aircraft in the hub and spoke system; or 2) develop new routes through secondary airports. An enlarged route system through secondary airports may increase the proportion of route monopolies in the air transport market.The monopoly optimal non linear pricing policy is well known in the case of one dimension (one instrument, one characteristic) but not in the case of several dimensions. This paper explores the robustness of the one dimensional screening model with respect to increasing the number of instruments and the number of characteristics. The objective of this paper is then to link and fill the gap in both literatures. One of the merits of the screening model has been to show that a great varieD" of economic questions (non linear pricing, product line choice, auction design, income taxation, regulation...) could be handled within the same framework.VCe study a case of non linear pricing (2 instruments (2 routes on which the airline pro_ddes customers with services), 2 characteristics (demand of services on these routes) and two values per characteristic (low and high demand of services on these routes)) and we show that none of the conclusions of the one dimensional analysis remain valid. In particular, upward incentive compatibility constraint may be binding at the optimum. As a consequence, they may be distortion at the top of the distribution. In addition to this, we show that the optimal solution often requires a kind of form of bundling, we explain explicitly distortions and show that it is sometimes optimal for the monopolist to only produce one good (instead of two) or to exclude some buyers from the market. Actually, this means that the monopolist cannot fully apply his monopoly power and is better off selling both goods independently.We then define all the possible solutions in the case of a quadratic cost function for a uniform
Optimization of optical nonlinearities in quantum cascade lasers
Bai, Jing
Nonlinearities in quantum cascade lasers (QCL's) have wide applications in wavelength tunability and ultra-short pulse generation. In this thesis, optical nonlinearities in InGaAs/AlInAs-based mid-infrared (MIR) QCL's with quadruple resonant levels are investigated. Design optimization for the second-harmonic generation (SHG) of the device is presented. Performance characteristics associated with the third-order nonlinearities are also analyzed. The design optimization for SHG efficiency is obtained utilizing techniques from supersymmetric quantum mechanics (SUSYQM) with both material-dependent effective mass and band nonparabolicity. Current flow and power output of the structure are analyzed by self-consistently solving rate equations for the carriers and photons. Nonunity pumping efficiency from one period of the QCL to the next is taken into account by including all relevant electron-electron (e-e) and longitudinal (LO) phonon scattering mechanisms between the injector/collector and active regions. Two-photon absorption processes are analyzed for the resonant cascading triple levels designed for enhancing SHG. Both sequential and simultaneous two-photon absorption processes are included in the rate-equation model. The current output characteristics for both the original and optimized structures are analyzed and compared. Stronger resonant tunneling in the optimized structure is manifested by enhanced negative differential resistance. Current-dependent linear optical output power is derived based on the steady-state photon populations in the active region. The second-harmonic (SH) power is derived from the Maxwell equations with the phase mismatch included. Due to stronger coupling between lasing levels, the optimized structure has both higher linear and nonlinear output powers. Phase mismatch effects are significant for both structures leading to a substantial reduction of the linear-to-nonlinear conversion efficiency. The optimized structure can be fabricated
Energy Technology Data Exchange (ETDEWEB)
Mihalache, D.; Panoiu, N.-C.; Moldoveanu, F.; Baboiu, D.-M. [Dept. of Theor. Phys., Inst. of Atomic Phys., Bucharest (Romania)
1994-09-21
We used the Riemann problem method with a 3*3 matrix system to find the femtosecond single soliton solution for a perturbed nonlinear Schroedinger equation which describes bright ultrashort pulse propagation in properly tailored monomode optical fibres. Compared with the Gel'fand-Levitan-Marchenko approach, the major advantage of the Riemann problem method is that it provides the general single soliton solution in a simple and compact form. Unlike the standard nonlinear Schroedinger equation, here the single soliton solution exhibits periodic evolution patterns. (author)
Optimal Control Of Nonlinear Wave Energy Point Converters
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Zhou, Qiang; Kramer, Morten
2013-01-01
In this paper the optimal control law for a single nonlinear point absorber in irregular sea-states is derived, and proven to be a closed-loop controller with feedback from measured displacement, velocity and acceleration of the floater. However, a non-causal integral control component dependent...... idea behind the control strategy is to enforce the stationary velocity response of the absorber into phase with the wave excitation force at any time. The controller is optimal under monochromatic wave excitation. It is demonstrated that the devised causal controller, in plane irregular sea states......, absorbs almost the same power as the optimal controller....
Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE
Zhang, Yan; Subbaram Naidu, D.; Cai, Chenxiao; Zou, Yun
2016-08-01
In this paper, the regulation problem of a class of nonlinear singularly perturbed discrete-time systems is investigated. Using the theory of singular perturbations and time scales, the nonlinear system is decoupled into reduced-order slow and fast (boundary layer) subsystems. Then, a composite controller consisting of two sub-controllers for the slow and fast subsystems is developed using the discrete-time state-dependent Riccati equation (D-SDRE). It is proved that the equilibrium point of the original closed-loop system with a composite controller is locally asymptotically stable. Moreover, the region of attraction of the closed-loop system is estimated by using linear matrix inequality. One example is given to illustrate the effectiveness of the results obtained.
Sun, Y; Liang, Y; Liu, Y Q; Gu, S; Yang, X; Guo, W; Shi, T; Jia, M; Wang, L; Lyu, B; Zhou, C; Liu, A; Zang, Q; Liu, H; Chu, N; Wang, H H; Zhang, T; Qian, J; Xu, L; He, K; Chen, D; Shen, B; Gong, X; Ji, X; Wang, S; Qi, M; Song, Y; Yuan, Q; Sheng, Z; Gao, G; Fu, P; Wan, B
2016-09-01
Evidence of a nonlinear transition from mitigation to suppression of the edge localized mode (ELM) by using resonant magnetic perturbations (RMPs) in the EAST tokamak is presented. This is the first demonstration of ELM suppression with RMPs in slowly rotating plasmas with dominant radio-frequency wave heating. Changes of edge magnetic topology after the transition are indicated by a gradual phase shift in the plasma response field from a linear magneto hydro dynamics modeling result to a vacuum one and a sudden increase of three-dimensional particle flux to the divertor. The transition threshold depends on the spectrum of RMPs and plasma rotation as well as perturbation amplitude. This means that edge topological changes resulting from nonlinear plasma response plays a key role in the suppression of ELM with RMPs.
Hu, Weipeng; Deng, Zichen; Yin, Tingting
2017-01-01
Exploring the dynamic behaviors of the damping nonlinear Schrödinger equation (NLSE) with periodic perturbation is a challenge in the field of nonlinear science, because the numerical approaches available for damping-driven dynamic systems may exhibit the artificial dissipation in different degree. In this paper, based on the generalized multi-symplectic idea, the local energy/momentum loss expressions as well as the approximate symmetric form of the linearly damping NLSE with periodic perturbation are deduced firstly. And then, the local energy/momentum losses are separated from the simulation results of the NLSE with small linear damping rate less than the threshold to insure structure-preserving properties of the scheme. Finally, the breakup process of the multisoliton state is simulated and the bifurcation of the discrete eigenvalues of the associated Zakharov-Shabat spectral problem is obtained to investigate the variation of the velocity as well as the amplitude of the solitons during the splitting process.
Optimal nonlinear feedback control of quasi-Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
朱位秋; 应祖光
1999-01-01
An innovative strategy for optimal nonlinear feedback control of linear or nonlinear stochastic dynamic systems is proposed based on the stochastic averaging method for quasi-Hamiltonian systems and stochastic dynamic programming principle. Feedback control forces of a system are divided into conservative parts and dissipative parts. The conservative parts are so selected that the energy distribution in the controlled system is as requested as possible. Then the response of the system with known conservative control forces is reduced to a controlled diffusion process by using the stochastic averaging method. The dissipative parts of control forces are obtained from solving the stochastic dynamic programming equation.
Energy Technology Data Exchange (ETDEWEB)
Boudesocque-Dubois, C.; Clarisse, J.M
2007-07-01
In the context of linear perturbation computations of planar or spherically symmetric flows, we propose numerical methods, in Lagrangian coordinates, for integrating the one-dimensional gas dynamics equations with nonlinear heat conduction and their linear perturbations. Numerical results are presented for different configurations, with or without flow motion. (authors)
Wang, Hong; Wang, Xicheng; Li, Zheng; Li, Keqiu
2016-01-01
The metabolic network model allows for an in-depth insight into the molecular mechanism of a particular organism. Because most parameters of the metabolic network cannot be directly measured, they must be estimated by using optimization algorithms. However, three characteristics of the metabolic network model, i.e., high nonlinearity, large amount parameters, and huge variation scopes of parameters, restrict the application of many traditional optimization algorithms. As a result, there is a growing demand to develop efficient optimization approaches to address this complex problem. In this paper, a Kriging-based algorithm aiming at parameter estimation is presented for constructing the metabolic networks. In the algorithm, a new infill sampling criterion, named expected improvement and mutual information (EI&MI), is adopted to improve the modeling accuracy by selecting multiple new sample points at each cycle, and the domain decomposition strategy based on the principal component analysis is introduced to save computing time. Meanwhile, the convergence speed is accelerated by combining a single-dimensional optimization method with the dynamic coordinate perturbation strategy when determining the new sample points. Finally, the algorithm is applied to the arachidonic acid metabolic network to estimate its parameters. The obtained results demonstrate the effectiveness of the proposed algorithm in getting precise parameter values under a limited number of iterations.
Institute of Scientific and Technical Information of China (English)
ZHENGChun-Long; ZHANGJie-Fang; CHENLi-Qun
2003-01-01
Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.
Directory of Open Access Journals (Sweden)
Ohanyan G.G.
2010-09-01
Full Text Available The quasi-adiabatic and quasi-isotherm regimes of propagation of high-frequency perturbation are considered in a thermal relaxing gas–fluid mixture. The simplified non-linear equations are obtained. It is shown that in the absence of heat transfer and under the quasi-adiabatic regime the form of propagation is soliton, or the shock wave in quasi-isotherm regime.
Ohanyan G.G.
2010-01-01
The quasi-adiabatic and quasi-isotherm regimes of propagation of high-frequency perturbation are considered in a thermal relaxing gas–fluid mixture. The simplified non-linear equations are obtained. It is shown that in the absence of heat transfer and under the quasi-adiabatic regime the form of propagation is soliton, or the shock wave in quasi-isotherm regime.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-03-17
He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient.
Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf → 161/2
Stevenson, P. M.
2016-09-01
Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf → 161/2, where the leading β-function coefficient vanishes. The Banks-Zaks (BZ) expansion in a0 ≡8/321 (161/2 -nf) is straightforward to obtain from perturbative results in MS ‾ or any renormalization scheme (RS) whose nf dependence is 'regular'. However, 'irregular' RS's are perfectly permissible and should ultimately lead to the same BZ results. We show here that the 'optimal' RS determined by the Principle of Minimal Sensitivity does yield the same BZ-expansion results when all orders of perturbation theory are taken into account. The BZ limit provides an arena for exploring optimized perturbation theory at arbitrarily high orders. These explorations are facilitated by a 'master equation' expressing the optimization conditions in the fixed-point limit. We find an intriguing strong/weak coupling duality a →a*2 / a about the fixed point a*.
Nonlinear Non-convex Optimization of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef
2013-01-01
Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...... in pumps and also to regulate the pressure at the end-user valves to a desired value. The optimization problem which is solved is a nonlinear and non-convex optimization. The barrier method is used to solve this problem. The modeling framework and the optimization technique which are used are general....... They can be used for a general hydraulic networks to optimize the leakage and energy consumption and to satisfy the demands at the end-users. The results in this paper show that the power consumption of the pumps is reduced....
Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion
Institute of Scientific and Technical Information of China (English)
Zhi-bin Liang
2007-01-01
In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.
Directory of Open Access Journals (Sweden)
Hong Qin
2003-01-01
Full Text Available Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the e-p instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the e-p instability, is studied for self-consistent equilibrium populations of protons and electrons.
Single-Dimension Perturbation Glowworm Swarm Optimization Algorithm for Block Motion Estimation
Directory of Open Access Journals (Sweden)
Xiangpin Liu
2013-01-01
Full Text Available In view of the fact that the classical fast motion estimation methods are easy to fall into local optimum and suffer the high computational cost, the convergence of the motion estimation method based on the swarm intelligence algorithm is very slow. A new block motion estimation method based on single-dimension perturbation glowworm swarm optimization algorithm is proposed. Single-dimension perturbation is a local search strategy which can improve the ability of local optimization. The proposed method not only has overcome the defect of falling into local optimum easily by taking use of both the global search ability of glowworm swarm optimization algorithm and the local optimization ability of single-dimension perturbation but also has reduced the computation complexity by using motion vector predictor and terminating strategies in view of the characteristic of video images. The experimental results show that the performance of the proposed method is better than that of other motion estimation methods for most video sequences, specifically for those video sequences with violent motion, and the searching precision has been improved obviously. Although the computational complexity of the proposed method is slightly higher than that of the classical methods, it is still far lower than that of full search method.
Non-linear DSGE Models and The Optimized Particle Filter
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper improves the accuracy and speed of particle filtering for non-linear DSGE models with potentially non-normal shocks. This is done by introducing a new proposal distribution which i) incorporates information from new observables and ii) has a small optimization step that minimizes...... the distance to the optimal proposal distribution. A particle filter with this proposal distribution is shown to deliver a high level of accuracy even with relatively few particles, and this filter is therefore much more efficient than the standard particle filter....
Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf→1612
Directory of Open Access Journals (Sweden)
P.M. Stevenson
2016-09-01
Full Text Available Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf→1612, where the leading β-function coefficient vanishes. The Banks–Zaks (BZ expansion in a0≡8321(1612−nf is straightforward to obtain from perturbative results in MS‾ or any renormalization scheme (RS whose nf dependence is ‘regular’. However, ‘irregular’ RS's are perfectly permissible and should ultimately lead to the same BZ results. We show here that the ‘optimal’ RS determined by the Principle of Minimal Sensitivity does yield the same BZ-expansion results when all orders of perturbation theory are taken into account. The BZ limit provides an arena for exploring optimized perturbation theory at arbitrarily high orders. These explorations are facilitated by a ‘master equation’ expressing the optimization conditions in the fixed-point limit. We find an intriguing strong/weak coupling duality a→a⁎2/a about the fixed point a⁎.
National Research Council Canada - National Science Library
Zhou, Xiao Ping; Lee, Victoria S; Wang, Emily Q; Jiang, Jack J
2009-01-01
...) and levodopa on patients with Parkinson's disease (PD). Methods: In this study, the effects of DBS and levodopa treatment on patients with PD were measured using perturbation, nonlinear dynamic, and perceptual analysis...
Optimal disturbances rejection control for singularly perturbed systems with time-delay
Institute of Scientific and Technical Information of China (English)
Zhang Baolin; Tang Gongyou; Zhao Yandong
2008-01-01
The optimal control design for singularly perturbed time-delay systems affected by external disturbances is considered. Based on the decomposition theory of singular perturbation, the system is decomposed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances. The optimal disturbances rejection control law of the slow subsystem is obtained by using the successive approximation approach (SAA) and feedforward compensation method. Further, the feedforward and feedback composite control (FFCC) law for the original problem is developed. The FFCC law consists of linear analytic terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint vector equations. A disturbance observer is introduced to make the FFCC law physically realizable. Numerical examples show that the proposed algorithm is effective.
Directory of Open Access Journals (Sweden)
Zhaolin Jiang
2014-01-01
Full Text Available We first give the block style spectral decomposition of arbitrary block skew circulant matrix with skew circulant blocks. Secondly, we obtain the singular value of block skew circulant matrix with skew circulant blocks as well. Finally, based on the block style spectral decomposition, we deal with the optimal backward perturbation analysis for the block skew circulant linear system with skew circulant blocks.
Kerswell, R R; Pringle, C C T; Willis, A P
2014-08-01
This article introduces and reviews recent work using a simple optimization technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system such that it transits from one stable state to another. The key idea is introduced within the framework of a finite-dimensional set of ordinary differential equations (ODEs) and then illustrated for a very simple system of two ODEs which possesses bistability. Then the transition to turbulence problem in fluid mechanics is used to show how the technique can be formulated for a spatially-extended system described by a set of partial differential equations (the well-known Navier-Stokes equations). Within that context, the optimization technique bridges the gap between (linear) optimal perturbation theory and the (nonlinear) dynamical systems approach to fluid flows. The fact that the technique has now been recently shown to work in this very high dimensional setting augurs well for its utility in other physical systems.
2002-06-01
IEEE TRANSACTIONS ON AUTOMATIC CONTROL , VOL. 47, NO. 6, JUNE 2002 1033 Application of Optimization Techniques to a Nonlinear Problem of Communication... IEEE TRANSACTIONS ON AUTOMATIC CONTROL , VOL. 47, NO. 6, JUNE 2002 We consider J source-destination pairs, each of which is assigned a fixed multihop...blocking probabilities are at the maximum permitted value. IEEE TRANSACTIONS ON AUTOMATIC CONTROL , VOL. 47, NO. 6, JUNE
Structural Optimization for Reliability Using Nonlinear Goal Programming
El-Sayed, Mohamed E.
1999-01-01
This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.
Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
Energy Technology Data Exchange (ETDEWEB)
Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)
2015-04-15
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.
Optimizing controllability of edge dynamics in complex networks by perturbing network structure
Pang, Shaopeng; Hao, Fei
2017-03-01
Using the minimum input signals to drive the dynamics in complex networks toward some desired state is a fundamental issue in the field of network controllability. For a complex network with the dynamical process defined on its edges, the controllability of this network is optimal if it can be fully controlled by applying one input signal to an arbitrary non-isolated vertex of it. In this paper, the adding-edge strategy and turning-edge strategy are proposed to optimize the controllability by minimum structural perturbations. Simulations and analyses indicate that the minimum number of adding-edges required for the optimal controllability is equal to the minimum number of turning-edges, and networks with positively correlated in- and out-degrees are easier to achieve optimal controllability. Furthermore, both the strategies have the capacity to reveal the relationship between certain structural properties of a complex network and its controllability of edge dynamics.
A new method for nonlinear optimization - experimental results
Energy Technology Data Exchange (ETDEWEB)
Loskovska, S.; Percinkova, B.
1994-12-31
In this paper an application of a new method for nonlinear optimization problems suggested and presented by B. Percinkova is performed. The method is originally developed and applicated on nonlinear systems. Basis of the method is following: A system of n-nonlinear equations gives as F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) = 0; 1 = 1, 2, ..., n and solution domain x{sub pi} {<=} x{sub i} {<=} x{sub ki} i = 1, 2, ..., n is modified by introducing a new variable z. The new system is given by: F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) = z; i = 1, 2, ..., n. The system defines a curve in (n + 1) dimensional space. System`s point X = (x{sub i}, x{sub 2}, x{sub 3}, ..., x{sub n}, z) that, the solution of the system is obtained using an interative procedure moving along the curve until the point with z = 0 is reached. In order to applicate method on optimization problems, a basic optimization model given with (min, max)F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) with the following optimization space: F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) ({<=}{>=})0 : i = 1, 2, ..., n is transformed into a system equivalent to system (2) by (dF/dx{sub i}) = z; i - 1, 2, ..., n. The main purpose of this work is to make relevant evaluation of the method by standard test problems.
Spin glasses and nonlinear constraints in portfolio optimization
Energy Technology Data Exchange (ETDEWEB)
Andrecut, M., E-mail: mircea.andrecut@gmail.com
2014-01-17
We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal portfolios, completely different from each other, and extremely sensitive to any changes in the input parameters of the problem, making the concept of rational decision making questionable. Here we reformulate the problem using a quadratic obligatory deposits constraint, and we show that from the physics point of view, finding an optimal portfolio amounts to calculating the mean-field magnetizations of a random Ising model with the constraint of a constant magnetization norm. We show that the model reduces to an eigenproblem, with 2N solutions, where N is the number of assets defining the portfolio. Also, in order to illustrate our results, we present a detailed numerical example of a portfolio of several risky common stocks traded on the Nasdaq Market.
A hybrid nonlinear programming method for design optimization
Rajan, S. D.
1986-01-01
Solutions to engineering design problems formulated as nonlinear programming (NLP) problems usually require the use of more than one optimization technique. Moreover, the interaction between the user (analysis/synthesis) program and the NLP system can lead to interface, scaling, or convergence problems. An NLP solution system is presented that seeks to solve these problems by providing a programming system to ease the user-system interface. A simple set of rules is used to select an optimization technique or to switch from one technique to another in an attempt to detect, diagnose, and solve some potential problems. Numerical examples involving finite element based optimal design of space trusses and rotor bearing systems are used to illustrate the applicability of the proposed methodology.
Spin glasses and nonlinear constraints in portfolio optimization
Andrecut, M.
2014-01-01
We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal portfolios, completely different from each other, and extremely sensitive to any changes in the input parameters of the problem, making the concept of rational decision making questionable. Here we reformulate the problem using a quadratic obligatory deposits constraint, and we show that from the physics point of view, finding an optimal portfolio amounts to calculating the mean-field magnetizations of a random Ising model with the constraint of a constant magnetization norm. We show that the model reduces to an eigenproblem, with 2N solutions, where N is the number of assets defining the portfolio. Also, in order to illustrate our results, we present a detailed numerical example of a portfolio of several risky common stocks traded on the Nasdaq Market.
Massive neutrinos in nonlinear large scale structure: A consistent perturbation theory
Levi, Michele
2016-01-01
A consistent formulation to incorporate massive neutrinos in the perturbation theory of the effective CDM+baryons fluid is introduced. In this formulation all linear k dependence in the growth functions of CDM+baryons perturbations, as well as all consequent additional mode coupling at higher orders, are taken into account to any desirable accuracy. Our formulation regards the neutrino fraction, which is constant in time after the non-relativistic transition of neutrinos, and much smaller than unity, as the coupling constant of the theory. Then the "bare" perturbations are those in the massless neutrino case when the neutrino fraction vanishes, and we consider the backreaction corrections due to the gravitational coupling of neutrinos. We derive the general equations for the "bare" perturbations, and backrecation corrections. Then, by employing exact time evolution with the proper analytic Green's function we explicitly derive the leading backreaction effect, and find precise agreement at the linear level. We...
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2006-01-01
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.
Yin, J. L.; Xing, Q. Q.; Tian, L. X.
2015-03-01
The behavior of non-smooth solitary waves switching to chaos is studied. Firstly, we present some singular homoclinic orbits of an unperturbed system. These singular homoclinic orbits correspond to non-smooth solutions. Secondly, we find that the peculiar solitary waves are more likely to be chaos by using the Melnikov theory. Finally, chaos thresholds under different amplitudes and frequencies of a periodic perturbation are given. One interesting finding is that there exists a peculiar perturbation frequency, which has significant effect on the system. The system is not well-controlled under this frequency. However, the system can be well controlled, when the frequency of the perturbation surpasses the peculiar perturbation frequency with fixed parameters of the unperturbed system.
The correlation function for density perturbations in an expanding universe. II - Nonlinear theory
Mcclelland, J.; Silk, J.
1977-01-01
A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies
Fitting Nonlinear Curves by use of Optimization Techniques
Hill, Scott A.
2005-01-01
MULTIVAR is a FORTRAN 77 computer program that fits one of the members of a set of six multivariable mathematical models (five of which are nonlinear) to a multivariable set of data. The inputs to MULTIVAR include the data for the independent and dependent variables plus the user s choice of one of the models, one of the three optimization engines, and convergence criteria. By use of the chosen optimization engine, MULTIVAR finds values for the parameters of the chosen model so as to minimize the sum of squares of the residuals. One of the optimization engines implements a routine, developed in 1982, that utilizes the Broydon-Fletcher-Goldfarb-Shanno (BFGS) variable-metric method for unconstrained minimization in conjunction with a one-dimensional search technique that finds the minimum of an unconstrained function by polynomial interpolation and extrapolation without first finding bounds on the solution. The second optimization engine is a faster and more robust commercially available code, denoted Design Optimization Tool, that also uses the BFGS method. The third optimization engine is a robust and relatively fast routine that implements the Levenberg-Marquardt algorithm.
Near time optimal control with perturbation estimation for flexible spacecraft slewing maneuvers
Institute of Scientific and Technical Information of China (English)
Cen Xiaofeng; Wang Qingchao; Ma Xingrui
2005-01-01
A feedforward approach for generating near time optimal controller for flexible spacecraft rest-to-rest maneuvers is presented with the objective insensitivity to modeling errors, parameter uncertainty and minimizing the residual energy of the flexible modes. The perturbation estimation of flexible appendages to the rigid-hub is accomplished simply via compare the output of real plant with the reference model, and the approach is based on combine this estimation with the bang-bang control for the rigid-hub modes through analysis the basic constraint and the additional constraint, i.e. zero coupling torque and zero coupling torque derivative for general two orders system and three orders system with considerate attitude acceleration mode near time optimal controls. These time optimal controls with control constraints and state constraints leads to forming a boundary- value problem, and resolved the problem using an iterative numerical algorithm.The near time optimal control with perturbation estimation shows a good robust to parameter uncertainty and can suppress the vibration and minimizing the residual energy. The capability of this approach is demonstrated through a numerical example in detail.
Simulation-based optimal Bayesian experimental design for nonlinear systems
Huan, Xun
2013-01-01
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters.Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics. © 2012 Elsevier Inc.
An hp symplectic pseudospectral method for nonlinear optimal control
Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong
2017-01-01
An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.
Global Optimization of Nonlinear Blend-Scheduling Problems
Directory of Open Access Journals (Sweden)
Pedro A. Castillo Castillo
2017-04-01
Full Text Available The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR and normalized multiparametric disaggregation technique (NMDT to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.
Mu, Mu; Dijkstra, Henk A
2004-01-01
Within a simple model context, the sensitivity and stability of the thermohaline circulation to finite amplitude perturbations is studied. A new approach is used to tackle this nonlinear problem. The method is based on the computation of the so-called Conditional Nonlinear Optimal Perturbation (CNOP) which is a nonlinear generalization of the linear singular vector approach (LSV). It is shown that linearly stable thermohaline circulation states can become nonlinearly unstable and the properties of the perturbations with optimal nonlinear growth are determined. An asymmetric nonlinear response to perturbations exists with respect to the sign of finite amplitude freshwater perturbations, on both thermally dominated and salinity dominated thermohaline flows. This asymmetry is due to the nonlinear interaction of the perturbations through advective processes.
Nonlinear Identification Using Orthogonal Forward Regression With Nested Optimal Regularization.
Hong, Xia; Chen, Sheng; Gao, Junbin; Harris, Chris J
2015-12-01
An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
Optimized interpolations and nonlinearity in numerical studies of woodwind instruments
Skouroupathis, A
2005-01-01
We study the impedance spectra of woodwind instruments with arbitrary axisymmetric geometry. We perform piecewise interpolations of the instruments' profile, using interpolating functions amenable to analytic solutions of the Webster equation. Our algorithm optimizes on the choice of such functions, while ensuring compatibility of wavefronts at the joining points. Employing a standard mathematical model of a single-reed mouthpiece as well as the time-domain reflection function, which we derive from our impedance results, we solve the Schumacher equation for the pressure evolution in time. We make analytic checks that, despite the nonlinearity in the reed model and in the evolution equation, solutions are unique and singularity-free.
Transmitter and Precoding Order Optimization for Nonlinear Downlink Beamforming
Michel, Thomas
2007-01-01
The downlink of a multiple-input multiple output (MIMO) broadcast channel (BC) is considered, where each receiver is equipped with a single antenna and the transmitter performs nonlinear Dirty-Paper Coding (DPC). We present an efficient algorithm that finds the optimum transmit filters and power allocation as well as the optimum precoding order(s) possibly affording time-sharing between individual DPC orders. Subsequently necessary and sufficient conditions for the optimality of an arbitrary precoding order are derived. Based on these we propose a suboptimal algorithm showing excellent performance and having low complexity.
A Projected Lagrangian Algorithm for Nonlinear Minimax Optimization.
1979-11-01
T Problem 5: Charalambous and Bandler (1976) # 1. f 1(x ) 2- + _ f3(x) = 2 exp(-x+ X2) Starting Pointz xO (1,..1)T 61 Problem 6: Rosen and Suzuki...Charalambous and Bandler ,#l) 2 3 1 6 6 6 (Rosen and Suzuki) 4 4 2 7 10 The results demonstrate that at least on a limited set of test problems the...and Numerical Methods for Stiff Differential Equations. Charalambous, C. and J.W. Bandler (1974). Nonlinear minimax optimization as a sequence of least
Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
Directory of Open Access Journals (Sweden)
Javier Zamora
2016-12-01
Full Text Available Interesting non-linear generalization of both Schrödinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT in Nobre et al. (Phys. Rev. Lett. 2011, 106, 140601. There is much current activity going on in this area. The non-linearity is governed by a real parameter q. Empiric hints suggest that the ensuing non-linear q-Schrödinger and q-Klein–Gordon equations are a natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for q − values close to unity (Plastino et al. (Nucl. Phys. A 2016, 955, 16–26, Nucl. Phys. A 2016, 948, 19–27. It might thus be difficult for q-values close to unity to ascertain whether one is dealing with solutions to the ordinary Schrödinger equation (whose free particle solutions are exponentials and for which q = 1 or with its NRT non-linear q-generalizations, whose free particle solutions are q-exponentials. In this work, we provide a careful analysis of the q ∼ 1 instance via a perturbative analysis of the NRT equations.
Stability analysis of nonlinear systems by multiple time scaling. [using perturbation methods
Morino, L.
1974-01-01
The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.
Scalar Perturbations on the background of Linearly and Nonlinearly Charged BTZ Black Holes
Tang, Zi-Yu; Zangeneh, Mahdi Kord; Wang, Bin; Saavedra, Joel
2016-01-01
We investigate the spacetime properties of BTZ black holes in Maxwell field and BornInfeld field and find rich properties in the spacetime structures when the model parameters vary. Employing the Landau-Lifshitz theory, we examine the thermodynamical phase transition in the charged BTZ holes. We further study the dynamical perturbation in the background of the charged BTZ black holes and find different properties of dynamical perturbations for the extreme and nonextreme charged BTZ black holes, which can serve as a new physical signal to indicate the phase transition between them.
Choosing Markovian Credit Migration Matrices by Nonlinear Optimization
Directory of Open Access Journals (Sweden)
Maximilian Hughes
2016-08-01
Full Text Available Transition matrices, containing credit risk information in the form of ratings based on discrete observations, are published annually by rating agencies. A substantial issue arises, as for higher rating classes practically no defaults are observed yielding default probabilities of zero. This does not always reflect reality. To circumvent this shortcoming, estimation techniques in continuous-time can be applied. However, raw default data may not be available at all or not in the desired granularity, leaving the practitioner to rely on given one-year transition matrices. Then, it becomes necessary to transform the one-year transition matrix to a generator matrix. This is known as the embedding problem and can be formulated as a nonlinear optimization problem, minimizing the distance between the exponential of a potential generator matrix and the annual transition matrix. So far, in credit risk-related literature, solving this problem directly has been avoided, but approximations have been preferred instead. In this paper, we show that this problem can be solved numerically with sufficient accuracy, thus rendering approximations unnecessary. Our direct approach via nonlinear optimization allows one to consider further credit risk-relevant constraints. We demonstrate that it is thus possible to choose a proper generator matrix with additional structural properties.
Non-linear and signal energy optimal asymptotic filter design
Directory of Open Access Journals (Sweden)
Josef Hrusak
2003-10-01
Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.
Goltsch, Mandy
Design denotes the transformation of an identified need to its physical embodiment in a traditionally iterative approach of trial and error. Conceptual design plays a prominent role but an almost infinite number of possible solutions at the outset of design necessitates fast evaluations. The corresponding practice of empirical equations and low fidelity analyses becomes obsolete in the light of novel concepts. Ever increasing system complexity and resource scarcity mandate new approaches to adequately capture system characteristics. Contemporary concerns in atmospheric science and homeland security created an operational need for unconventional configurations. Unmanned long endurance flight at high altitudes offers a unique showcase for the exploration of new design spaces and the incidental deficit of conceptual modeling and simulation capabilities. Structural and aerodynamic performance requirements necessitate light weight materials and high aspect ratio wings resulting in distinct structural and aeroelastic response characteristics that stand in close correlation with natural vibration modes. The present research effort evolves around the development of an efficient and accurate optimization algorithm for high aspect ratio wings subject to natural frequency constraints. Foundational corner stones are beam dimensional reduction and modal perturbation redesign. Local and global analyses inherent to the former suggest corresponding levels of local and global optimization. The present approach departs from this suggestion. It introduces local level surrogate models to capacitate a methodology that consists of multi level analyses feeding into a single level optimization. The innovative heart of the new algorithm originates in small perturbation theory. A sequence of small perturbation solutions allows the optimizer to make incremental movements within the design space. It enables a directed search that is free of costly gradients. System matrices are decomposed
Mirus, Kevin Andrew
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
Jiang, Zhaolin; Shen, Nuo; Zhou, Jianwei
2013-01-01
We first give the style spectral decomposition of a special skew circulant matrix C and then get the style decomposition of arbitrary skew circulant matrix by making use of the Kronecker products between the elements of first row in skew circulant and the special skew circulant C. Besides that, we obtain the singular value of skew circulant matrix as well. Finally, we deal with the optimal backward perturbation analysis for the linear system with skew circulant coefficient matrix on the base of its style spectral decomposition. PMID:24369488
Khellat, M
2016-01-01
We first consider the idea of renormalization group-induced estimates, in the context of optimization procedures, for the Brodsky-Lepage-Mackenzie approach to generate higher-order contributions for QCD perturbative series. Secondly, we develop the deviation pattern approach (DPA) in which through a series of comparisons between lower-order RG-induced estimates and the corresponding analytical calculations, we modify higher-order RG-induced estimates. Finally, using the normal estimation procedure and DPA, we get estimates of $\\alpha_s^4$ corrections for the Bjorken sum rule of polarized deed-inelastic scattering and for the non-singlet contribution to the Adler function.
Cheng, Longjiu; Cai, Wensheng; Shao, Xueguang
2005-03-01
An energy-based perturbation and a new idea of taboo strategy are proposed for structural optimization and applied in a benchmark problem, i.e., the optimization of Lennard-Jones (LJ) clusters. It is proved that the energy-based perturbation is much better than the traditional random perturbation both in convergence speed and searching ability when it is combined with a simple greedy method. By tabooing the most wide-spread funnel instead of the visited solutions, the hit rate of other funnels can be significantly improved. Global minima of (LJ) clusters up to 200 atoms are found with high efficiency.
Noise and nonlinear estimation with optimal schemes in DTI.
Özcan, Alpay
2010-11-01
In general, the estimation of the diffusion properties for diffusion tensor experiments (DTI) is accomplished via least squares estimation (LSE). The technique requires applying the logarithm to the measurements, which causes bad propagation of errors. Moreover, the way noise is injected to the equations invalidates the least squares estimate as the best linear unbiased estimate. Nonlinear estimation (NE), despite its longer computation time, does not possess any of these problems. However, all of the conditions and optimization methods developed in the past are based on the coefficient matrix obtained in a LSE setup. In this article, NE for DTI is analyzed to demonstrate that any result obtained relatively easily in a linear algebra setup about the coefficient matrix can be applied to the more complicated NE framework. The data, obtained using non-optimal and optimized diffusion gradient schemes, are processed with NE. In comparison with LSE, the results show significant improvements, especially for the optimization criterion. However, NE does not resolve the existing conflicts and ambiguities displayed with LSE methods.
Wu, Huai-Ning; Li, Mao-Mao; Guo, Lei
2015-07-01
This paper studies the finite-horizon optimal guaranteed cost control (GCC) problem for a class of time-varying uncertain nonlinear systems. The aim of this problem is to find a robust state feedback controller such that the closed-loop system has not only a bounded response in a finite duration of time for all admissible uncertainties but also a minimal guaranteed cost. A neural network (NN) based approximate optimal GCC design is developed. Initially, by modifying the cost function to account for the nonlinear perturbation of system, the optimal GCC problem is transformed into a finite-horizon optimal control problem of the nominal system. Subsequently, with the help of the modified cost function together with a parametrized bounding function for all admissible uncertainties, the solution to the optimal GCC problem is given in terms of a parametrized Hamilton-Jacobi-Bellman (PHJB) equation. Then, a NN method is developed to solve offline the PHJB equation approximately and thus obtain the nearly optimal GCC policy. Furthermore, the convergence of approximate PHJB equation and the robust admissibility of nearly optimal GCC policy are also analyzed. Finally, by applying the proposed design method to the entry guidance problem of the Mars lander, the achieved simulation results show the effectiveness of the proposed controller.
Institute of Scientific and Technical Information of China (English)
鲁世平
2003-01-01
By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second-order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second- order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.
Propagation of Weakly Guided Waves in a Kerr Nonlinear Medium using a Perturbation Approach
Energy Technology Data Exchange (ETDEWEB)
Dacles-Mariani, J; Rodrigue, G
2004-10-06
The equations are represented in a simplified format with only a few leading terms needed in the expansion. The set of equations are then solved numerically using vector finite element method. To validate the algorithm, they analyzed a two-dimensional rectangular waveguide consisting of a linear core and nonlinear identical cladding. The exact nonlinear solutions for three different modes of propagations, TE0, TE1, and TE2 modes are generated and compared with the computed solutions. Next, they investigate the effect of a more intense monochromatic field on the propagation of a 'weak' optical field in a fully three-dimensional cylindrical waveguide.
Directory of Open Access Journals (Sweden)
Teffera M. Asfaw
2016-01-01
Full Text Available Let X be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space X⁎. Let T:X⊇DT→2X⁎ be maximal monotone of type Γdϕ (i.e., there exist d≥0 and a nondecreasing function ϕ:0,∞→0,∞ with ϕ(0=0 such that 〈v⁎,x-y〉≥-dx-ϕy for all x∈DT, v⁎∈Tx, and y∈X,L:X⊃D(L→X⁎ be linear, surjective, and closed such that L-1:X⁎→X is compact, and C:X→X⁎ be a bounded demicontinuous operator. A new degree theory is developed for operators of the type L+T+C. The surjectivity of L can be omitted provided that RL is closed, L is densely defined and self-adjoint, and X=H, a real Hilbert space. The theory improves the degree theory of Berkovits and Mustonen for L+C, where C is bounded demicontinuous pseudomonotone. New existence theorems are provided. In the case when L is monotone, a maximality result is included for L and L+T. The theory is applied to prove existence of weak solutions in X=L20,T;H01Ω of the nonlinear equation given by ∂u/∂t-∑i=1N(∂/∂xiAix,u,∇u+Hλx,u,∇u=fx,t, x,t∈QT; ux,t=0, x,t∈∂QT; and ux,0=ux,T, x∈Ω, where λ>0, QT=Ω×0,T, ∂QT=∂Ω×0,T, Aix,u,∇u=∂/∂xiρx,u,∇u+aix,u,∇u (i=1,2,…,N, Hλx,u,∇u=-λΔu+gx,u,∇u, Ω is a nonempty, bounded, and open subset of RN with smooth boundary, and ρ,ai,g:Ω¯×R×RN→R satisfy suitable growth conditions. In addition, a new existence result is given concerning existence of weak solutions for nonlinear wave equation with nonmonotone nonlinearity.
Mode perturbation method for optimal guided wave mode and frequency selection.
Philtron, J H; Rose, J L
2014-09-01
With a thorough understanding of guided wave mechanics, researchers can predict which guided wave modes will have a high probability of success in a particular nondestructive evaluation application. However, work continues to find optimal mode and frequency selection for a given application. This "optimal" mode could give the highest sensitivity to defects or the greatest penetration power, increasing inspection efficiency. Since material properties used for modeling work may be estimates, in many cases guided wave mode and frequency selection can be adjusted for increased inspection efficiency in the field. In this paper, a novel mode and frequency perturbation method is described and used to identify optimal mode points based on quantifiable wave characteristics. The technique uses an ultrasonic phased array comb transducer to sweep in phase velocity and frequency space. It is demonstrated using guided interface waves for bond evaluation. After searching nearby mode points, an optimal mode and frequency can be selected which has the highest sensitivity to a defect, or gives the greatest penetration power. The optimal mode choice for a given application depends on the requirements of the inspection.
Tools for the analysis of dose optimization: III. Pointwise sensitivity and perturbation analysis.
Sobotta, B; Söhn, M; Pütz, M; Alber, M
2008-11-21
The major challenge in intensity-modulated radiotherapy planning is to find the right balance between tumor control and normal tissue sparing. The most desirable solution is never physically feasible, and a compromise has to be found. One possible way to approach this problem is constrained optimization. In this context, it is worthwhile to quantitatively predict the impact of adjustments of the constraints on the optimum dose distribution. This has been dealt with in regard to cost functions in a previous paper. The aim of the present paper is to introduce spatial resolution to this formalism. Our method reveals the active constraints in a target subvolume that was previously selected by the practitioner for its insufficient dose. This is useful if a multitude of constraints can be the cause of a cold spot. The response of the optimal dose distribution to an adjustment of constraints (perturbation) is predicted. We conclude with a clinical example.
Tools for the analysis of dose optimization: III. Pointwise sensitivity and perturbation analysis
Energy Technology Data Exchange (ETDEWEB)
Sobotta, B; Soehn, M; Puetz, M; Alber, M [Abt. Medizinische Physik, Radiologische Uniklinik, Universitaet Tuebingen, 72076 Tuebingen (Germany)], E-mail: benjamin.sobotta@med.uni-tuebingen.de
2008-11-21
The major challenge in intensity-modulated radiotherapy planning is to find the right balance between tumor control and normal tissue sparing. The most desirable solution is never physically feasible, and a compromise has to be found. One possible way to approach this problem is constrained optimization. In this context, it is worthwhile to quantitatively predict the impact of adjustments of the constraints on the optimum dose distribution. This has been dealt with in regard to cost functions in a previous paper. The aim of the present paper is to introduce spatial resolution to this formalism. Our method reveals the active constraints in a target subvolume that was previously selected by the practitioner for its insufficient dose. This is useful if a multitude of constraints can be the cause of a cold spot. The response of the optimal dose distribution to an adjustment of constraints (perturbation) is predicted. We conclude with a clinical example.
Nonlinear Phenomena and Resonant Parametric Perturbation Control in QR-ZCS Buck DC-DC Converters
Hsieh, Fei-Hu; Liu, Feng-Shao; Hsieh, Hui-Chang
The purpose of this study is to investigate the chaotic phenomena and to control in current-mode controlled quasi-resonant zero-current-switching (QR-ZCS) DC-DC buck converters, and to present control of chaos by resonant parametric perturbation control methods. First of all, MATLAB/SIMULINK is used to derive a mathematical model for QR-ZCS DC-DC buck converters, and to simulate the converters to observe the waveform of output voltages, inductance currents and phase-plane portraits from the period-doubling bifurcation to chaos by changing the load resistances. Secondly, using resonant parametric perturbation control in QR-ZCS buck DC-DC converters, the simulation results of the chaotic converter form chaos state turn into stable state period 1, and improve ripple amplitudes of converters under the chaos, to verify the validity of the proposes method.
Weisberg, D. B.; Paz-Soldan, C.; Lanctot, M. J.; Strait, E. J.; Evans, T. E.
2016-10-01
The plasma response to proposed 3D coil geometries in the DIII-D tokamak is investigated using the linear MHD plasma response code MARS-F. An extensive examination of low- and high-field side coil arrangements shows the potential to optimize the coupling between imposed non-axisymmetric magnetic perturbations and the total plasma response by varying the toroidal and poloidal spectral content of the applied field. Previous work has shown that n=2 and n=3 perturbations can suppress edge-localized modes (ELMs) in cases where the applied field's coupling to resonant surfaces is enhanced by amplifying marginally-stable kink modes. This research is extended to higher n-number configurations of 2 to 3 rows with up to 12 coils each in order to advance the physical understanding and optimization of both the resonant and non-resonant responses. Both in- and ex-vessel configurations are considered. The plasma braking torque is also analyzed, and coil geometries with favorable plasma coupling characteristics are discussed. Work supported by GA internal funds.
\\alpha_S from $F_\\pi$ and Renormalization Group Optimized Perturbation
Kneur, J -L
2013-01-01
A variant of variationally optimized perturbation, incorporating renormalization group properties in a straightforward way, uniquely fixes the variational mass interpolation in terms of the anomalous mass dimension. It is used at three successive orders to calculate the nonperturbative ratio $F_\\pi/\\Lambda$ of the pion decay constant and the basic QCD scale in the MSbar scheme. We demonstrate the good stability and (empirical) convergence properties of this modified perturbative series for this quantity, and provide simple and generic cures to previous problems of the method, principally the generally non-unique and non-real optimal solutions beyond lowest order. Using the experimental $F_\\pi$ input value we determine \\Lambda^{n_f=2}\\simeq 359^{+38}_{-25} \\pm 5 MeV and \\Lambda^{n_f=3}=317^{+14}_{-7} \\pm 13 MeV, where the first quoted errors are our estimate of theoretical uncertainties of the method, which we consider conservative. The second uncertainties come from the present uncertainties in F_\\pi/F and F_...
Nonlinear perturbations of systems of partial differential equations with constant coefficients
Directory of Open Access Journals (Sweden)
Carmen J. Vanegas
2000-01-01
Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.
Energy Technology Data Exchange (ETDEWEB)
Doroshkevich, A.G.; Zel' dovich, Y.B.; Syunyaev, R.A.; Khlopov, M.Y.
1980-07-01
A discussion is given of the influence that a finite rest mass for the neutrino would have on the phenomenon of ''missing mass'' in galaxies and clusters of galaxies, on the nonlinear stage in the evolution of primordial irregularities, and on the problem of observing neutral hydrogen in the spectrum of distant quasars.
Institute of Scientific and Technical Information of China (English)
CHENGYan
2003-01-01
In this paper,the fixed-point theorem is used to estimated an asymptotic solution of intial val-ue problems for a class of third nonlinear differential equations which has double initial-layer properties.We obtain the uniformly valid asymptotic expansion of any orders including boundary layers.
Nonlinear Burn Control and Operating Point Optimization in ITER
Boyer, Mark; Schuster, Eugenio
2013-10-01
Control of the fusion power through regulation of the plasma density and temperature will be essential for achieving and maintaining desired operating points in fusion reactors and burning plasma experiments like ITER. In this work, a volume averaged model for the evolution of the density of energy, deuterium and tritium fuel ions, alpha-particles, and impurity ions is used to synthesize a multi-input multi-output nonlinear feedback controller for stabilizing and modulating the burn condition. Adaptive control techniques are used to account for uncertainty in model parameters, including particle confinement times and recycling rates. The control approach makes use of the different possible methods for altering the fusion power, including adjusting the temperature through auxiliary heating, modulating the density and isotopic mix through fueling, and altering the impurity density through impurity injection. Furthermore, a model-based optimization scheme is proposed to drive the system as close as possible to desired fusion power and temperature references. Constraints are considered in the optimization scheme to ensure that, for example, density and beta limits are avoided, and that optimal operation is achieved even when actuators reach saturation. Supported by the NSF CAREER award program (ECCS-0645086).
Design optimization of a twist compliant mechanism with nonlinear stiffness
Tummala, Y.; Frecker, M. I.; Wissa, A. A.; Hubbard, J. E., Jr.
2014-10-01
A contact-aided compliant mechanism called a twist compliant mechanism (TCM) is presented in this paper. This mechanism has nonlinear stiffness when it is twisted in both directions along its axis. The inner core of the mechanism is primarily responsible for its flexibility in one twisting direction. The contact surfaces of the cross-members and compliant sectors are primarily responsible for its high stiffness in the opposite direction. A desired twist angle in a given direction can be achieved by tailoring the stiffness of a TCM. The stiffness of a compliant twist mechanism can be tailored by varying thickness of its cross-members, thickness of the core and thickness of its sectors. A multi-objective optimization problem with three objective functions is proposed in this paper, and used to design an optimal TCM with desired twist angle. The objective functions are to minimize the mass and maximum von-Mises stress observed, while minimizing or maximizing the twist angles under specific loading conditions. The multi-objective optimization problem proposed in this paper is solved for an ornithopter flight research platform as a case study, with the goal of using the TCM to achieve passive twisting of the wing during upstroke, while keeping the wing fully extended and rigid during the downstroke. Prototype TCMs have been fabricated using 3D printing and tested. Testing results are also presented in this paper.
Robust Homography Estimation Based on Nonlinear Least Squares Optimization
Directory of Open Access Journals (Sweden)
Wei Mou
2014-01-01
Full Text Available The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers.
Indoor Wireless Localization-hybrid and Unconstrained Nonlinear Optimization Approach
Directory of Open Access Journals (Sweden)
R. Jayabharathy
2013-07-01
Full Text Available In this study, a hybrid TOA/RSSI wireless localization is proposed for accurate positioning in indoor UWB systems. The major problem in indoor localization is the effect of Non-Line of Sight (NLOS propagation. To mitigate the NLOS effects, an unconstrained nonlinear optimization approach is utilized to process Time-of-Arrival (TOA and Received Signal Strength (RSS in the location system.TOA range measurements and path loss model are used to discriminate LOS and NLOS conditions. The weighting factors assigned by hypothesis testing, is used for solving the objective function in the proposed approach. This approach is used for describing the credibility of the TOA range measurement. Performance of the proposed technique is done based on MATLAB simulation. The result shows that the proposed technique performs well and achieves improved positioning under severe NLOS conditions.
Robust C subroutines for non-linear optimization
DEFF Research Database (Denmark)
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems. The intention is that the routines should use the currently best algorithms available. All routines have standardized calls, and the user does not have...... by changing 1 to 0. The present report is a new and updated version of a previous report NI-91-03 with the same title, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated from Fortran to C. The reason for writing the present report is that some...... of the C subroutines have been replaced by more effective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modi ed to some extent. For a description of the original Fortran subroutines see the report [17]. The software...
Optimal operating points of oscillators using nonlinear resonators.
Kenig, Eyal; Cross, M C; Villanueva, L G; Karabalin, R B; Matheny, M H; Lifshitz, Ron; Roukes, M L
2012-11-01
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources.
Improved simple optimization (SOPT algorithm for unconstrained non-linear optimization problems
Directory of Open Access Journals (Sweden)
J. Thomas
2016-09-01
Full Text Available In the recent years, population based meta-heuristic are developed to solve non-linear optimization problems. These problems are difficult to solve using traditional methods. Simple optimization (SOPT algorithm is one of the simple and efficient meta-heuristic techniques to solve the non-linear optimization problems. In this paper, SOPT is compared with some of the well-known meta-heuristic techniques viz. Artificial Bee Colony algorithm (ABC, Particle Swarm Optimization (PSO, Genetic Algorithm (GA and Differential Evolutions (DE. For comparison, SOPT algorithm is coded in MATLAB and 25 standard test functions for unconstrained optimization having different characteristics are run for 30 times each. The results of experiments are compared with previously reported results of other algorithms. Promising and comparable results are obtained for most of the test problems. To improve the performance of SOPT, an improvement in the algorithm is proposed which helps it to come out of local optima when algorithm gets trapped in it. In almost all the test problems, improved SOPT is able to get the actual solution at least once in 30 runs.
A Bohmian approach to the perturbations of non-linear Klein--Gordon equation
Indian Academy of Sciences (India)
FARAMARZ RAHMANI; MEHDI GOLSHANI; MOHSEN SARBISHEI
2016-08-01
In the framework of Bohmian quantum mechanics, the Klein--Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave $\\phi(x)$ in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein--Gordon equation? We examine this approach for $\\phi_{4}(x)$ and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.
Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation.
Dmitriev, Sergey V.; Shigenari, Takeshi
2002-06-01
Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.
Nonlinearly-constrained optimization using asynchronous parallel generating set search.
Energy Technology Data Exchange (ETDEWEB)
Griffin, Joshua D.; Kolda, Tamara Gibson
2007-05-01
Many optimization problems in computational science and engineering (CS&E) are characterized by expensive objective and/or constraint function evaluations paired with a lack of derivative information. Direct search methods such as generating set search (GSS) are well understood and efficient for derivative-free optimization of unconstrained and linearly-constrained problems. This paper addresses the more difficult problem of general nonlinear programming where derivatives for objective or constraint functions are unavailable, which is the case for many CS&E applications. We focus on penalty methods that use GSS to solve the linearly-constrained problems, comparing different penalty functions. A classical choice for penalizing constraint violations is {ell}{sub 2}{sup 2}, the squared {ell}{sub 2} norm, which has advantages for derivative-based optimization methods. In our numerical tests, however, we show that exact penalty functions based on the {ell}{sub 1}, {ell}{sub 2}, and {ell}{sub {infinity}} norms converge to good approximate solutions more quickly and thus are attractive alternatives. Unfortunately, exact penalty functions are discontinuous and consequently introduce theoretical problems that degrade the final solution accuracy, so we also consider smoothed variants. Smoothed-exact penalty functions are theoretically attractive because they retain the differentiability of the original problem. Numerically, they are a compromise between exact and {ell}{sub 2}{sup 2}, i.e., they converge to a good solution somewhat quickly without sacrificing much solution accuracy. Moreover, the smoothing is parameterized and can potentially be adjusted to balance the two considerations. Since many CS&E optimization problems are characterized by expensive function evaluations, reducing the number of function evaluations is paramount, and the results of this paper show that exact and smoothed-exact penalty functions are well-suited to this task.
Directory of Open Access Journals (Sweden)
Ching-Hung Lee
2011-01-01
Full Text Available This paper proposes a new type fuzzy neural systems, denoted IT2RFNS-A (interval type-2 recurrent fuzzy neural system with asymmetric membership function, for nonlinear systems identification and control. To enhance the performance and approximation ability, the triangular asymmetric fuzzy membership function (AFMF and TSK-type consequent part are adopted for IT2RFNS-A. The gradient information of the IT2RFNS-A is not easy to obtain due to the asymmetric membership functions and interval valued sets. The corresponding stable learning is derived by simultaneous perturbation stochastic approximation (SPSA algorithm which guarantees the convergence and stability of the closed-loop systems. Simulation and comparison results for the chaotic system identification and the control of Chua's chaotic circuit are shown to illustrate the feasibility and effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Zhaohui Chen
2013-01-01
Full Text Available The delay-dependent exponential L2-L∞ performance analysis and filter design are investigated for stochastic systems with mixed delays and nonlinear perturbations. Based on the delay partitioning and integral partitioning technique, an improved delay-dependent sufficient condition for the existence of the L2-L∞ filter is established, by choosing an appropriate Lyapunov-Krasovskii functional and constructing a new integral inequality. The full-order filter design approaches are obtained in terms of linear matrix inequalities (LMIs. By solving the LMIs and using matrix decomposition, the desired filter gains can be obtained, which ensure that the filter error system is exponentially stable with a prescribed L2-L∞ performance γ. Numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.
Directory of Open Access Journals (Sweden)
Hamid Reza Karimi
2009-01-01
Full Text Available The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.
Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering
Energy Technology Data Exchange (ETDEWEB)
Rampf, Cornelius [Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen, Physikzentrum RWTH-Melaten, D-52056 Aachen (Germany); Buchert, Thomas, E-mail: rampf@physik.rwth-aachen.de, E-mail: buchert@obs.univ-lyon1.fr [Université de Lyon, Observatoire de Lyon, Centre de Recherche Astrophysique de Lyon, CNRS UMR 5574: Université Lyon 1 and École Normale Supérieure de Lyon, 9 avenue Charles André, F-69230 Saint-Genis-Laval (France)
2012-06-01
We investigate the Lagrangian perturbation theory of a homogeneous and isotropic universe in the non-relativistic limit, and derive the solutions up to the fourth order. These solutions are needed for example for the next-to-leading order correction of the (resummed) Lagrangian matter bispectrum, which we study in an accompanying paper. We focus on flat cosmologies with a vanishing cosmological constant, and provide an in-depth description of two complementary approaches used in the current literature. Both approaches are solved with two different sets of initial conditions — both appropriate for modelling the large-scale structure. Afterwards we consider only the fastest growing mode solution, which is not affected by either of these choices of initial conditions. Under the reasonable approximation that the linear density contrast is evaluated at the initial Lagrangian position of the fluid particle, we obtain the nth-order displacement field in the so-called initial position limit: the nth order displacement field consists of 3(n-1) integrals over n linear density contrasts, and obeys self-similarity. Then, we find exact relations between the series in Lagrangian and Eulerian perturbation theory, leading to identical predictions for the density contrast and the peculiar-velocity divergence up to the fourth order.
Optimization of nonlinear structural resonance using the incremental harmonic balance method
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2015-01-01
We present an optimization procedure for tailoring the nonlinear structural resonant response with time-harmonic loads. A nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinea...
Nishimichi, Takahiro; Nakamichi, Masashi; Taruya, Atsushi; Yahata, Kazuhiro; Shirata, Akihito; Saito, Shun; Nomura, Hidenori; Yamamoto, Kazuhiro; Suto, Yasushi
2007-01-01
An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\\lesssim$ 1%) relative to the prediction in {\\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.
Cai, Lanlan; Li, Peng; Luo, Qi; Zhai, Pengcheng; Zhang, Qingjie
2017-03-01
As no single thermoelectric material has presented a high figure-of-merit (ZT) over a very wide temperature range, segmented thermoelectric generators (STEGs), where the p- and n-legs are formed of different thermoelectric material segments joined in series, have been developed to improve the performance of thermoelectric generators. A crucial but difficult problem in a STEG design is to determine the optimal values of the geometrical parameters, like the relative lengths of each segment and the cross-sectional area ratio of the n- and p-legs. Herein, a multi-parameter and nonlinear optimization method, based on the Improved Powell Algorithm in conjunction with the discrete numerical model, was implemented to solve the STEG's geometrical optimization problem. The multi-parameter optimal results were validated by comparison with the optimal outcomes obtained from the single-parameter optimization method. Finally, the effect of the hot- and cold-junction temperatures on the geometry optimization was investigated. Results show that the optimal geometry parameters for maximizing the specific output power of a STEG are different from those for maximizing the conversion efficiency. Data also suggest that the optimal geometry parameters and the interfacial temperatures of the adjacent segments optimized for maximum specific output power or conversion efficiency vary with changing hot- and cold-junction temperatures. Through the geometry optimization, the CoSb3/Bi2Te3-based STEG can obtain a maximum specific output power up to 1725.3 W/kg and a maximum efficiency of 13.4% when operating at a hot-junction temperature of 823 K and a cold-junction temperature of 298 K.
A new determination of $\\alpha_S$ from Renormalization Group Optimized Perturbation
Kneur, J-L
2013-01-01
A new version of the so-called optimized perturbation (OPT), implementing consistently renormalization group properties, is used to calculate the nonperturbative ratio $F_\\pi/\\overline\\Lambda$ of the pion decay constant and the basic QCD scale in the $\\overline{MS}$ scheme. Using the experimental $F_\\pi$ input value it provides a new determination of $\\overline\\Lambda$ for $n_f=2$ and $n_f=3$, and of the QCD coupling constant $\\overline\\alpha_S $ at various scales once combined with a standard perturbative evolution. The stability and empirical convergence properties of the RGOPT modified series is demonstrated up to the third order. We examine the difference sources of theoretical uncertainties and obtain $\\overline\\alpha_S (m_Z) =0.1174 ^{+.0010}_{-.0005} \\pm .001 \\pm .0005_{evol}$, where the first errors are estimates of the intrinsic theoretical uncertainties of our method, and the second errors come from present uncertainties in $F_\\pi/F_0$, where $F_0$ is $F_\\pi$ in the exact chiral $SU(3)$ limit.
Energy Technology Data Exchange (ETDEWEB)
Munaò, Gianmarco, E-mail: gmunao@unime.it; Costa, Dino; Caccamo, Carlo [Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina (Italy); Gámez, Francisco [C/Clavel 101, Mairena del Aljarafe, 41927 Seville (Spain); Sciortino, Francesco [Dipartimento di Fisica and CNR-ISC, Università di Roma “Sapienza,” Piazzale Aldo Moro 2, 00185 Roma (Italy); Giacometti, Achille [Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S.Marta DD2137, Venezia I-30123 (Italy)
2015-06-14
We investigate thermodynamic properties of anisotropic colloidal dumbbells in the frameworks provided by the Reference Interaction Site Model (RISM) theory and an Optimized Perturbation Theory (OPT), this latter based on a fourth-order high-temperature perturbative expansion of the free energy, recently generalized to molecular fluids. Our model is constituted by two identical tangent hard spheres surrounded by square-well attractions with same widths and progressively different depths. Gas-liquid coexistence curves are obtained by predicting pressures, free energies, and chemical potentials. In comparison with previous simulation results, RISM and OPT agree in reproducing the progressive reduction of the gas-liquid phase separation as the anisotropy of the interaction potential becomes more pronounced; in particular, the RISM theory provides reasonable predictions for all coexistence curves, bar the strong anisotropy regime, whereas OPT performs generally less well. Both theories predict a linear dependence of the critical temperature on the interaction strength, reproducing in this way the mean-field behavior observed in simulations; the critical density—that drastically drops as the anisotropy increases—turns to be less accurate. Our results appear as a robust benchmark for further theoretical studies, in support to the simulation approach, of self-assembly in model colloidal systems.
Energy Technology Data Exchange (ETDEWEB)
Nishimura, Seiya, E-mail: n-seiya@kobe-kosen.ac.jp [Kobe City College of Technology, Kobe, Hyogo 651-2194 (Japan)
2014-12-15
Resonant magnetic perturbations (RMPs) produce magnetic islands in toroidal plasmas. Self-healing (annihilation) of RMP-induced magnetic islands has been observed in helical systems, where a possible mechanism of the self-healing is shielding of RMP penetration by plasma flows, which is well known in tokamaks. Thus, fundamental physics of RMP shielding is commonly investigated in both tokamaks and helical systems. In order to check this mechanism, detailed informations of magnetic island phases are necessary. In experiments, measurement of radial magnetic responses is relatively easy. In this study, based on a theoretical model of rotating magnetic islands, behavior of radial magnetic fields during the self-healing is investigated. It is confirmed that flips of radial magnetic fields are typically observed during the self-healing. Such behavior of radial magnetic responses is also observed in LHD experiments.
NONLINEAR COMPLEX DYNAMIC PHENOMENA OF THE PERTURBED METALLIC BAR CONSIDERING DISSIPATING EFFECT
Institute of Scientific and Technical Information of China (English)
ZHAO Guang-hui; ZHANG Nian-mei; YANG Gui-tong
2005-01-01
Considering Peierls-Nabarro effect, one-dimensional finite metallic bar subjected with periodic field was researched under Neumann boundary condition. Dynamics of this system was described with displacement by perturbed sine-Gordon type equation.Finite difference scheme with fourth-order central differences in space and second-order central differences in time was used to simulate dynamic responses of this system. For the metallic bar with specified sizes and physical features, effect of amplitude of external driving on dynamic behavior of the bar was investigated under initial "breather" condition. Four kinds of typical dynamic behaviors are shown: x-independent simple harmonic motion;harmonic motion with single wave; quasi-periodic motion with single wave; temporal determine dynamic features.
Modified Lagrangian and Least Root Approaches for General Nonlinear Optimization Problems
Institute of Scientific and Technical Information of China (English)
W. Oettli; X.Q. Yang
2002-01-01
In this paper we study nonlinear Lagrangian methods for optimization problems with side constraints.Nonlinear Lagrangian dual problems are introduced and their relations with the original problem are established.Moreover, a least root approach is investigated for these optimization problems.
Optimization Formulations for the Maximum Nonlinear Buckling Load of Composite Structures
DEFF Research Database (Denmark)
Lindgaard, Esben; Lund, Erik
2011-01-01
, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems...... solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization. © 2010 Springer-Verlag....
Programmable Nonlinear ADC Using Optimal-Sized ROM
K Dinesh; Anvekar, *; Sonde, BE
1991-01-01
A new programmable successive approximation ADC useful for realizing nonlinear transfer characteristics often required in instrumentation and communications is presented. This nonlinear ADC (NADC) requires a much smaller sized ROM than an NADC reported earlier
Zhang, Songchuan; Xia, Youshen
2016-12-28
Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an ℓ₁-norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.
Gradient-based optimization in nonlinear structural dynamics
DEFF Research Database (Denmark)
Dou, Suguang
The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider, fr...
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2006-01-01
A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally,by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.
Impact of resonant magnetic perturbations on nonlinearly driven modes in drift-wave turbulence
Energy Technology Data Exchange (ETDEWEB)
Leconte, M. [WCI Center for Fusion Theory, NFRI (Korea, Republic of); Diamond, P. H. [WCI Center for Fusion Theory, NFRI (Korea, Republic of); CMTFO and CASS, UCSD, California 92093 (United States)
2012-05-15
In this work, we study the effects of resonant magnetic perturbations (RMPs) on turbulence, flows, and confinement in the framework of resistive drift wave turbulence. We extend the Hasegawa-Wakatani model to include RMP fields. The effect of the RMPs is to induce a linear coupling between the zonal electric field and the zonal density gradient, which drives the system to a state of electron radial force balance for large ({delta}B{sub r}/B{sub 0}). Both the vorticity flux (Reynolds stress) and particle flux are modulated. We derive an extended predator prey model which couples zonal potential and density dynamics to the evolution of turbulence intensity. This model has both turbulence drive and RMP amplitude as control parameters and predicts a novel type of transport bifurcation in the presence of RMPs. We find states that are similar to the ZF-dominated state of the standard predator-prey model, but for which the power threshold is now a function of the RMP strength. For small RMP amplitude, the energy of zonal flows decreases and the turbulence energy increases with ({delta}B{sub r}/B{sub 0}), corresponding to a damping of zonal flows.
Institute of Scientific and Technical Information of China (English)
牛晓花; 潘祖梁
2006-01-01
A new method based on Lie-B(a)cklund symmetry method to solve the perturbed nonlinear evolution equations is presented. New approximate solutions of perturbed nonlinear evolution equations stemming from the exact solutions of unperturbed equations are obtained.This method is a generalization of Burde's Lie point symmetry technique.
Particle Swarm Optimization-Proximal Point Algorithm for Nonlinear Complementarity Problems
Chai Jun-Feng; Wang Shu-Yan
2013-01-01
A new algorithm is presented for solving the nonlinear complementarity problem by combining the particle swarm and proximal point algorithm, which is called the particle swarm optimization-proximal point algorithm. The algorithm mainly transforms nonlinear complementarity problems into unconstrained optimization problems of smooth functions using the maximum entropy function and then optimizes the problem using the proximal point algorithm as the outer algorithm and particle swarm algorithm a...
A new method of determining the optimal embedding dimension based on nonlinear prediction
Institute of Scientific and Technical Information of China (English)
Meng Qing-Fang; Peng Yu-Hua; Xue Pei-Jun
2007-01-01
A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.
Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2016-01-01
/softening behavior of nonlinear mechanical systems. The iterative optimization procedure consists of calculation of nonlinear normal modes, solving an adjoint equation system for sensitivity analysis and an update of design variables using a mathematical programming tool. We demonstrate the method with examples......Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening...
Yuan, Jinlong; Zhang, Xu; Liu, Chongyang; Chang, Liang; Xie, Jun; Feng, Enmin; Yin, Hongchao; Xiu, Zhilong
2016-09-01
Time-delay dynamical systems, which depend on both the current state of the system and the state at delayed times, have been an active area of research in many real-world applications. In this paper, we consider a nonlinear time-delay dynamical system of dha-regulonwith unknown time-delays in batch culture of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumonia. Some important properties and strong positive invariance are discussed. Because of the difficulty in accurately measuring the concentrations of intracellular substances and the absence of equilibrium points for the time-delay system, a quantitative biological robustness for the concentrations of intracellular substances is defined by penalizing a weighted sum of the expectation and variance of the relative deviation between system outputs before and after the time-delays are perturbed. Our goal is to determine optimal values of the time-delays. To this end, we formulate an optimization problem in which the time delays are decision variables and the cost function is to minimize the biological robustness. This optimization problem is subject to the time-delay system, parameter constraints, continuous state inequality constraints for ensuring that the concentrations of extracellular and intracellular substances lie within specified limits, a quality constraint to reflect operational requirements and a cost sensitivity constraint for ensuring that an acceptable level of the system performance is achieved. It is approximated as a sequence of nonlinear programming sub-problems through the application of constraint transcription and local smoothing approximation techniques. Due to the highly complex nature of this optimization problem, the computational cost is high. Thus, a parallel algorithm is proposed to solve these nonlinear programming sub-problems based on the filled function method. Finally, it is observed that the obtained optimal estimates for the time-delays are highly satisfactory
Directory of Open Access Journals (Sweden)
Akemi Gálvez
2013-01-01
Full Text Available Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor’s method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Andreani, Roberto; Friedlander, Ana; Mello, Margarida P.; Santos, Sandra A.
2005-06-01
In this work we show that the mixed nonlinear complementarity problem may be formulated as an equivalent nonlinear bound-constrained optimization problem that preserves the smoothness of the original data. One may thus take advantage of existing codes for bound-constrained optimization. This approach is implemented and tested by means of an extensive set of numerical experiments, showing promising results. The mixed nonlinear complementarity problems considered in the tests arise from the discretization of a motion planning problem concerning a set of rigid 3D bodies in contact in the presence of friction. We solve the complementarity problem associated with a single time frame, thus calculating the contact forces and accelerations of the bodies involved.
Feng, Jie; Ding, Ruiqiang; Li, Jianping; Liu, Deqiang
2016-09-01
The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors (BVs) are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector (NLLV) scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram-Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more components in analysis errors than the BVs. In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random perturbation (RP) technique, and the BV method, as well as its improved version—the ensemble transform Kalman filter (ETKF) method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
Institute of Scientific and Technical Information of China (English)
ZHANG Juliang; ZHANG Xiangsun
2001-01-01
In this paper, we use the smoothing penalty function proposed in [1] as the merit function of SQP method for nonlinear optimization with inequality constraints. The global convergence of the method is obtained.
Energy Technology Data Exchange (ETDEWEB)
Hillstrom, K. E.
1976-02-01
A simulation test technique was developed to evaluate and compare unconstrained nonlinear optimization computer algorithms. Descriptions of the test technique, test problems, computer algorithms tested, and test results are provided. (auth)
Directory of Open Access Journals (Sweden)
Asghar Vatani Oskouie
2016-12-01
Full Text Available In this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. To approach this aim the analytical formulas of secant stiffness matrix are presented. The models were validated and used to perform investigating different parameters affecting the shape optimization. Numerical examples utilized for this investigating sensitivity analysis with detailed discussions presented.
A Composite Algorithm for Mixed Integer Constrained Nonlinear Optimization.
1980-01-01
algorithm (FLEX) developed by Paviani and Himmelblau [53] is a direct search algorithm for constrained, nonlinear problems. It uses a variation on the...given in an appendix to Himmelblau [32]. Two changes were made to the program as listed in the rcference. Between card number 1340 and 1350 the...1972, pp. 293-308 (32] Himmelblau , D. M., Applied Nonlinear Programming, McGraw-Hill, 1972 (33] Himmelblau , D. M., "A Uniform Evaluation of Unconstrained
Directory of Open Access Journals (Sweden)
Hancao Li
2012-01-01
Full Text Available We develop optimal respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. Specifically, we use classical calculus of variations minimization techniques to derive an optimal airflow pattern for inspiratory and expiratory breathing cycles. The physiological interpretation of the optimality criteria used involves the minimization of work of breathing and lung volume acceleration for the inspiratory phase, and the minimization of the elastic potential energy and rapid airflow rate changes for the expiratory phase. Finally, we numerically integrate the resulting nonlinear two-point boundary value problems to determine the optimal airflow patterns over the inspiratory and expiratory breathing cycles.
Li, Hancao; Haddad, Wassim M
2012-01-01
We develop optimal respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. Specifically, we use classical calculus of variations minimization techniques to derive an optimal airflow pattern for inspiratory and expiratory breathing cycles. The physiological interpretation of the optimality criteria used involves the minimization of work of breathing and lung volume acceleration for the inspiratory phase, and the minimization of the elastic potential energy and rapid airflow rate changes for the expiratory phase. Finally, we numerically integrate the resulting nonlinear two-point boundary value problems to determine the optimal airflow patterns over the inspiratory and expiratory breathing cycles.
Distributed Optimization for a Class of Nonlinear Multiagent Systems With Disturbance Rejection.
Wang, Xinghu; Hong, Yiguang; Ji, Haibo
2016-07-01
The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.
Institute of Scientific and Technical Information of China (English)
朱卫平; 黄黔
2002-01-01
In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinearbehaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite elementare expanded by taking root-mean-square value of circumferential strains of the shells as aperturbation parameter. The load steps and the iteration times are not cs arbitrary andunpredictable as in usual nonlinear analysis. Instead, there are certain relations betweenthe load steps and the displacement increments, and no need of iteration for each loadstep. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander' s nonlinear geometric equations of moderate smallrotation are used, and the shell made of more than one material ply is also considered.
Institute of Scientific and Technical Information of China (English)
HSUChaohsing; CHENTsongyi; PanJengshyang
2005-01-01
In this paper, a phase-amplitude perturbation method of an adaptive array factor based on the genetic algorithm is proposed. The design for an optimal beam pattern of an adaptive antenna is able to not only suppress interference by placing nulls at the directions of the interfering sources but also provide a maximized main lobe in the direction of the desired signal, i.e., to maximizethe Signal interference ratio (SIR). In order to achieve this goal, a kind of new convergent skill called the two-way convergent method for genetic algorithms is proposed. The phase-amplitude perturbation method is applied to realize the optimal beam pattern of an adaptively linear array antenna. The Genetic algorithms are applied to find the optimal phase-amplitude weighting vector of adaptive array factor. An optimal beam pattern of linear array is derived by phase-amplitude perturbations using a genetic algorithm. Computer simulation result is given to demonstrate the effectiveness of the proposed method.
Gonçalves, P. B.; Silva, F. M. A.; Del Prado, Z. J. G. N.
2008-08-01
In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application, and models of reduced complexity are attractive in many cases where time-consuming numerical procedures are required. This paper discusses the derivation of discrete low-dimensional models for the nonlinear vibration analysis of thin cylindrical shells. In order to understand the peculiarities inherent to this class of structural problems, the nonlinear vibrations and dynamic stability of a circular cylindrical shell subjected to static and dynamic loads are analyzed. This choice is based on the fact that cylindrical shells exhibit a highly nonlinear behavior under both static and dynamic loads. Geometric nonlinearities due to finite-amplitude shell motions are considered by using Donnell's nonlinear shallow-shell theory. A perturbation procedure, validated in previous studies, is used to derive a general expression for the nonlinear vibration modes and the discretized equations of motion are obtained by the Galerkin method using modal expansions for the displacements that satisfy all the relevant boundary and symmetry conditions. Next, the model is analyzed via the Karhunen-Loève expansion to investigate the relative importance of each mode obtained by the perturbation solution on the nonlinear response and total energy of the system. The responses of several low-dimensional models are compared. It is shown that rather low-dimensional but properly selected models can describe with good accuracy the response of the shell up to very large vibration amplitudes.
Royston, T. J.; Singh, R.
1996-07-01
While significant non-linear behavior has been observed in many vibration mounting applications, most design studies are typically based on the concept of linear system theory in terms of force or motion transmissibility. In this paper, an improved analytical strategy is presented for the design optimization of complex, active of passive, non-linear mounting systems. This strategy is built upon the computational Galerkin method of weighted residuals, and incorporates order reduction and numerical continuation in an iterative optimization scheme. The overall dynamic characteristics of the mounting system are considered and vibratory power transmission is minimized via adjustment of mount parameters by using both passive and active means. The method is first applied through a computational example case to the optimization of basic passive and active, non-linear isolation configurations. It is found that either active control or intentionally introduced non-linearity can improve the mount's performance; but a combination of both produces the greatest benefit. Next, a novel experimental, active, non-linear isolation system is studied. The effect of non-linearity on vibratory power transmission and active control are assessed via experimental measurements and the enhanced Galerkin method. Results show how harmonic excitation can result in multiharmonic vibratory power transmission. The proposed optimization strategy offers designers some flexibility in utilizing both passive and active means in combination with linear and non-linear components for improved vibration mounts.
Robust Optimal Design of a Nonlinear Dynamic Vibration Absorber Combining Sensitivity Analysis
Directory of Open Access Journals (Sweden)
R.A. Borges
2010-01-01
Full Text Available Dynamic vibration absorbers are discrete devices developed in the beginning of the last century used to attenuate the vibrations of different engineering structures. They have been used in several engineering applications, such as ships, power lines, aeronautic structures, civil engineering constructions subjected to seismic induced excitations, compressor systems, etc. However, in the context of nonlinear dynamics, few works have been proposed regarding the robust optimal design of nonlinear dynamic vibration absorbers. In this paper, a robust optimization strategy combined with sensitivity analysis of systems incorporating nonlinear dynamic vibration absorbers is proposed. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to nonlinear systems. Due to the numerical procedure used to solve the nonlinear equations, the sensitivities addressed herein are computed from the first-order finite-difference approximations. With the aim of increasing the efficiency of the nonlinear dynamic absorber into a frequency band of interest, and to augment the robustness of the optimal design, a robust optimization strategy combined with the previous sensitivities is addressed. After presenting the underlying theoretical foundations, the proposed robust design methodology is performed for a two degree-of-freedom system incorporating a nonlinear dynamic vibration absorber. Based on the obtained results, the usefulness of the proposed methodology is highlighted.
Koyuncu, A.; Cigeroglu, E.; Özgüven, H. N.
2017-10-01
In this study, a new approach is proposed for identification of structural nonlinearities by employing cascaded optimization and neural networks. Linear finite element model of the system and frequency response functions measured at arbitrary locations of the system are used in this approach. Using the finite element model, a training data set is created, which appropriately spans the possible nonlinear configurations space of the system. A classification neural network trained on these data sets then localizes and determines the types of all nonlinearities associated with the nonlinear degrees of freedom in the system. A new training data set spanning the parametric space associated with the determined nonlinearities is created to facilitate parametric identification. Utilizing this data set, initially, a feed forward regression neural network is trained, which parametrically identifies the classified nonlinearities. Then, the results obtained are further improved by carrying out an optimization which uses network identified values as starting points. Unlike identification methods available in literature, the proposed approach does not require data collection from the degrees of freedoms where nonlinear elements are attached, and furthermore, it is sufficiently accurate even in the presence of measurement noise. The application of the proposed approach is demonstrated on an example system with nonlinear elements and on a real life experimental setup with a local nonlinearity.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.
Directory of Open Access Journals (Sweden)
Jun Shuai
2013-11-01
Full Text Available A new approach using optimization technique for constructing low-dimensional dynamical systems of nonlinear partial differential equations (PDEs is presented. After the spatial basis functions of the nonlinear PDEs are chosen, spatial basis functions expansions combined with weighted residual methods are used for time/space separation and truncation to obtain a high-dimensional dynamical system. Secondly, modes of lower-dimensional dynamical systems are obtained by linear combination from the modes of the high-dimensional dynamical systems (ordinary differential equations of nonlinear PDEs. An error function for matrix of the linear combination coefficients is derived, and a simple algorithm to determine the optimal combination matrix is also introduced. A numerical example shows that the optimal dynamical system can use much smaller number of modes to capture the dynamics of nonlinear partial differential equations.
Optimal Control Problems for Nonlinear Variational Evolution Inequalities
Directory of Open Access Journals (Sweden)
Eun-Young Ju
2013-01-01
Full Text Available We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.
Reliability optimization of friction-damped systems using nonlinear modes
Krack, Malte; Tatzko, Sebastian; Panning-von Scheidt, Lars; Wallaschek, Jörg
2014-06-01
A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is achieved subject to parameter uncertainties. The practicability of the approach regarding the extensive amount of required design evaluations is strictly related to the computational efficiency of the nonlinear dynamic analysis. Therefore, it is proposed to employ a recently developed parametric reduced order model (ROM) based on nonlinear modes of vibration, which can facilitate a decrease of the computational burden by several orders of magnitude.
A Novel Nonlinear Programming Model for Distribution Protection Optimization
Zambon, Eduardo; Bossois, Débora Z.; Garcia, Berilhes B.; Azeredo, Elias F.
2009-01-01
This paper presents a novel nonlinear binary programming model designed to improve the reliability indices of a distribution network. This model identifies the type and location of protection devices that should be installed in a distribution feeder and is a generalization of the classical optimizat
Institute of Scientific and Technical Information of China (English)
朱卫平; 黄黔
2002-01-01
The finite-element-displacement-perturbation method (FEDPM)for thegeometric nonlinear behaviors of shells of revolution subjected to pure bending moments orlateral forces in one of their meridional planes ( Ⅰ ) was employed to calculate the stressdistributions and the stiffness of the bellows. Firstly, by applying the first-orderperturbation solution ( the linear solution ) of the FEDPM to the bellows, the obtainedresults were compared with those of the general solution and the initial parameter integrationsolution proposed by the present authors earlier, as well as of the experiments and the FEAby others. It is shown that the FEDPM is with good precision and reliability, and as it waspointed out in ( Ⅰ ) the abrupt changes of the meridian curvature of bellows would not affectthe use of the usual straight element. Then the nonlinear behaviors of the bellows werediscussed. As expected, the nonlinear effects mainly come from the bellows ring plate, andthe wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishingof the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. Inaddition, when the pure bending moments act on the bellows, each convolution has thesame stress distributions calculated by the linear solution and other linear theories, but bythe present nonlinear solution they vary with respect to the convolutions of the bellows. Yetfor most bellows, the linear solutions are valid in practice.
Van Dijk, N.P.
2012-01-01
This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself.
Application of nonlinear optimization method to sensitivity analysis of numerical model
Institute of Scientific and Technical Information of China (English)
XU Hui; MU Mu; LUO Dehai
2004-01-01
A nonlinear optimization method is applied to sensitivity analysis of a numerical model. Theoretical analysis and numerical experiments indicate that this method can give not only a quantitative assessment whether the numerical model is able to simulate the observations or not, but also the initial field that yields the optimal simulation. In particular, when the simulation results are apparently satisfactory, and sometimes both model error and initial error are considerably large, the nonlinear optimization method, under some conditions, can identify the error that plays a dominant role.
Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity
Institute of Scientific and Technical Information of China (English)
Sen-Shan Pan; Xiao-Tong Fu; Wei-Guo Zhangx
2011-01-01
This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler's upper bound of algebraic degree. Also a class of 1-resilient functions on any number n ＞ 2 of variables with at least sub-optimal algebraic immunity is provided.
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
Wang, Qiang; Mu, M.; Dijkstra, H.A.
2012-01-01
A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors i
Directory of Open Access Journals (Sweden)
Yongquan Zhou
2013-01-01
Full Text Available In view of the traditional numerical method to solve the nonlinear equations exist is sensitive to initial value and the higher accuracy of defects. This paper presents an invasive weed optimization (IWO algorithm which has population diversity with the heuristic global search of differential evolution (DE algorithm. In the iterative process, the global exploration ability of invasive weed optimization algorithm provides effective search area for differential evolution; at the same time, the heuristic search ability of differential evolution algorithm provides a reliable guide for invasive weed optimization. Based on the test of several typical nonlinear equations and a circle packing problem, the results show that the differential evolution invasive weed optimization (DEIWO algorithm has a higher accuracy and speed of convergence, which is an efficient and feasible algorithm for solving nonlinear systems of equations.
Directory of Open Access Journals (Sweden)
Paras Bhatnagar
2012-10-01
Full Text Available Kaul and Kaur [7] obtained necessary optimality conditions for a non-linear programming problem by taking the objective and constraint functions to be semilocally convex and their right differentials at a point to be lower semi-continuous. Suneja and Gupta [12] established the necessary optimality conditions without assuming the semilocal convexity of the objective and constraint functions but their right differentials at the optimal point to be convex. Suneja and Gupta [13] established necessary optimality conditions for an efficient solution of a multiobjective non-linear programming problem by taking the right differentials of the objective functions and constraintfunctions at the efficient point to be convex. In this paper we obtain some results for a properly efficient solution of a multiobjective non-linear fractional programming problem involving semilocally convex and related functions by assuming generalized Slater type constraint qualification.
Tatsumi, Keiji
2017-06-01
Recently, the gradient method with perturbation (GP) was proposed for metaheuristic methods of solving continuous global optimization problems. Its updating system based on the steepest descent method is chaotic because of its perturbations along the standard basis vectors, which can strengthen the diversification of search. The sufficient condition for its chaoticity was theoretically shown, which implies that two kinds of influence degrees of the perturbations in the updating system should be greater than some constants. In this paper, we extend the updating system of the GP into a more general one for metaheuristic methods, which does not necessarily require the descent direction of the objective function, and which can have perturbations along appropriate orthogonal basis vectors for each problem. Furthermore, since the condition for the chaoticity shown in the previous work is too restricted for practical use, we theoretically show a weaker sufficient condition for the extended system, which is derived by varying the constant lower bounds for the two kinds of influence degrees.
Energy Technology Data Exchange (ETDEWEB)
Miles, A
2004-04-27
In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen-helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. In this dissertation, we present a computational study of unstable systems driven by high Mach number shock and blast waves. Using multi-physics radiation hydrodynamics codes and theoretical models, we consider the late nonlinear instability evolution of single mode, few mode, and multimode interfaces. We rely primarily on 2D calculations but present recent 3D results as well. For planar multimode systems, we show that compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (IC's) by allowing for memory of the initial conditions to be retained in the mix-width at all times. The loss of transverse spectral information is demonstrated, however, along with the existence of a quasi-self-similar regime over short time intervals. Aspects of the IC's are shown to have a strong effect on the time to transition to the quasi-self-similar regime. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. We point to recent stellar calculations that predict IC's we find incompatible with self-similarity, and
Energy Technology Data Exchange (ETDEWEB)
Miles, Aaron R. [Univ. of Maryland, College Park, MD (United States)
2004-01-01
In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen-helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. In this dissertation, we present a computational study of unstable systems driven by high Mach number shock and blast waves. Using multi-physics radiation hydrodynamics codes and theoretical models, we consider the late nonlinear instability evolution of single mode, few mode, and multimode interfaces. We rely primarily on 2D calculations but present recent 3D results as well. For planar multimode systems, we show that compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (IC's) by allowing for memory of the initial conditions to be retained in the mix-width at all times. The loss of transverse spectral information is demonstrated, however, along with the existence of a quasi-self-similar regime over short time intervals. Aspects of the IC's are shown to have a strong effect on the time to transition to the quasi-self-similar regime. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. We point to recent stellar calculations that predict IC's we find incompatible with self-similarity, and
Fault Diagnosis of Nonlinear Systems Based on Hybrid PSOSA Optimization Algorithm
Institute of Scientific and Technical Information of China (English)
Ling-Lai Li; Dong-Hua Zhou; Ling Wang
2007-01-01
Fault diagnosis of nonlinear systems is of great importance in theory and practice, and the parameter estimation method is an effective strategy. Based on the framework of moving horizon estimation, fault parameters are identified by a proposed intelligent optimization algorithm called PSOSA, which could avoid premature convergence of standard particle swarm optimization (PSO) by introducing the probabilistic jumping property of simulated annealing (SA). Simulations on a three-tank system show the effectiveness of this optimization based fault diagnosis strategy.
Nonlinear optimization of buoyancy-driven ventilation flow
Nabi, Saleh; Grover, Piyush; Caulfield, C. P.
2016-11-01
We consider the optimization of buoyancy-driven flows governed by Boussinesq equations using the Direct-Adjoint-Looping method. We use incompressible Reynolds-averaged Navier-Stokes (RANS) equations, derive the corresponding adjoint equations and solve the resulting sensitivity equations with respect to inlet conditions. For validation, we solve a series of inverse-design problems, for which we recover known globally optimal solutions. For a displacement ventilation scenario with a line source, the numerical results are compared with analytically obtained optimal inlet conditions available from classical plume theory. Our results show that depending on Archimedes number, defined as the ratio of the inlet Reynolds number to the Rayleigh number associated with the plume, qualitatively different optimal solutions are obtained. For steady and transient plumes, and subject to an enthalpy constraint on the incoming flow, we identify boundary conditions leading to 'optimal' temperature distributions in the occupied zone.
Trajectory optimization for vehicles using control vector parameterization and nonlinear programming
Energy Technology Data Exchange (ETDEWEB)
Spangelo, I.
1994-12-31
This thesis contains a study of optimal trajectories for vehicles. Highly constrained nonlinear optimal control problems have been solved numerically using control vector parameterization and nonlinear programming. Control vector parameterization with shooting has been described in detail to provide the reader with the theoretical background for the methods which have been implemented, and which are not available in standard text books. Theoretical contributions on accuracy analysis and gradient computations have also been presented. Optimal trajectories have been computed for underwater vehicles controlled in all six degrees of freedom by DC-motor driven thrusters. A class of nonlinear optimal control problems including energy-minimization, possibly combined with time minimization and obstacle avoidance, has been developed. A program system has been specially designed and written in the C language to solve this class of optimal control problems. Control vector parameterization with single shooting was used. This special implementation has made it possible to perform a detailed analysis, and to investigate numerical details of this class of optimization methods which would have been difficult using a general purpose CVP program system. The results show that this method for solving general optimal control problems is well suited for use in guidance and control of marine vehicles. Results from rocket trajectory optimization has been studied in this work to bring knowledge from this area into the new area of trajectory optimization of marine vehicles. 116 refs., 24 figs., 23 tabs.
An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems
Emran Tohidi; Atena Pasban; Kilicman, A.; S. Lotfi Noghabi
2013-01-01
This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover,...
Decentralized observers for optimal stabilization of large class of nonlinear interconnected systems
BEL HAJ FREJ, GHAZI; Thabet, Assem; Boutayeb, Mohamed; Aoun, Mohamed
2016-01-01
International audience; This paper focuses on the design of decentralized state observers based on optimal guaranteed cost control for a class of systems which are composed of linear subsystems coupled by non-linear time-varying interconnections. One of the main contributions lies in the use of the differential mean value theorem (DMVT) to simplify the design of estimation and control matrices gains. This has the advantage of introducing a general condition on the nonlinear time-varying inter...
Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems
Directory of Open Access Journals (Sweden)
Jianke Zhang
2013-01-01
Full Text Available The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper.
Heli Hu; Dan Zhao; Qingling Zhang
2013-01-01
The sliding mode control and optimization are investigated for a class of nonlinear neutral systems with the unmatched nonlinear term. In the framework of Lyapunov stability theory, the existence conditions for the designed sliding surface and the stability bound ${\\alpha }^{\\ast }$ are derived via twice transformations. The further results are to develop an efficient sliding mode control law with tuned parameters to attract the state trajectories onto the sliding surface in finit...
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Y. Orlov
2002-01-01
Full Text Available The paper is intended to be of tutorial value for Schwartz' distributions theory in nonlinear setting. Mathematical models are presented for nonlinear systems which admit both standard and impulsive inputs. These models are governed by differential equations in distributions whose meaning is generalized to involve nonlinear, non single-valued operating over distributions. The set of generalized solutions of these differential equations is defined via closure, in a certain topology, of the set of the conventional solutions corresponding to standard integrable inputs. The theory is exemplified by mechanical systems with impulsive phenomena, optimal impulsive feedback synthesis, sampled-data filtering of stochastic and deterministic dynamic systems.
Performance characteristics and optimal analysis of a nonlinear diode refrigerator
Institute of Scientific and Technical Information of China (English)
Wang Xiu-Mei; He Ji-Zhou; Liang Hong-Ni
2011-01-01
This paper establishes a model of a nonlinear diode refrigerator consisting of two diodes switched in the opposite directions and located in two heat reservoirs with different temperatures. Based on the theory of thermal fluctuations, the expressions of the heat flux absorbed from the heat reservoirs are derived. After the heat leak between the two reservoirs is considered, the cooling rate and the coefficient of performance are obtained analytically. The influence of the heat leak and the temperature ratio on the performance characteristics of the refrigerator is analysed in detail.
Optimal frequency conversion in the nonlinear stage of modulation instability
Bendahmane, A; Kudlinski, A; Szriftgiser, P; Conforti, M; Wabnitz, S; Trillo, S
2015-01-01
We investigate multi-wave mixing associated with the strongly pump depleted regime of induced modulation instability (MI) in optical fibers. For a complete transfer of pump power into the sideband modes, we theoretically and experimentally demonstrate that it is necessary to use a much lower seeding modulation frequency than the peak MI gain value. Our analysis shows that a record 95 % of the input pump power is frequency converted into the comb of sidebands, in good quantitative agreement with analytical predictions based on the simplest exact breather solution of the nonlinear Schr\\"odinger equation.
A General Nonlinear Optimization Algorithm for Lower Bound Limit Analysis
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...
Directory of Open Access Journals (Sweden)
Shaolong Chen
2016-01-01
Full Text Available Parameter estimation is an important problem in nonlinear system modeling and control. Through constructing an appropriate fitness function, parameter estimation of system could be converted to a multidimensional parameter optimization problem. As a novel swarm intelligence algorithm, chicken swarm optimization (CSO has attracted much attention owing to its good global convergence and robustness. In this paper, a method based on improved boundary chicken swarm optimization (IBCSO is proposed for parameter estimation of nonlinear systems, demonstrated and tested by Lorenz system and a coupling motor system. Furthermore, we have analyzed the influence of time series on the estimation accuracy. Computer simulation results show it is feasible and with desirable performance for parameter estimation of nonlinear systems.
On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
朱位秋; 应祖光
2004-01-01
A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed.The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
Institute of Scientific and Technical Information of China (English)
朱位秋; 应祖光
2004-01-01
A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
Heifetz, H Vitoshkin E; Harnik, N
2012-01-01
The three dimensional optimal energy growth mechanism, in plane parallel shear flows, is reexamined in terms of the role of vortex stretching and the interplay between the span-wise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille, and mixing layer shear profiles is robust and resembles localized plane-waves in regions where the background shear is large. The waves are tilted with the shear when the span-wise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification reflects on the optimal energy growth. This perspective provides an understanding of the three dimensional growth solely from the two dimensional dynamics on the shear plane.
Optimal control of nonlinear continuous-time systems in strict-feedback form.
Zargarzadeh, Hassan; Dierks, Travis; Jagannathan, Sarangapani
2015-10-01
This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.
A BPTT-like Min-Max Optimal Control Algorithm for Nonlinear Systems
Milić, Vladimir; Kasać, Josip; Majetić, Dubravko; Šitum, Željko
2010-09-01
This paper presents a conjugate gradient-based algorithm for feedback min-max optimal control of nonlinear systems. The algorithm has a backward-in-time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one-layer neural network. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient methods, Adams method for solving ODEs and automatic differentiation (AD), to provide an effective, novel algorithm for solving numerically optimally min-max control problems. The proposed algorithm is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem with control and state vector constraints.
Directory of Open Access Journals (Sweden)
Mahdi Sohrabi-Haghighat
2014-06-01
Full Text Available In this paper, a new algorithm based on SQP method is presented to solve the nonlinear inequality constrained optimization problem. As compared with the other existing SQP methods, per single iteration, the basic feasible descent direction is computed by solving at most two equality constrained quadratic programming. Furthermore, there is no need for any auxiliary problem to obtain the coefficients and update the parameters. Under some suitable conditions, the global and superlinear convergence are shown. Keywords: Global convergence, Inequality constrained optimization, Nonlinear programming problem, SQP method, Superlinear convergence rate.
Institute of Scientific and Technical Information of China (English)
Ronghua Huan; Lincong Chen; Weiliang Jin; Weiqiu Zhu
2009-01-01
An optimal vibration control strategy for partially observable nonlinear quasi Hamil-tonian systems with actuator saturation is proposed. First, a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged Ito stochas-tic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle, respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control efficiency.
Optimization of Nonlinear Transport-Production Task of Medical Waste
Michlowicz, Edward
2012-09-01
The paper reflects on optimization of transportation - production tasks for the processing of medical waste. For the existing network of collection points and processing plants, according to its algorithm, the optimal allocation of tasks to the cost of transport to the respective plants has to be determined. It was assumed that the functions determining the processing costs are polynomials of the second degree. To solve the problem, a program written in MatLab environment equalization algorithm based on a marginal cost JCC was used.
Directory of Open Access Journals (Sweden)
Sirada Pinjai
2013-01-01
Full Text Available This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.
Liu, Pin-Lin
2015-07-01
This paper studies the problem of the stability analysis of interval time-varying delay systems with nonlinear perturbations. Based on the Lyapunov-Krasovskii functional (LKF), a sufficient delay-range-dependent criterion for asymptotic stability is derived in terms of linear matrix inequality (LMI) and integral inequality approach (IIA) and delayed decomposition approach (DDA). Further, the delay range is divided into two equal segments for stability analysis. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Two well-known examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.
A monotonic method for solving nonlinear optimal control problems
Salomon, Julien
2009-01-01
Initially introduced in the framework of quantum control, the so-called monotonic algorithms have shown excellent numerical results when dealing with various bilinear optimal control problems. This paper aims at presenting a unified formulation of such procedures and the intrinsic assumptions they require. In this framework, we prove the feasibility of the general algorithm. Finally, we explain how these assumptions can be relaxed.
Directory of Open Access Journals (Sweden)
Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
Modeling and Optimization of Vehicle Suspension Employing a Nonlinear Fluid Inerter
Directory of Open Access Journals (Sweden)
Yujie Shen
2016-01-01
Full Text Available An ideal inerter has been applied to various vibration engineering fields because of its superior vibration isolation performance. This paper proposes a new type of fluid inerter and analyzes the nonlinearities including friction and nonlinear damping force caused by the viscosity of fluid. The nonlinear model of fluid inerter is demonstrated by the experiments analysis. Furthermore, the full-car dynamic model involving the nonlinear fluid inerter is established. It has been detected that the performance of the vehicle suspension may be influenced by the nonlinearities of inerter. So, parameters of the suspension system including the spring stiffness and the damping coefficient are optimized by means of QGA (quantum genetic algorithm, which combines the genetic algorithm and quantum computing. Results indicate that, compared with the original nonlinear suspension system, the RMS (root-mean-square of vertical body acceleration of optimized suspension has decreased by 9.0%, the RMS of pitch angular acceleration has decreased by 19.9%, and the RMS of roll angular acceleration has decreased by 9.6%.
Nonlinear stochastic optimal bounded control of hysteretic systems with actuator saturation
Institute of Scientific and Technical Information of China (English)
Rong-hua HUAN; Wei-qiu ZHU; Yong-jun WU
2008-01-01
A modified nonlinear stochastic optimal bounded control strategy for random excited hysteretic systems with actuator saturation is proposed. First, a controlled hysteretic system is converted into an equivalent nonlinear nonhysteretic stochastic system. Then, the partially averaged It6 stochastic differential equation and dynamical programming equation are established, respectively, by using the stochastic averaging method for quasi non-integrable Hamiltonian systems and stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged It6 equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.
Directory of Open Access Journals (Sweden)
Gao Dexin
2012-10-01
Full Text Available This paper concentrates on the solution of state feedback exact linearization zero steady-state error optimal control problem for nonlinear systems affected by external disturbances. Firstly, the nonlinear system model with external disturbances is converted to quasi-linear system model by differential homeomorphism. Using Internal Model Optional Control (IMOC, the disturbances compensator is designed, which exactly offset the impact of external disturbances on the system. Taking the system and the disturbances compensator in series, a new augmented system is obtained. Then the zero steady-state error optimal control problem is transformed into the optimal regulator design problem of an augmented system, and the optimal static error feedback control law is designed according to the different quadratic performance index. At last, the simulation results show the effectiveness of the method.
Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.
Institute of Scientific and Technical Information of China (English)
Changshui Feng; Weiqiu Zhu
2008-01-01
A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Ito equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov (FPK) equation associated with the completed averaged Ito equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.
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Mohd Ariffanan Mohd Basri
2015-09-01
Full Text Available Quadrotor unmanned aerial vehicle (UAV is an unstable nonlinear control system. Therefore, the development of a high performance controller for such a multi-input and multi-output (MIMO system is important. The backstepping controller (BC has been successfully applied to control a variety of nonlinear systems. Conventionally, control parameters of a BC are usually chosen arbitrarily. The problems in this method are the adjustment is time demanding and a designer can never tell exactly what are the optimal control parameters should be selected. In this paper, the contribution is focused on an optimal control design for stabilization and trajectory tracking of a quadrotor UAV. Firstly, a dynamic model of the aerial vehicle is mathematically formulated. Then, an optimal backstepping controller (OBC is proposed. The particle swarm optimization (PSO algorithm is used to compute control parameters of the OBC. Finally, simulation results of a highly nonlinear quadrotor system are presented to demonstrate the effectiveness of the proposed control method. From the simulation results it is observed that the OBC tuned by PSO provides a high control performance of an autonomous quadrotor UAV.
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Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
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B. Shank
2014-11-01
Full Text Available We present a detailed thermal and electrical model of superconducting transition edge sensors (TESs connected to quasiparticle (qp traps, such as the W TESs connected to Al qp traps used for CDMS (Cryogenic Dark Matter Search Ge and Si detectors. We show that this improved model, together with a straightforward time-domain optimal filter, can be used to analyze pulses well into the nonlinear saturation region and reconstruct absorbed energies with optimal energy resolution.
Nonlinear program based optimization of boost and buck-boost converter designs
Rahman, S.; Lee, F. C.
1981-01-01
The facility of an Augmented Lagrangian (ALAG) multiplier based nonlinear programming technique is demonstrated for minimum-weight design optimizations of boost and buck-boost power converters. Certain important features of ALAG are presented in the framework of a comprehensive design example for buck-boost power converter design optimization. The study provides refreshing design insight of power converters and presents such information as weight and loss profiles of various semiconductor components and magnetics as a function of the switching frequency.
Shank, B; Cabrera, B; Kreikebaum, J M; Moffatt, R; Redl, P; Young, B A; Brink, P L; Cherry, M; Tomada, A
2014-01-01
We present a detailed thermal and electrical model of superconducting transition edge sensors (TESs) connected to quasiparticle (qp) traps, such as the W TESs connected to Al qp traps used for CDMS (Cryogenic Dark Matter Search) Ge and Si detectors. We show that this improved model, together with a straightforward time-domain optimal filter, can be used to analyze pulses well into the nonlinear saturation region and reconstruct absorbed energies with optimal energy resolution.
RCLED Optimization and Nonlinearity Compensation in a Polymer Optical Fiber DMT System
Directory of Open Access Journals (Sweden)
Pu Miao
2016-09-01
Full Text Available In polymer optical fiber (POF systems, the nonlinear transfer function of the resonant cavity light emitting diode (RCLED drastically degrades the communication performance. After investigating the characteristics of the RCLED nonlinear behavior, an improved digital look-up-table (LUT pre-distorter, based on an adaptive iterative algorithm, is proposed. Additionally, the system parameters, including the bias current, the average electrical power, the LUT size and the step factor are also jointly optimized to achieve a trade-off between the system linearity, reliability and the computational complexity. With the proposed methodology, both the operating point and efficiency of RCLED are enhanced. Moreover, in the practical 50 m POF communication system with the discrete multi-tone (DMT modulation, the bit error rate performance is improved by over 12 dB when RCLED is operating in the nonlinear region. Therefore, the proposed pre-distorter can both resist the nonlinearity and improve the operating point of RCLED.
Directory of Open Access Journals (Sweden)
Aijia Ouyang
2015-01-01
Full Text Available Nonlinear Muskingum models are important tools in hydrological forecasting. In this paper, we have come up with a class of new discretization schemes including a parameter θ to approximate the nonlinear Muskingum model based on general trapezoid formulas. The accuracy of these schemes is second order, if θ≠1/3, but interestingly when θ=1/3, the accuracy of the presented scheme gets improved to third order. Then, the present schemes are transformed into an unconstrained optimization problem which can be solved by a hybrid invasive weed optimization (HIWO algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the present methods. The numerical results substantiate the fact that the presented methods have better precision in estimating the parameters of nonlinear Muskingum models.
Simple procedures for imposing constraints for nonlinear least squares optimization
Energy Technology Data Exchange (ETDEWEB)
Carvalho, R. [Petrobras, Rio de Janeiro (Brazil); Thompson, L.G.; Redner, R.; Reynolds, A.C. [Univ. of Tulsa, OK (United States)
1995-12-31
Nonlinear regression method (least squares, least absolute value, etc.) have gained acceptance as practical technology for analyzing well-test pressure data. Even for relatively simple problems, however, commonly used algorithms sometimes converge to nonfeasible parameter estimates (e.g., negative permeabilities) resulting in a failure of the method. The primary objective of this work is to present a new method for imaging the objective function across all boundaries imposed to satisfy physical constraints on the parameters. The algorithm is extremely simple and reliable. The method uses an equivalent unconstrained objective function to impose the physical constraints required in the original problem. Thus, it can be used with standard unconstrained least squares software without reprogramming and provides a viable alternative to penalty functions for imposing constraints when estimating well and reservoir parameters from pressure transient data. In this work, the authors also present two methods of implementing the penalty function approach for imposing parameter constraints in a general unconstrained least squares algorithm. Based on their experience, the new imaging method always converges to a feasible solution in less time than the penalty function methods.
Yagi, Kiyoshi; Otaki, Hiroki
2014-02-28
A perturbative extension to optimized coordinate vibrational self-consistent field (oc-VSCF) is proposed based on the quasi-degenerate perturbation theory (QDPT). A scheme to construct the degenerate space (P space) is developed, which incorporates degenerate configurations and alleviates the divergence of perturbative expansion due to localized coordinates in oc-VSCF (e.g., local O-H stretching modes of water). An efficient configuration selection scheme is also implemented, which screens out the Hamiltonian matrix element between the P space configuration (p) and the complementary Q space configuration (q) based on a difference in their quantum numbers (λpq = ∑s|ps - qs|). It is demonstrated that the second-order vibrational QDPT based on optimized coordinates (oc-VQDPT2) smoothly converges with respect to the order of the mode coupling, and outperforms the conventional one based on normal coordinates. Furthermore, an improved, fast algorithm is developed for optimizing the coordinates. First, the minimization of the VSCF energy is conducted in a restricted parameter space, in which only a portion of pairs of coordinates is selectively transformed. A rational index is devised for this purpose, which identifies the important coordinate pairs to mix from others that may remain unchanged based on the magnitude of harmonic coupling induced by the transformation. Second, a cubic force field (CFF) is employed in place of a quartic force field, which bypasses intensive procedures that arise due to the presence of the fourth-order force constants. It is found that oc-VSCF based on CFF together with the pair selection scheme yields the coordinates similar in character to the conventional ones such that the final vibrational energy is affected very little while gaining an order of magnitude acceleration. The proposed method is applied to ethylene and trans-1,3-butadiene. An accurate, multi-resolution potential, which combines the MP2 and coupled-cluster with singles
Optimal experimental design for non-linear models theory and applications
Kitsos, Christos P
2013-01-01
This book tackles the Optimal Non-Linear Experimental Design problem from an applications perspective. At the same time it offers extensive mathematical background material that avoids technicalities, making it accessible to non-mathematicians: Biologists, Medical Statisticians, Sociologists, Engineers, Chemists and Physicists will find new approaches to conducting their experiments. The book is recommended for Graduate Students and Researchers.
Lacivita, Valentina; Rérat, Michel; Kirtman, Bernard; Ferrero, Mauro; Orlando, Roberto; Dovesi, Roberto
2009-11-01
The high-frequency dielectric ɛ and the first nonlinear electric susceptibility χ(2) tensors of crystalline potassium dihydrogen phosphate (KH2PO4) are calculated by using the coupled perturbed Hartree-Fock and Kohn-Sham methods as implemented in the CRYSTAL code. The effect of basis sets of increasing size on ɛ and χ(2) is explored. Five different levels of theory, namely, local-density approximation, generalized gradient approximation (PBE), hybrids (B3LYP and PBE0), and HF are compared using the experimental and theoretical structures corresponding not only to the tetragonal geometry I4d2 at room temperature but also to the orthorhombic phase Fdd2 at low temperature. Comparison between the two phases and their optical behavior is made. The calculated results for the tetragonal phase are in good agreement with the experimental data.
Directory of Open Access Journals (Sweden)
Li Wang
2017-02-01
Full Text Available The ability to obtain appropriate parameters for an advanced pressurized water reactor (PWR unit model is of great significance for power system analysis. The attributes of that ability include the following: nonlinear relationships, long transition time, intercoupled parameters and difficult obtainment from practical test, posed complexity and difficult parameter identification. In this paper, a model and a parameter identification method for the PWR primary loop system were investigated. A parameter identification process was proposed, using a particle swarm optimization (PSO algorithm that is based on random perturbation (RP-PSO. The identification process included model variable initialization based on the differential equations of each sub-module and program setting method, parameter obtainment through sub-module identification in the Matlab/Simulink Software (Math Works Inc., Natick, MA, USA as well as adaptation analysis for an integrated model. A lot of parameter identification work was carried out, the results of which verified the effectiveness of the method. It was found that the change of some parameters, like the fuel temperature and coolant temperature feedback coefficients, changed the model gain, of which the trajectory sensitivities were not zero. Thus, obtaining their appropriate values had significant effects on the simulation results. The trajectory sensitivities of some parameters in the core neutron dynamic module were interrelated, causing the parameters to be difficult to identify. The model parameter sensitivity could be different, which would be influenced by the model input conditions, reflecting the parameter identifiability difficulty degree for various input conditions.
Siade, A. J.; Prommer, H.; Welter, D.
2014-12-01
Groundwater management and remediation requires the implementation of numerical models in order to evaluate the potential anthropogenic impacts on aquifer systems. In many situations, the numerical model must, not only be able to simulate groundwater flow and transport, but also geochemical and biological processes. Each process being simulated carries with it a set of parameters that must be identified, along with differing potential sources of model-structure error. Various data types are often collected in the field and then used to calibrate the numerical model; however, these data types can represent very different processes and can subsequently be sensitive to the model parameters in extremely complex ways. Therefore, developing an appropriate weighting strategy to address the contributions of each data type to the overall least-squares objective function is not straightforward. This is further compounded by the presence of potential sources of model-structure errors that manifest themselves differently for each observation data type. Finally, reactive transport models are highly nonlinear, which can lead to convergence failure for algorithms operating on the assumption of local linearity. In this study, we propose a variation of the popular, particle swarm optimization algorithm to address trade-offs associated with the calibration of one data type over another. This method removes the need to specify weights between observation groups and instead, produces a multi-dimensional Pareto front that illustrates the trade-offs between data types. We use the PEST++ run manager, along with the standard PEST input/output structure, to implement parallel programming across multiple desktop computers using TCP/IP communications. This allows for very large swarms of particles without the need of a supercomputing facility. The method was applied to a case study in which modeling was used to gain insight into the mobilization of arsenic at a deepwell injection site
Zhang, Chao; Ren, Pinyi; Peng, Jingbo; Wei, Guo; Du, Qinghe; Wang, Yichen
2011-01-01
In this paper, we propose an optimal relay power allocation of an Amplify-and-Forward relay networks with non-linear power amplifiers. Based on Bussgang Linearization Theory, we depict the non-linear amplifying process into a linear system, which lets analyzing system performance easier. To obtain spatial diversity, we design a complete practical framework of a non-linear distortion aware receiver. Consider a total relay power constraint, we propose an optimal power allocation scheme to maxim...
Nonlinear Thermodynamic Analysis and Optimization of a Carnot Engine Cycle
Directory of Open Access Journals (Sweden)
Michel Feidt
2016-06-01
Full Text Available As part of the efforts to unify the various branches of Irreversible Thermodynamics, the proposed work reconsiders the approach of the Carnot engine taking into account the finite physical dimensions (heat transfer conductances and the finite speed of the piston. The models introduce the irreversibility of the engine by two methods involving different constraints. The first method introduces the irreversibility by a so-called irreversibility ratio in the entropy balance applied to the cycle, while in the second method it is emphasized by the entropy generation rate. Various forms of heat transfer laws are analyzed, but most of the results are given for the case of the linear law. Also, individual cases are studied and reported in order to provide a simple analytical form of the results. The engine model developed allowed a formal optimization using the calculus of variations.
Robust C subroutines for non-linear optimization
DEFF Research Database (Denmark)
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
to worry about special parameters controlling the iterations. For convenience we include an option for numerical checking of the user s implementation of the gradient. Note that another report [3] presents a collection of robust subroutines for both unconstrained and constrained optimization...... by changing 1 to 0. The present report is a new and updated version of a previous report NI-91-03 with the same title, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated from Fortran to C. The reason for writing the present report is that some...... of the C subroutines have been replaced by more effective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modi ed to some extent. For a description of the original Fortran subroutines see the report [17]. The software...
Energy Technology Data Exchange (ETDEWEB)
Huang, Xiaobiao; Safranek, James
2014-09-01
Nonlinear dynamics optimization is carried out for a low emittance upgrade lattice of SPEAR3 in order to improve its dynamic aperture and Touschek lifetime. Two multi-objective optimization algorithms, a genetic algorithm and a particle swarm algorithm, are used for this study. The performance of the two algorithms are compared. The result shows that the particle swarm algorithm converges significantly faster to similar or better solutions than the genetic algorithm and it does not require seeding of good solutions in the initial population. These advantages of the particle swarm algorithm may make it more suitable for many accelerator optimization applications.
A nonlinear optimization approach for UPFC power flow control and voltage security
Kalyani, Radha Padma
This dissertation provides a nonlinear optimization algorithm for the long term control of Unified Power Flow Controller (UPFC) to remove overloads and voltage violations by optimized control of power flows and voltages in the power network. It provides a control strategy for finding the long term control settings of one or more UPFCs by considering all the possible settings and all the (N-1) topologies of a power network. Also, a simple evolutionary algorithm (EA) has been proposed for the placement of more than one UPFC in large power systems. In this publication dissertation, Paper 1 proposes the algorithm and provides the mathematical and empirical evidence. Paper 2 focuses on comparing the proposed algorithm with Linear Programming (LP) based corrective method proposed in literature recently and mitigating cascading failures in larger power systems. EA for placement along with preliminary results of the nonlinear optimization is given in Paper 3.
Optimal Parameter Tuning in a Predictive Nonlinear Control Method for a Mobile Robot
Directory of Open Access Journals (Sweden)
D. Hazry
2006-01-01
Full Text Available This study contributes to a new optimal parameter tuning in a predictive nonlinear control method for stable trajectory straight line tracking with a non-holonomic mobile robot. In this method, the focus lies in finding the optimal parameter estimation and to predict the path that the mobile robot will follow for stable trajectory straight line tracking system. The stability control contains three parameters: 1 deflection parameter for the traveling direction of the mobile robot 2 deflection parameter for the distance across traveling direction of the mobile robot and 3 deflection parameter for the steering angle of the mobile robot . Two hundred and seventy three experimental were performed and the results have been analyzed and described herewith. It is found that by using a new optimal parameter tuning in a predictive nonlinear control method derived from the extension of kinematics model, the movement of the mobile robot is stabilized and adhered to the reference posture
Yang, Xiong; Liu, Derong; Wang, Ding
2014-03-01
In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton-Jacobi-Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov's direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated.
Jacobi, Martin Nilsson; Jonsson, Per R
2011-07-01
Conservation and management of natural resources and biodiversity need improved criteria to select functional networks of protected areas. The connectivity within networks due to dispersal is rarely considered, partly because it is unclear how connectivity information can be included in the selection of protected areas. We present a novel and general method that applies eigenvalue perturbation theory (EPT) to select optimum networks of protected areas based on connectivity. At low population densities, characteristic of threatened populations, this procedure selects networks that maximize the growth rate of the overall network. This method offers an improved link between connectivity and metapopulation dynamics. Our framework is applied to connectivities estimated for marine larvae and demonstrates that, for open populations, the best strategy is to protect areas acting as both strong donors and recipients of recruits. It should be possible to implement an EPT framework for connectivity analysis into existing holistic tools for design of protected areas.
Guevara, V R
2004-02-01
A nonlinear programming optimization model was developed to maximize margin over feed cost in broiler feed formulation and is described in this paper. The model identifies the optimal feed mix that maximizes profit margin. Optimum metabolizable energy level and performance were found by using Excel Solver nonlinear programming. Data from an energy density study with broilers were fitted to quadratic equations to express weight gain, feed consumption, and the objective function income over feed cost in terms of energy density. Nutrient:energy ratio constraints were transformed into equivalent linear constraints. National Research Council nutrient requirements and feeding program were used for examining changes in variables. The nonlinear programming feed formulation method was used to illustrate the effects of changes in different variables on the optimum energy density, performance, and profitability and was compared with conventional linear programming. To demonstrate the capabilities of the model, I determined the impact of variation in prices. Prices for broiler, corn, fish meal, and soybean meal were increased and decreased by 25%. Formulations were identical in all other respects. Energy density, margin, and diet cost changed compared with conventional linear programming formulation. This study suggests that nonlinear programming can be more useful than conventional linear programming to optimize performance response to energy density in broiler feed formulation because an energy level does not need to be set.
Evolution of optimal Hill coefficients in nonlinear public goods games.
Archetti, Marco; Scheuring, István
2016-10-07
In evolutionary game theory, the effect of public goods like diffusible molecules has been modelled using linear, concave, sigmoid and step functions. The observation that biological systems are often sigmoid input-output functions, as described by the Hill equation, suggests that a sigmoid function is more realistic. The Michaelis-Menten model of enzyme kinetics, however, predicts a concave function, and while mechanistic explanations of sigmoid kinetics exist, we lack an adaptive explanation: what is the evolutionary advantage of a sigmoid benefit function? We analyse public goods games in which the shape of the benefit function can evolve, in order to determine the optimal and evolutionarily stable Hill coefficients. We find that, while the dynamics depends on whether output is controlled at the level of the individual or the population, intermediate or high Hill coefficients often evolve, leading to sigmoid input-output functions that for some parameters are so steep to resemble a step function (an on-off switch). Our results suggest that, even when the shape of the benefit function is unknown, biological public goods should be modelled using a sigmoid or step function rather than a linear or concave function.
Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture
Directory of Open Access Journals (Sweden)
Lei Wang
2011-01-01
Full Text Available In batch culture of glycerol biodissimilation to 1,3-propanediol (1,3-PD, the aim of adding glycerol is to obtain as much 1,3-PD as possible. Taking the yield intensity of 1,3-PD as the performance index and the initial concentration of biomass, glycerol, and terminal time as the control vector, we propose an optimal control model subject to a multistage nonlinear dynamical system and constraints of continuous state. A computational approach is constructed to seek the solution of the above model. Firstly, we transform the optimal control problem into the one with fixed terminal time. Secondly, we transcribe the optimal control model into an unconstrained one based on the penalty functions and an extension of the state space. Finally, by approximating the control function with simple functions, we transform the unconstrained optimal control problem into a sequence of nonlinear programming problems, which can be solved using gradient-based optimization techniques. The convergence analysis and optimality function of the algorithm are also investigated. Numerical results show that, by employing the optimal control, the concentration of 1,3-PD at the terminal time can be increased, compared with the previous results.
Constrained Optimal Stochastic Control of Non-Linear Wave Energy Point Absorbers
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Chen, Jian-Bing; Kramer, Morten
2014-01-01
The paper deals with the stochastic optimal control of a wave energy point absorber with strong nonlinear buoyancy forces using the reactive force from the electric generator on the absorber as control force. The considered point absorber has only one degree of freedom, heave motion, which is used...... presented in the paper. The effect of nonlinear buoyancy force – in comparison to linear buoyancy force – and constraints of the controller on the power outtake of the device have been studied in details and supported by numerical simulations....
On the algebraic representation of certain optimal non-linear binary codes
Greferath, Marcus
2011-01-01
This paper investigates some optimal non-linear codes, in particular cyclic codes, by considering them as (non-linear) codes over Z_4. We use the Fourier transform as well as subgroups of the unit group of a group ring to analyse these codes. In particular we find a presentation of Best's (10, 40, 4) code as a coset of a subgroup in the unit group of a ring, and derive a simple decoding algorithm from this presentation. We also apply this technique to analyse Julin's (12, 144, 4) code and the (12, 24, 12) Hadamard code, as well as to construct a (14, 56, 6) binary code.
Directory of Open Access Journals (Sweden)
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
Shoemaker, Christine; Wan, Ying
2016-04-01
Optimization of nonlinear water resources management issues which have a mixture of fixed (e.g. construction cost for a well) and variable (e.g. cost per gallon of water pumped) costs has been not well addressed because prior algorithms for the resulting nonlinear mixed integer problems have required many groundwater simulations (with different configurations of decision variable), especially when the solution space is multimodal. In particular heuristic methods like genetic algorithms have often been used in the water resources area, but they require so many groundwater simulations that only small systems have been solved. Hence there is a need to have a method that reduces the number of expensive groundwater simulations. A recently published algorithm for nonlinear mixed integer programming using surrogates was shown in this study to greatly reduce the computational effort for obtaining accurate answers to problems involving fixed costs for well construction as well as variable costs for pumping because of a substantial reduction in the number of groundwater simulations required to obtain an accurate answer. Results are presented for a US EPA hazardous waste site. The nonlinear mixed integer surrogate algorithm is general and can be used on other problems arising in hydrology with open source codes in Matlab and python ("pySOT" in Bitbucket).
Inversion of dispersion coefficient in water quality model using optimal perturbation algorithm
Institute of Scientific and Technical Information of China (English)
Hong-tao NIE; Jian-hua TAO
2009-01-01
As a primary parameter in the water quality model for shallow bays,the dispersion coefficient is traditionally determined with a trial-and-error method,which is time-consuming and requires much experience.In this paper,based on the measured data of chemical oxygen demand(COD),the dispersion coefficient is calculated using an inversion method.In the process,the regularization method is applied to treat the ill-posedness.and an operator identity perturbation method is used to obtain the solution.Using the model with an inverted dispersion coefficient,the distributions of COD,inorganic nitrogen(IN),and inorganic phosphorus(IP)in Bohai Bay are predicted and compared with the measured data.The results indicate that the method is feasible and the inverted dispersion coefficient can be used to predict other pollutant distribution.This method may also be further extended to the inversion of other parameters in the water quality model.
Simplex sliding mode control for nonlinear uncertain systems via chaos optimization
Energy Technology Data Exchange (ETDEWEB)
Lu, Zhao; Shieh, Leang-San; Chen, Guanrong; Coleman, Norman P
2005-02-01
As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method.
Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.
Duarte, Belmiro P M; Wong, Weng Kee; Oliveira, Nuno M C
2016-02-15
We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D-, A- and E-optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D-optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.
Lu, Can-can; Bai, Long
2017-06-01
The nonlinear dissipation heat devices are proposed by means of generalizing the low-dissipation heat devices to the quadratic order case. The dimensionless formulas of the output (input) power and the efficiency (coefficient of performance) for the nonlinear dissipation heat engines (refrigerators) are derived in terms of characteristic parameters for heat devices and the dimensional analysis. Based on the trade-off criterion, the optimal performance of the nonlinear dissipation heat devices is discussed in depth, and some system-specific properties for the nonlinear dissipation heat devices under the trade-off optimization are also uncovered. Our results may provide practical insight for designing actual heat engines and refrigerators.
Saviz, M. R.
2015-11-01
In this paper a nonlinear approach to studying the vibration characteristic of laminated composite plate with surface-bonded piezoelectric layer/patch is formulated, based on the Green Lagrange type of strain-displacements relations, by incorporating higher-order terms arising from nonlinear relations of kinematics into mathematical formulations. The equations of motion are obtained through the energy method, based on Lagrange equations and by using higher-order shear deformation theories with von Karman-type nonlinearities, so that transverse shear strains vanish at the top and bottom surfaces of the plate. An isoparametric finite element model is provided to model the nonlinear dynamics of the smart plate with piezoelectric layer/ patch. Different boundary conditions are investigated. Optimal locations of piezoelectric patches are found using a genetic algorithm to maximize spatial controllability/observability and considering the effect of residual modes to reduce spillover effect. Active attenuation of vibration of laminated composite plate is achieved through an optimal control law with inequality constraint, which is related to the maximum and minimum values of allowable voltage in the piezoelectric elements. To keep the voltages of actuator pairs in an allowable limit, the Pontryagin’s minimum principle is implemented in a system with multi-inequality constraint of control inputs. The results are compared with similar ones, proving the accuracy of the model especially for the structures undergoing large deformations. The convergence is studied and nonlinear frequencies are obtained for different thickness ratios. The structural coupling between plate and piezoelectric actuators is analyzed. Some examples with new features are presented, indicating that the piezo-patches significantly improve the damping characteristics of the plate for suppressing the geometrically nonlinear transient vibrations.
Metzler, Holger; Müller, Markus; Sierra, Carlos A.
2017-04-01
Carbon fluxes in the ocean-atmosphere-biosphere system are governed by nonlinear processes, which are usually modeled by a system of ordinary differential equations. It is very difficult to analyze such nonlinear models and to predict their future behavior, particularly their internal age structure: How old is the carbon in different pools (ages) and how old is the carbon that leaves the system (transit times)? How is this age structure modified by the addition of fossil fuel emissions? To answer these questions, we developed a new mathematical approach that allows us to compute and visualize the age structure of models of well mixed pools even if they are nonlinear and nonautonomous. We do not only consider mean ages and mean transit times, but entire distributions. Consequently, we can consider important statistics such as the median, quantiles, or the variance. We applied this mathematical approach to a nonlinear global carbon model consisting of three pools (atmosphere, surface ocean, and terrestrial biosphere) and driven by four emission scenarios (RCP3-PD, RCP4.5, RCP6, RCP8.5). Results showed that the addition of fossil fuels modifies the age structure of C in the atmosphere by drastically increasing its proportion of young carbon. We found little differences among predicted mean ages for the four emission scenarios, but changes in the overall distributions were large with effects on median, quantiles and variance. In the short-term, fossil-fuel emissions have an important effect on the amount of carbon that is exchanged among Earth's main C reservoirs. In the long-term, most added C will eventually end up in the deep ocean, but the time required to return to pre-industrial C age distributions is largely dependent on emission scenarios.
Bond, Alan M; Duffy, Noel W; Elton, Darrell M; Fleming, Barry D
2009-11-01
Under most experimental conditions, a distinctly nonlinear background current is encountered in all forms of voltammetry which arises from the potential dependence of the capacitance. The nonlinear background current has been successfully modeled under large amplitude sinusoidal ac voltammetric conditions with a fourth order polynomial. The model was applied to a dummy cell containing a nonideal ceramic capacitor and commonly used electrodes. The nonlinearity in behavior of the background capacitance is particularly significant when considering the discrimination between the Faradaic and background contributions in the higher order harmonics resolved in ac voltammetry by Fourier transform-inverse Fourier transform approaches and in the simulation of the background current and hence double-layer capacitance as a function of potential. Typically, measurable background current under large amplitude conditions is detectable in the dc and fundamental to fourth harmonic components in large amplitude ac voltammetry. For analytical purposes, this background current can be corrected on a per harmonic basis without the need for any model. Background correction has been successfully applied to the first four harmonics for the oxidation of ferrocenemonocarboxylic acid over the concentration range of 5-500 microM in aqueous 0.5 M NaCl solution.
Fully Nonlinear Boussinesq-Type Equations with Optimized Parameters for Water Wave Propagation
Institute of Scientific and Technical Information of China (English)
荆海晓; 刘长根; 龙文; 陶建华
2015-01-01
For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with padé approximation.
Fully nonlinear Boussinesq-type equations with optimized parameters for water wave propagation
Jing, Hai-xiao; Liu, Chang-gen; Long, Wen; Tao, Jian-hua
2015-06-01
For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with padé approximation.
Study on Rail Profile Optimization Based on the Nonlinear Relationship between Profile and Wear Rate
Directory of Open Access Journals (Sweden)
Jianxi Wang
2017-01-01
Full Text Available This paper proposes a rail profile optimization method that takes account of wear rate within design cycle so as to minimize rail wear at the curve in heavy haul railway and extend the service life of rail. Taking rail wear rate as the object function, the vertical coordinate of rail profile at range optimization as independent variable, and the geometric characteristics and grinding depth of rail profile as constraint conditions, the support vector machine regression theory was used to fit the nonlinear relationship between rail profile and its wear rate. Then, the profile optimization model was built. Based on the optimization principle of genetic algorithm, the profile optimization model was solved to achieve the optimal rail profile. A multibody dynamics model was used to check the dynamic performance of carriage running on optimal rail profile. The result showed that the average relative error of support vector machine regression model remained less than 10% after a number of training processes. The dynamic performance of carriage running on optimized rail profile met the requirements on safety index and stability. The wear rate of optimized profile was lower than that of standard profile by 5.8%; the allowable carrying gross weight increased by 12.7%.
Infinite horizon self-learning optimal control of nonaffine discrete-time nonlinear systems.
Wei, Qinglai; Liu, Derong; Yang, Xiong
2015-04-01
In this paper, a novel iterative adaptive dynamic programming (ADP)-based infinite horizon self-learning optimal control algorithm, called generalized policy iteration algorithm, is developed for nonaffine discrete-time (DT) nonlinear systems. Generalized policy iteration algorithm is a general idea of interacting policy and value iteration algorithms of ADP. The developed generalized policy iteration algorithm permits an arbitrary positive semidefinite function to initialize the algorithm, where two iteration indices are used for policy improvement and policy evaluation, respectively. It is the first time that the convergence, admissibility, and optimality properties of the generalized policy iteration algorithm for DT nonlinear systems are analyzed. Neural networks are used to implement the developed algorithm. Finally, numerical examples are presented to illustrate the performance of the developed algorithm.
Institute of Scientific and Technical Information of China (English)
Shuo Zhang,Yan Zhao,Min Li,; Jianhui Zhao
2015-01-01
The global y optimal recursive filtering problem is stu-died for a class of systems with random parameter matrices, stochastic nonlinearities, correlated noises and missing measure-ments. The stochastic nonlinearities are presented in the system model to reflect multiplicative random disturbances, and the addi-tive noises, process noise and measurement noise, are assumed to be one-step autocorrelated as wel as two-step cross-correlated. A series of random variables is introduced as the missing rates governing the intermittent measurement losses caused by un-favorable network conditions. The aim of the addressed filtering problem is to design an optimal recursive filter for the uncertain systems based on an innovation approach such that the filtering error is global y minimized at each sampling time. A numerical simulation example is provided to il ustrate the effectiveness and applicability of the proposed algorithm.
Series-based approximate approach of optimal tracking control for nonlinear systems with time-delay
Institute of Scientific and Technical Information of China (English)
Gongyou Tang; Mingqu Fan
2008-01-01
The optimal output tracking control (OTC) problem for nonlinear systems with time-delay is considered.Using a series-based approx-imate approach,the original OTC problem is transformed into iteration solving linear two-point boundary value problems without time-delay.The OTC law obtained consists of analytical linear feedback and feedforward terms and a nonlinear compensation term with an infinite series of the adjoint vectors.By truncating a finite sum of the adjoint vector series,an approximate optimal tracking control law is obtained.A reduced-order reference input observer is constructed to make the feedforward term physically realizable.Simulation exam-pies are used to test the validity of the series-based approximate approach.
Chen, Hao; Zhong, Shouming; Li, Min; Liu, Xingwen; Adu-Gyamfi, Fehrs
2016-07-01
In this paper, a novel delay partitioning method is proposed by introducing the theory of geometric progression for the stability analysis of T-S fuzzy systems with interval time-varying delays and nonlinear perturbations. Based on the common ratio α, the delay interval is unequally separated into multiple subintervals. A newly modified Lyapunov-Krasovskii functional (LKF) is established which includes triple-integral terms and augmented factors with respect to the length of every related proportional subintervals. In addition, a recently developed free-matrix-based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. This innovative development can dramatically enhance the efficiency of obtaining the maximum upper bound of the time delay. Finally, much less conservative stability criteria are presented. Numerical examples are conducted to demonstrate the significant improvements of this proposed approach.
Wu, Xiaomao; Schelly, Z. A.; Vastano, John A.
1994-07-01
Results of studies of the limited Explodator model in a continuous-flow stirred tank reactor (CSTR) under square wave perturbation of the flow rate are reported. The perturbation is applied in such a way that the system is alternately attracted to two different periodic attractors in the parameter region close the Hopf bifurcation point. The system is shown to display a variety of entrainment bands, birhythmicity, quasiperiodicity, resonance-like phenomenon, period doubling and intermittency routes to chaos, and a complicated window structure of the chaotic region. In addition, a novel phenomenon, “intermittent alternative laminar oscillations”, was observed in a chaotic regime sandwiched between two entrainment bands. Transient chaos occurs in one of the entrainment bands, which intimates chaos in the adjacent regime. Positive Lyapunov exponents were found to be associated with the chaotic behavior. The folding and stretching property of the chaotic attractors was analyzed through stroboscopic representations. The deterministic nature of the chaotic behavior was confirmed by the quadratic-like curve formed in the one-dimensional map.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Nonlinear time series prediction is studied by using an improved least squares support vector machine (LSSVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization.We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.
A NONMONOTONE TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION SUBJECT TO GENERAL CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
Hongchao Zhang
2003-01-01
In this paper we present a nonmonotone trust region algorithm for general nonlinear constrained optimization problems. The main idea of this paper is to combine Yuan's technique[1] with a nonmonotone method similar to Ke and Han [2]. This new algorithm may not only keep the robust properties of the algorithm given by Yuan, but also have some advantages led by the nonmonotone technique. Under very mild conditions, global convergence for the algorithm is given. Numerical experiments demonstrate the efficiency of the algorithm.
Field computation in non-linear magnetic media using particle swarm optimization
Energy Technology Data Exchange (ETDEWEB)
Adly, A.A. E-mail: amradlya@intouch.com; Abd-El-Hafiz, S.K
2004-05-01
This paper presents an automated particle swarm optimization approach using which field computations may be carried out in devices involving non-linear magnetic media. Among the advantages of the proposed approach are its ability to handle complex geometries and its computational efficiency. The proposed approach has been implemented and computations were carried out for an electromagnet subject to different DC excitation conditions. These computations showed good agreement with the results obtained by the finite-element approach.
A New Subspace Correction Method for Nonlinear Unconstrained Convex Optimization Problems
Institute of Scientific and Technical Information of China (English)
Rong-liang CHEN; Jin-ping ZENG
2012-01-01
This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S.Nash in 2000 and the subspace correction algorithm proposed by X.Tai and J.Xu in 2001.Under some reasonable assumptions,we obtain the convergence as well as a convergence rate estimate for the algorithm.Numerical results show that the algorithm is effective.
The solution of singular optimal control problems using direct collocation and nonlinear programming
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
DEFF Research Database (Denmark)
Petersen, Lars Norbert; Jørgensen, John Bagterp; Rawlings, James B.
2015-01-01
In this paper, we develop an economically optimizing Nonlinear Model Predictive Controller (E-NMPC) for a complete spray drying plant with multiple stages. In the E-NMPC the initial state is estimated by an extended Kalman Filter (EKF) with noise covariances estimated by an autocovariance least...... squares method (ALS). We present a model for the spray drying plant and use this model for simulation as well as for prediction in the E-NMPC. The open-loop optimal control problem in the E-NMPC is solved using the single-shooting method combined with a quasi-Newton Sequential Quadratic programming (SQP...
Role of the conjugated spacer in the optimization of second-order nonlinear chromophores
Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.
2009-08-01
We investigate the role of the conjugated spacer in the optimization of the first hyperpolarizability of organic chromophores. We propose a novel strategy for the optimization of the first hyperpolarizability that is based on the variation of the degree of conjugation for the bridge that separates the donor and acceptors at the end of push-pull type chromophores. The correlation between the type of conjugated spacer and the experimental nonlinear performance of the chromophores is investigated and interpreted in the context of the quantum limits.
Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani
2017-03-01
This paper presents an approximate optimal control of nonlinear continuous-time systems in affine form by using the adaptive dynamic programming (ADP) with event-sampled state and input vectors. The knowledge of the system dynamics is relaxed by using a neural network (NN) identifier with event-sampled inputs. The value function, which becomes an approximate solution to the Hamilton-Jacobi-Bellman equation, is generated by using event-sampled NN approximator. Subsequently, the NN identifier and the approximated value function are utilized to obtain the optimal control policy. Both the identifier and value function approximator weights are tuned only at the event-sampled instants leading to an aperiodic update scheme. A novel adaptive event sampling condition is designed to determine the sampling instants, such that the approximation accuracy and the stability are maintained. A positive lower bound on the minimum inter-sample time is guaranteed to avoid accumulation point, and the dependence of inter-sample time upon the NN weight estimates is analyzed. A local ultimate boundedness of the resulting nonlinear impulsive dynamical closed-loop system is shown. Finally, a numerical example is utilized to evaluate the performance of the near-optimal design. The net result is the design of an event-sampled ADP-based controller for nonlinear continuous-time systems.
Approximate optimal control for a class of nonlinear discrete-time systems with saturating actuators
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we solve the approximate optimal control problem for a class of nonlinear discrete-time systems with saturating actu- ators via greedy iterative Heuristic Dynamic Programming (GI-HDP) algorithm. In order to deal with the saturating problem of actu- ators, a novel nonquadratic functional is developed. Based on the nonquadratic functional, the GI-HDP algorithm is introduced to obtain the optimal saturated controller with a rigorous convergence analysis. For facilitating the implementation of the iterative algo- rithm, three neural networks are used to approximate the value function, compute the optimal control policy and model the unknown plant, respectively. An example is given to demonstrate the validity of the proposed optimal control scheme.
Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao
2017-01-10
Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the H∞ optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest L₂-gain and the associated H∞ optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.
A differentiable reformulation for E-optimal design of experiments in nonlinear dynamic biosystems.
Telen, Dries; Van Riet, Nick; Logist, Flip; Van Impe, Jan
2015-06-01
Informative experiments are highly valuable for estimating parameters in nonlinear dynamic bioprocesses. Techniques for optimal experiment design ensure the systematic design of such informative experiments. The E-criterion which can be used as objective function in optimal experiment design requires the maximization of the smallest eigenvalue of the Fisher information matrix. However, one problem with the minimal eigenvalue function is that it can be nondifferentiable. In addition, no closed form expression exists for the computation of eigenvalues of a matrix larger than a 4 by 4 one. As eigenvalues are normally computed with iterative methods, state-of-the-art optimal control solvers are not able to exploit automatic differentiation to compute the derivatives with respect to the decision variables. In the current paper a reformulation strategy from the field of convex optimization is suggested to circumvent these difficulties. This reformulation requires the inclusion of a matrix inequality constraint involving positive semidefiniteness. In this paper, this positive semidefiniteness constraint is imposed via Sylverster's criterion. As a result the maximization of the minimum eigenvalue function can be formulated in standard optimal control solvers through the addition of nonlinear constraints. The presented methodology is successfully illustrated with a case study from the field of predictive microbiology.
Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.
Duarte, Belmiro P M; Wong, Weng Kee
2015-08-01
This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.
Optimal control for nonlinear dynamical system of microbial fed-batch culture
Liu, Chongyang
2009-10-01
In fed-batch culture of glycerol bio-dissimilation to 1, 3-propanediol (1, 3-PD), the aim of adding glycerol is to obtain as much 1, 3-PD as possible. So a proper feeding rate is required during the process. Taking the concentration of 1, 3-PD at the terminal time as the performance index and the feeding rate of glycerol as the control function, we propose an optimal control model subject to a nonlinear dynamical system and constraints of continuous state and non-stationary control. A computational approach is constructed to seek the solution of the above model in two aspects. On the one hand we transcribe the optimal control model into an unconstrained one based on the penalty functions and an extension of the state space; on the other hand, by approximating the control function with simple functions, we transform the unconstrained optimal control problem into a sequence of nonlinear programming problems, which can be solved using gradient-based optimization techniques. The convergence analysis of this approximation is also investigated. Numerical results show that, by employing the optimal control policy, the concentration of 1, 3-PD at the terminal time can be increased considerably.
A Space-Time Finite Element Model for Design and Control Optimization of Nonlinear Dynamic Response
Directory of Open Access Journals (Sweden)
P.P. Moita
2008-01-01
Full Text Available A design and control sensitivity analysis and multicriteria optimization formulation is derived for flexible mechanical systems. This formulation is implemented in an optimum design code and it is applied to the nonlinear dynamic response. By extending the spatial domain to the space-time domain and treating the design variables as control variables that do not change with time, the design space is included in the control space. Thus, one can unify in one single formulation the problems of optimum design and optimal control. Structural dimensions as well as lumped damping and stiffness parameters plus control driven forces, are considered as decision variables. The dynamic response and its sensitivity with respect to the design and control variables are discretized via space-time finite elements, and are integrated at-once, as it is traditionally used for static response. The adjoint system approach is used to determine the design sensitivities. Design optimization numerical examples are performed. Nonlinear programming and optimality criteria may be used for the optimization process. A normalized weighted bound formulation is used to handle multicriteria problems.
Hocker, David Lance
The control of quantum systems occurs across a broad range of length and energy scales in modern science, and efforts have demonstrated that locating suitable controls to perform a range of objectives has been widely successful. The justification for this success arises from a favorable topology of a quantum control landscape, defined as a mapping of the controls to a cost function measuring the success of the operation. This is summarized in the landscape principle that no suboptimal extrema exist on the landscape for well-suited control problems, explaining a trend of successful optimizations in both theory and experiment. This dissertation explores what additional lessons may be gleaned from the quantum control landscape through numerical and theoretical studies. The first topic examines the experimentally relevant problem of assessing and reducing disturbances due to noise. The local curvature of the landscape is found to play an important role on noise effects in the control of targeted quantum unitary operations, and provides a conceptual framework for assessing robustness to noise. Software for assessing noise effects in quantum computing architectures was also developed and applied to survey the performance of current quantum control techniques for quantum computing. A lack of competition between robustness and perfect unitary control operation was discovered to fundamentally limit noise effects, and highlights a renewed focus upon system engineering for reducing noise. This convergent behavior generally arises for any secondary objective in the situation of high primary objective fidelity. The other dissertation topic examines the utility of quantum control for a class of nonlinear Hamiltonians not previously considered under the landscape principle. Nonlinear Schrodinger equations are commonly used to model the dynamics of Bose-Einstein condensates (BECs), one of the largest known quantum objects. Optimizations of BEC dynamics were performed in which the
Directory of Open Access Journals (Sweden)
P. P. Hallan
2008-01-01
Full Text Available The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear stability of the equilibrium point of the Robe's (1977 restricted circular three-body problem has been studied when the density parameter K is zero. By applying Kolmogorov-Arnold-Moser (KAM theory, it has been found that the equilibrium point is stable for all mass ratios μ in the range of linear stability 8/9+(2/3((43/25ϵ1−(10/3ϵ<μ<1, where ϵ and ϵ1 are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratios μ1=0.93711086−1.12983217ϵ+1.50202694ϵ1, μ2 = 0.9672922−0.5542091ϵ+ 1.2443968ϵ1, μ3=0.9459503−0.70458206ϵ+ 1.28436549ϵ1, μ4=0.9660792−0.30152273ϵ + 1.11684064ϵ1, μ5=0.893981−2.37971679ϵ + 1.22385421ϵ1, where the theory is not applicable.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, C.; Gallego, S.; Ortuno, M.; Neipp, C. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-11-26
A modified He's homotopy perturbation method (HHPM) is used to calculate the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x{sup 1/3}. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified HHPM works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 0.6% for small and large values of oscillation amplitude, while this relative error is 0.17% for the second iteration and as low as 0.024% when the third approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that the former is very effective and convenient.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The impact of sulfate aerosol, ClOx and NOx perturbations for two different magnitudes of CH4 sources on lower stratospheric ozone is studied by using a heterogeneous chemical system that consists of 19 species belonging to 5 chemical families (oxygen, hydrogen, nitrogen, chlorine and carbon). The results show that the present modeled photochemical system can present several different solutions, for instance,periodic states and multi-equilibrium states appearing in turn under certain parameter domains, through chlorine chemistry and nitrogen chemistry together with sulfate aerosol as well as the increasing magnitude of CH4 sources. The existence of catastrophic transitions could produce a dramatic reduction in the ozone concentration with the increase of external sources.
Hu, Mingxiao; Shen, Liangzhong; Zan, Xiangzhen; Shang, Xuequn; Liu, Wenbin
2016-05-19
Boolean networks are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long-term behavior of systems. In this paper, we investigate the less-studied one-bit perturbation, which falls under the category of structural intervention. Previous works focused on finding the optimal one-bit perturbation to maximally alter the steady-state distribution (SSD) of undesirable states through matrix perturbation theory. However, the application of the SSD is limited to Boolean networks with about ten genes. In 2007, Xiao et al. proposed to search the optimal one-bit perturbation by altering the sizes of the basin of attractions (BOAs). However, their algorithm requires close observation of the state-transition diagram. In this paper, we propose an algorithm that efficiently determines the BOA size after a perturbation. Our idea is that, if we construct the basin of states for all states, then the size of the BOA of perturbed networks can be obtained just by updating the paths of the states whose transitions have been affected. Results from both synthetic and real biological networks show that the proposed algorithm performs better than the exhaustive SSD-based algorithm and can be applied to networks with about 25 genes.
Molde, H.; Zwick, D.; Muskulus, M.
2014-12-01
Support structures for offshore wind turbines are contributing a large part to the total project cost, and a cost saving of a few percent would have considerable impact. At present support structures are designed with simplified methods, e.g., spreadsheet analysis, before more detailed load calculations are performed. Due to the large number of loadcases only a few semimanual design iterations are typically executed. Computer-assisted optimization algorithms could help to further explore design limits and avoid unnecessary conservatism. In this study the simultaneous perturbation stochastic approximation method developed by Spall in the 1990s was assessed with respect to its suitability for support structure optimization. The method depends on a few parameters and an objective function that need to be chosen carefully. In each iteration the structure is evaluated by time-domain analyses, and joint fatigue lifetimes and ultimate strength utilization are computed from stress concentration factors. A pseudo-gradient is determined from only two analysis runs and the design is adjusted in the direction that improves it the most. The algorithm is able to generate considerably improved designs, compared to other methods, in a few hundred iterations, which is demonstrated for the NOWITECH 10 MW reference turbine.
Nonlinear optimal control of bypass transition in a boundary layer flow
Xiao, Dandan; Papadakis, George
2017-05-01
The central aim of the paper is to apply and assess a nonlinear optimal control strategy to suppress bypass transition, due to bimodal interactions [T. A. Zaki and P. A. Durbin, "Mode interaction and the bypass route to transition," J. Fluid Mech. 531, 85 (2005)] in a zero-pressure-gradient boundary layer. To this end, a Lagrange variational formulation is employed that results in a set of adjoint equations. The optimal wall actuation (blowing and suction from a control slot) is found by solving iteratively the nonlinear Navier-Stokes and the adjoint equations in a forward/backward loop using direct numerical simulation. The optimization is performed in a finite time horizon. Large values of optimization horizon result in the instability of the adjoint equations. The control slot is located exactly in the region of transition. The results show that the control is able to significantly reduce the objective function, which is defined as the spatial and temporal integral of the quadratic deviation from the Blasius profile plus a term that quantifies the control cost. The physical mechanism with which the actuation interacts with the flow field is investigated and analysed in relation to the objective function employed. Examination of the joint probability density function shows that the control velocity is correlated with the streamwise velocity in the near wall region but this correlation is reduced as time elapses. The spanwise averaged velocity is distorted by the control action, resulting in a significant reduction of the skin friction coefficient. Results are presented with and without zero-net mass flow constraint of the actuation velocity. The skin friction coefficient drops below the laminar value if there is no mass constraint; it remains however larger than laminar when this constraint is imposed. Results are also compared with uniform blowing using the same time-average velocity obtained from the nonlinear optimal algorithm.
Mothersill, Carmel; Seymour, Colin
2012-07-01
Our recent data suggest there is a physical component to the bystander signal induced by radiation exposure and that alternative medicine techniques such as Reiki and acupuncture or exposures to weak EM fields alter the response of cells to direct irradiation and either altered bystander signal production or altered the response of cells receiving bystander signals. Our proposed mechanism to explain these findings is that perturbation of electromagnetic (EM) fields is central to the induction of low radiation dose responses especially non-targeted bystander effects. In this presentation we review the alternative medicine data and other data sets from our laboratory which test our hypothesis that perturbation of bio-fields will modulate radiation response in the low dose region. The other data sets include exposure to MRI, shielding using lead and or Faraday cages, the use of physical barriers to bystander signal transmission and the use of membrane channel blockers. The data taken together strongly suggest that EM field perturbation can modulate low dose response and that in fact the EM field rather than the targeted deposition of ionizing energy in the DNA may be the key determinant of dose response in a cell or organism The results also lead us to suspect that at least when chemical transmission is blocked, bystander signals can be transmitted by other means. Our recent experiments suggest light signals and volatiles are not likely. We conclude that alternative medicine and other techniques involving electromagnetic perturbations can modify the response of cells to low doses of ionizing radiation and can induce bystander effects similar to those seen in medium transfer experiments. In addition to the obvious implications for mechanistic studies of low dose effects, this could perhaps provide a novel target to exploit in space radiation protection and in optimizing therapeutic gain during radiotherapy.
Perturbative treatment of the non-linear q-Schr\\"odinger and q-Klein-Gordon equations
Zamora, D J; Plastino, A; Ferri, G L
2016-01-01
Interesting nonlinear generalization of both Schr\\"odinger's and Klein-Gordon's equations have been recently advanced by Tsallis, Rego-Monteiro, and Tsallis (NRT) in [Phys. Rev. Lett. {\\bf 106}, 140601 (2011)]. There is much current activity going on in this area. The non-linearity is governed by a real parameter $q$. It is a fact that the ensuing non linear q-Schr\\"odinger and q-Klein-Gordon equations are natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for $q-$values close to unity [Nucl. Phys. A {\\bf 955}, 16 (2016), Nucl. Phys. A {\\bf 948}, 19 (2016)]. It is also well known that q-exponential behavior is found in quite different settings. An explanation for such phenomenon was given in [Physica A {\\bf 388}, 601 (2009)] with reference to empirical scenarios in which data are collected via set-ups that effect a normalization plus data's pre-processing. Precisely, the ensuing normalized output was there shown to be q-exponentially distributed if the input dat...
Gottlieb, Sigal
2015-04-10
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.
Chen, Jie; Li, Jiahong; Yang, Shuanghua; Deng, Fang
2016-07-21
The identification of the nonlinearity and coupling is crucial in nonlinear target tracking problem in collaborative sensor networks. According to the adaptive Kalman filtering (KF) method, the nonlinearity and coupling can be regarded as the model noise covariance, and estimated by minimizing the innovation or residual errors of the states. However, the method requires large time window of data to achieve reliable covariance measurement, making it impractical for nonlinear systems which are rapidly changing. To deal with the problem, a weighted optimization-based distributed KF algorithm (WODKF) is proposed in this paper. The algorithm enlarges the data size of each sensor by the received measurements and state estimates from its connected sensors instead of the time window. A new cost function is set as the weighted sum of the bias and oscillation of the state to estimate the "best" estimate of the model noise covariance. The bias and oscillation of the state of each sensor are estimated by polynomial fitting a time window of state estimates and measurements of the sensor and its neighbors weighted by the measurement noise covariance. The best estimate of the model noise covariance is computed by minimizing the weighted cost function using the exhaustive method. The sensor selection method is in addition to the algorithm to decrease the computation load of the filter and increase the scalability of the sensor network. The existence, suboptimality and stability analysis of the algorithm are given. The local probability data association method is used in the proposed algorithm for the multitarget tracking case. The algorithm is demonstrated in simulations on tracking examples for a random signal, one nonlinear target, and four nonlinear targets. Results show the feasibility and superiority of WODKF against other filtering algorithms for a large class of systems.
Institute of Scientific and Technical Information of China (English)
张文安; 俞立
2007-01-01
This paper concerns the delay-dependent robust stability problem of uncertain neutral systems with mixed neutral and discrete delays. Nonlinear time-varying parameter perturbations are considered. Based on the newly established integral inequalities, the neutral-delay-dependent and discretedelay-dependent stability criterion is derived without using a fixed model transformation. The condition is presented in terms of linear matrix inequality and can be easily solved by existing convex optimization techniques. A numerical example is given to demonstrate the less conservatism of the proposed results.
Samareh, Hossein; Khoshrou, Seyed Hassan; Shahriar, Kourosh; Ebadzadeh, Mohammad Mehdi; Eslami, Mohammad
2017-09-01
When particle's wave velocity resulting from mining blasts exceeds a certain level, then the intensity of produced vibrations incur damages to the structures around the blasting regions. Development of mathematical models for predicting the peak particle velocity (PPV) based on the properties of the wave emission environment is an appropriate method for better designing of blasting parameters, since the probability of incurred damages can considerably be mitigated by controlling the intensity of vibrations at the building sites. In this research, first out of 11 blasting and geo-mechanical parameters of rock masses, four parameters which had the greatest influence on the vibrational wave velocities were specified using regression analysis. Thereafter, some models were developed for predicting the PPV by nonlinear regression analysis (NLRA) and artificial neural network (ANN) with correlation coefficients of 0.854 and 0.662, respectively. Afterward, the coefficients associated with the parameters in the NLRA model were optimized using optimization particle swarm-genetic algorithm. The values of PPV were estimated for 18 testing dataset in order to evaluate the accuracy of the prediction and performance of the developed models. By calculating statistical indices for the test recorded maps, it was found that the optimized model can predict the PPV with a lower error than the other two models. Furthermore, considering the correlation coefficient (0.75) between the values of the PPV measured and predicted by the optimized nonlinear model, it was found that this model possesses a more desirable performance for predicting the PPV than the other two models.
Institute of Scientific and Technical Information of China (English)
张立卫; Robert Ebihart Msigwa
2014-01-01
Mathematical programs with complementarity constraints are an important class of optimi-zation problems ,which have important applications in science and engineering .For examples ,the road capacity expansion problem in transportation and the DICE model in economics are such kind of problems .Traditional nonlinear programming solvers can not be used to solve mathematical programs with complementarity constraints ,because conventional constraint qualifications do not hold for the constraint sets ,and smooth approximationmethods are proposed to overcome such a difficulty .This paper considers the perturbation approach based on the smoothed Fischer-Burmeister function for a class of optimization problems with complementarity constraints .We prove that the optimal value of the perturbed problem converges to that of the original problem and the outer limit of the solution set for the perturbed problem is contained in the solution set of the original problem w hen the smoothing parameter μ↘0 .We explain w hy the conventionally used constraint qualifications are easily satisfied and present the first-order necessary optimality conditions and the second-order sufficient optimality conditions for the perturbed problems .%互补约束优化问题是一类重要的最优化问题，在科学和工程中有着重要的应用。交通规划的道路扩容问题，经济学领域的DICE模型都是互补约束优化问题。这类问题因为约束集合不满足通常的约束规范而不能用传统的非线性规划方法处理，往往用光滑近似的方法来克服这一困难。考虑一类互补约束优化问题的基于光滑化Fischer-Burmeister 函数的扰动方法。证明了当光滑化参数μ↘0时扰动问题的值收敛到原问题的最优值，扰动问题的最优解集合的外极限包含在问题最优解集合中。说明扰动问题很容易满足通常的约束规范，并给出扰动问题的一阶必要性最优条件和二阶充分性最优条件。
Optimal forcing perturbations for regional flow patterns conditioning polar low development
Kristiansen, Jørn; Iversen, Trond; Jung, Thomas; Barkmeijer, Jan
2013-04-01
olar lows are short lived maritime mesoscale cyclones that develop because of processes unique to the Polar Regions. In the ice-free Nordic and Barents Seas they are associated with violent weather during wintertime and form in cold air outbreaks underneath a cold through. The longer predictability of the large-scales may provide early warnings of the potential for polar lows. We investigate the rare events when the atmosphere is highly sensitive to small external forcings that excite changes in the variability of the North Atlantic Oscillation (NAO). Employing a numerical weather prediction model, the period 1957-2002 is sampled for 4-day optimal forcing sensitivity patterns (FSPs). The highly sensitive events are relatively well-defined. A flow pattern resembling the negative-phase NAO is identified as a potential precursor of the most unpredictable transitions in the NAO. The least sensitive events are dominated by a coinciding cyclonic circulation. In the former there is high polar low potential (40-45%) in the northern North Atlantic but it is low south of Iceland. The least sensitive events display high potential along the storm track reaching 80% south of Iceland. The FSPs tend to either strengthen or hamper the transition toward the negative-phase NAO. The strengthened circulation makes the atmosphere favourable in 70% of the events for the formation of polar lows in the Nordic and Barents Seas with high potentials also in the North Sea. From the hampered transition we learn that in the Nordic Seas high- and low-pressure systems can produce similar levels of polar low potential. Temperature and momentum are equally important forcing variables and there are positive feedbacks between them. The forcing is dominantly in-situ and strongest in mid-troposphere. The variability is more localized and larger than the average. Close to the surface the FSPs appear influenced by the Norwegian current.
Braess, Dietrich; Dette, Holger
2004-01-01
We consider maximin and Bayesian D -optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior distribution for these parameters is available. It was observed empirically by many authors that an increase of uncertainty in the prior information (i.e. a larger range for the parameter space in the maximin criterion or a larger variance of the ...
Optimal Energy Measurement in Nonlinear Systems: An Application of Differential Geometry
Fixsen, Dale J.; Moseley, S. H.; Gerrits, T.; Lita, A.; Nam, S. W.
2014-01-01
Design of TES microcalorimeters requires a tradeoff between resolution and dynamic range. Often, experimenters will require linearity for the highest energy signals, which requires additional heat capacity be added to the detector. This results in a reduction of low energy resolution in the detector. We derive and demonstrate an algorithm that allows operation far into the nonlinear regime with little loss in spectral resolution. We use a least squares optimal filter that varies with photon energy to accommodate the nonlinearity of the detector and the non-stationarity of the noise. The fitting process we use can be seen as an application of differential geometry. This recognition provides a set of well-developed tools to extend our work to more complex situations. The proper calibration of a nonlinear microcalorimeter requires a source with densely spaced narrow lines. A pulsed laser multi-photon source is used here, and is seen to be a powerful tool for allowing us to develop practical systems with significant detector nonlinearity. The combination of our analysis techniques and the multi-photon laser source create a powerful tool for increasing the performance of future TES microcalorimeters.
Kitaura, Francisco-Shu; Scoccola, Claudia; Chuang, Chia-Hsun; Müller, Volker; Yepes, Gustavo; Prada, Francisco
2014-01-01
We present a method to produce mock galaxy catalogues with efficient perturbation theory schemes, which match the number density, power spectra and bispectra in real and in redshift space from N-body simulations. The essential contribution of this work is the way in which we constrain the bias parameters in the PATCHY-code. In addition of aiming at reproducing the two-point statistics, we seek the set of bias parameters, which constrain the univariate halo probability distribution function (PDF) encoding higher-order correlation functions. We demonstrate that halo catalogues based on the same underlying dark matter field with a fix halo number density, and accurately matching the power spectrum (within 2%), can lead to very different bispectra depending on the adopted halo bias model. A model ignoring the shape of the halo PDF can lead to deviations up to factors of 2. The catalogues obtained additionally constraining the shape of the halo PDF can significantly lower the discrepancy in the three-point statist...
Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems
Energy Technology Data Exchange (ETDEWEB)
Lee, Se Jung; Park, Gyung Jin [Hanyang University, Seoul (Korea, Republic of)
2014-05-15
In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency.
Optimal Control of Nonlinear Hydraulic Networks in the Presence of Disturbance
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Leth, John-Josef; Kallesøe, Carsten;
2014-01-01
Water leakage is an important component of water loss. Many methods have emerged from urban water supply systems for leakage control, but it still remains a challenge in many countries. Pressure management is an effective way to reduce the leakage in a system. It can also reduce the power consump...... control problem is the interior point method. The method which is used in this paper can be used for a general hydraulic networks to optimize the leakage and energy consumption and to satisfy the demands at the end-users....... consumption. To this end, an optimal control strategy is proposed in this paper. In the water supply system model, the hydraulic resistance of the valve is estimated by the real data from a water supply system and it is considered to be a disturbance. The method which is used to solve the nonlinear optimal...
Cavity-enhanced second harmonic generation via nonlinear-overlap optimization
Lin, Zin; Loncar, Marko; Johnson, Steven G; Rodriguez, Alejandro W
2015-01-01
We describe an approach based on topology optimization that enables automatic discovery of wavelength-scale photonic structures for achieving high-efficiency second-harmonic generation (SHG). A key distinction from previous formulation and designs that seek to maximize Purcell factors at individual frequencies is that our method not only aims to achieve frequency matching (across an entire octave) and large radiative lifetimes, but also optimizes the equally important nonlinear--coupling figure of merit $\\bar{\\beta}$, involving a complicated spatial overlap-integral between modes. We apply this method to the particular problem of optimizing micropost and grating-slab cavities (one-dimensional multilayered structures) and demonstrate that a variety of material platforms can support modes with the requisite frequencies, large lifetimes $Q \\gtrsim 10^3$, small modal volumes $\\sim (\\lambda/n)^3$, and extremely large $\\bar{\\beta} \\gtrsim 10^{-2}$, orders of magnitude larger than the state of the art.
Directory of Open Access Journals (Sweden)
Chein-Shan Liu
2014-01-01
Full Text Available To solve an unconstrained nonlinear minimization problem, we propose an optimal algorithm (OA as well as a globally optimal algorithm (GOA, by deflecting the gradient direction to the best descent direction at each iteration step, and with an optimal parameter being derived explicitly. An invariant manifold defined for the model problem in terms of a locally quadratic function is used to derive a purely iterative algorithm and the convergence is proven. Then, the rank-two updating techniques of BFGS are employed, which result in several novel algorithms as being faster than the steepest descent method (SDM and the variable metric method (DFP. Six numerical examples are examined and compared with exact solutions, revealing that the new algorithms of OA, GOA, and the updated ones have superior computational efficiency and accuracy.
Directory of Open Access Journals (Sweden)
Zhi-Wen Zhu
2015-01-01
Full Text Available A kind of high-aspect-ratio shape memory alloy (SMA composite wing is proposed to reduce the wing’s fluttering. The nonlinear dynamic characteristics and optimal control of the SMA composite wings subjected to in-plane stochastic excitation are investigated where the great bending under the flight loads is considered. The stochastic stability of the system is analyzed, and the system’s response is obtained. The conditions of stochastic Hopf bifurcation are determined, and the probability density of the first-passage time is obtained. Finally, the optimal control strategy is proposed. Numerical simulation shows that the stability of the system varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the reliability of the system is improved through optimal control, and the first-passage time is delayed. Finally, the effects of the control strategy are proved by experiments. The results of this paper are helpful for engineering applications of SMA.
Schroeter, Jens; Wunsch, Carl
1986-01-01
The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.
A general non-linear optimization algorithm for lower bound limit analysis
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...... load optimization problem. and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non-linear yield criteria. Copyright (C) 2002 John Wiley Sons. Ltd....
Hartmann, Armin; Van Der Kooij, Anita J; Zeeck, Almut
2009-07-01
In explorative regression studies, linear models are often applied without questioning the linearity of the relations between the predictor variables and the dependent variable, or linear relations are taken as an approximation. In this study, the method of regression with optimal scaling transformations is demonstrated. This method does not require predefined nonlinear functions and results in easy-to-interpret transformations that will show the form of the relations. The method is illustrated using data from a German multicenter project on the indication criteria for inpatient or day clinic psychotherapy treatment. The indication criteria to include in the regression model were selected with the Lasso, which is a tool for predictor selection that overcomes the disadvantages of stepwise regression methods. The resulting prediction model indicates that treatment status is (approximately) linearly related to some criteria and nonlinearly related to others.
Controller Parameter Optimization for Nonlinear Systems Using Enhanced Bacteria Foraging Algorithm
Directory of Open Access Journals (Sweden)
V. Rajinikanth
2012-01-01
Full Text Available An enhanced bacteria foraging optimization (EBFO algorithm-based Proportional + integral + derivative (PID controller tuning is proposed for a class of nonlinear process models. The EBFO algorithm is a modified form of standard BFO algorithm. A multiobjective performance index is considered to guide the EBFO algorithm for discovering the best possible value of controller parameters. The efficiency of the proposed scheme has been validated through a comparative study with classical BFO, adaptive BFO, PSO, and GA based controller tuning methods proposed in the literature. The proposed algorithm is tested in real time on a nonlinear spherical tank system. The real-time results show that, EBFO tuned PID controller gives a smooth response for setpoint tracking performance.
Nonlinear approach for oil field optimization based on gas lift optimization
Energy Technology Data Exchange (ETDEWEB)
Khamehchi, Ehsan; Rashidi, Fariborz [Amirkabir Univ. of Technology, Tehran (Iran). Faculty of Chemical Engineering; Karimi, Behrooz [Amirkabir Univ. of Technology, Tehran (Iran). Faculty of Industrial Engineering; Pourafshary, Peyman [Tehran Univ. (Iran). Petroleum Engineering Inst.
2009-12-15
When the initial energy of a virgin reservoir is not sufficient or when this energy falls below a certain limit after a production history, the production rates won't be able to meet economic margins. It is then time for artificial lift methods to come to aid. Among which, gas lift is the most commonly used scenario. Being somehow an ancient tool with an age of over a century, gas lift is though still a challenging problem when overall optimization is the concern. When the injection gas is of limited supply the problem is finding the best gas allocation scheme. However there are ever more cases emerging in certain geographic localities where the gas supplies are usually unlimited. The optimization problem then totally relates to the wellbore and completion string and fully engages with multiphase flow concepts. In the present study an intelligent genetic algorithm has been developed to simultaneously optimize all role playing factors, namely gas injection rate, injection depth and tubing diameter towards the maximum oil production rate with the water cut and injection pressure as the restrictions. The computations and real field data are mutually compared. (orig.)
Fan, Quan-Yong; Yang, Guang-Hong
2017-01-01
The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies.
DSP Approach to the Design of Nonlinear Optical Devices
Directory of Open Access Journals (Sweden)
Steve Blair
2005-06-01
Full Text Available Discrete-time signal processing (DSP tools have been used to analyze numerous optical filter configurations in order to optimize their linear response. In this paper, we propose a DSP approach to design nonlinear optical devices by treating the desired nonlinear response in the weak perturbation limit as a discrete-time filter. Optimized discrete-time filters can be designed and then mapped onto a specific optical architecture to obtain the desired nonlinear response. This approach is systematic and intuitive for the design of nonlinear optical devices. We demonstrate this approach by designing autoregressive (AR and autoregressive moving average (ARMA lattice filters to obtain a nonlinear phase shift response.
On large-scale nonlinear programming techniques for solving optimal control problems
Energy Technology Data Exchange (ETDEWEB)
Faco, J.L.D.
1994-12-31
The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO - Gradient REduit pour la Commande Optimale - is discussed.
Liu, Tianyu; Jiao, Licheng; Ma, Wenping; Shang, Ronghua
2017-03-01
In this paper, an improved quantum-behaved particle swarm optimization (CL-QPSO), which adopts a new collaborative learning strategy to generate local attractors for particles, is proposed to solve nonlinear numerical problems. Local attractors, which directly determine the convergence behavior of particles, play an important role in quantum-behaved particle swarm optimization (QPSO). In order to get a promising and efficient local attractor for each particle, a collaborative learning strategy is introduced to generate local attractors in the proposed algorithm. Collaborative learning strategy consists of two operators, namely orthogonal operator and comparison operator. For each particle, orthogonal operator is used to discover the useful information that lies in its personal and global best positions, while comparison operator is used to enhance the particle's ability of jumping out of local optima. By using a probability parameter, the two operators cooperate with each other to generate local attractors for particles. A comprehensive comparison of CL-QPSO with some state-of-the-art evolutionary algorithms on nonlinear numeric optimization functions demonstrates the effectiveness of the proposed algorithm.
Discrete homotopy analysis for optimal trading execution with nonlinear transient market impact
Curato, Gianbiagio; Gatheral, Jim; Lillo, Fabrizio
2016-10-01
Optimal execution in financial markets is the problem of how to trade a large quantity of shares incrementally in time in order to minimize the expected cost. In this paper, we study the problem of the optimal execution in the presence of nonlinear transient market impact. Mathematically such problem is equivalent to solve a strongly nonlinear integral equation, which in our model is a weakly singular Urysohn equation of the first kind. We propose an approach based on Homotopy Analysis Method (HAM), whereby a well behaved initial trading strategy is continuously deformed to lower the expected execution cost. Specifically, we propose a discrete version of the HAM, i.e. the DHAM approach, in order to use the method when the integrals to compute have no closed form solution. We find that the optimal solution is front loaded for concave instantaneous impact even when the investor is risk neutral. More important we find that the expected cost of the DHAM strategy is significantly smaller than the cost of conventional strategies.
Tofighi, Elham; Mahdizadeh, Amin
2016-09-01
This paper addresses the problem of automatic tuning of weighting coefficients for the nonlinear model predictive control (NMPC) of wind turbines. The choice of weighting coefficients in NMPC is critical due to their explicit impact on efficiency of the wind turbine control. Classically, these weights are selected based on intuitive understanding of the system dynamics and control objectives. The empirical methods, however, may not yield optimal solutions especially when the number of parameters to be tuned and the nonlinearity of the system increase. In this paper, the problem of determining weighting coefficients for the cost function of the NMPC controller is formulated as a two-level optimization process in which the upper- level PSO-based optimization computes the weighting coefficients for the lower-level NMPC controller which generates control signals for the wind turbine. The proposed method is implemented to tune the weighting coefficients of a NMPC controller which drives the NREL 5-MW wind turbine. The results are compared with similar simulations for a manually tuned NMPC controller. Comparison verify the improved performance of the controller for weights computed with the PSO-based technique.
Xu, Hao; Jagannathan, Sarangapani
2013-03-01
The stochastic optimal controller design for the nonlinear networked control system (NNCS) with uncertain system dynamics is a challenging problem due to the presence of both system nonlinearities and communication network imperfections, such as random delays and packet losses, which are not unknown a priori. In the recent literature, neuro dynamic programming (NDP) techniques, based on value and policy iterations, have been widely reported to solve the optimal control of general affine nonlinear systems. However, for realtime control, value and policy iterations-based methodology are not suitable and time-based NDP techniques are preferred. In addition, output feedback-based controller designs are preferred for implementation. Therefore, in this paper, a novel NNCS representation incorporating the system uncertainties and network imperfections is introduced first by using input and output measurements for facilitating output feedback. Then, an online neural network (NN) identifier is introduced to estimate the control coefficient matrix, which is subsequently utilized for the controller design. Subsequently, the critic and action NNs are employed along with the NN identifier to determine the forward-in-time, time-based stochastic optimal control of NNCS without using value and policy iterations. Here, the value function and control inputs are updated once a sampling instant. By using novel NN weight update laws, Lyapunov theory is used to show that all the closed-loop signals and NN weights are uniformly ultimately bounded in the mean while the approximated control input converges close to its target value with time. Simulation results are included to show the effectiveness of the proposed scheme.
Economic Optimization of Spray Dryer Operation using Nonlinear Model Predictive Control
DEFF Research Database (Denmark)
Petersen, Lars Norbert; Poulsen, Niels Kjølstad; Niemann, Hans Henrik
2014-01-01
In this paper we investigate an economically optimizing Nonlinear Model Predictive Control (E-NMPC) for a spray drying process. By simulation we evaluate the economic potential of this E-NMPC compared to a conventional PID based control strategy. Spray drying is the preferred process to reduce......-shooting method combined with a quasi-Newton Sequential Quadratic Programming (SQP) algorithm and the adjoint method for computation of gradients. The E-NMPC improves the cost of spray drying by 26.7% compared to conventional PI control in our simulations....
An Optimal Homotopy Asymptotic Approach Applied to Nonlinear MHD Jeffery-Hamel Flow
Directory of Open Access Journals (Sweden)
Vasile Marinca
2011-01-01
Full Text Available A simple and effective procedure is employed to propose a new analytic approximate solution for nonlinear MHD Jeffery-Hamel flow. This technique called the Optimal Homotopy Asymptotic Method (OHAM does not depend upon any small/large parameters and provides us with a convenient way to control the convergence of the solution. The examples given in this paper lead to the conclusion that the accuracy of the obtained results is growing along with increasing the number of constants in the auxiliary function, which are determined using a computer technique. The results obtained through the proposed method are in very good agreement with the numerical results.
Optimization of coherent optical OFDM transmitter using DP-IQ modulator with nonlinear response
Chang, Sun Hyok; Kang, Hun-Sik; Moon, Sang-Rok; Lee, Joon Ki
2016-07-01
In this paper, we investigate the performance of dual polarization orthogonal frequency division multiplexing (DP-OFDM) signal generation when the signal is generated by a DP-IQ optical modulator. The DP-IQ optical modulator is made of four parallel Mach-Zehnder modulators (MZMs) which have nonlinear responses and limited extinction ratios. We analyze the effects of the MZM in the DP-OFDM signal generation by numerical simulation. The operating conditions of the DP-IQ modulator are optimized to have the best performance of the DP-OFDM signal.
DEFF Research Database (Denmark)
Petersen, Lars Norbert; Poulsen, Niels Kjølstad; Niemann, Hans Henrik;
2015-01-01
In this paper, we compare the performance of an economically optimizing Nonlinear Model Predictive Controller (E-NMPC) to a linear tracking Model Predictive Controller (MPC) for a spray drying plant. We find in this simulation study, that the economic performance of the two controllers are almost...... equal. We evaluate the economic performance with an industrially recorded disturbance scenario, where unmeasured disturbances and model mismatch are present. The state of the spray dryer, used in the E-NMPC and MPC, is estimated using Kalman Filters with noise covariances estimated by a maximum...
Global stability, periodic solutions, and optimal control in a nonlinear differential delay model
Directory of Open Access Journals (Sweden)
Anatoli F. Ivanov
2010-09-01
Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.
Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming
Shi, Yun. Y.; Nelson, R. L.; Young, D. H.
1990-01-01
The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
Naseradinmousavi, Peiman
In this dissertation, the actuator-valve systems as a critical part of the automation system are analyzed. Using physics-based high fidelity modeling, this research provides a set of tools to help understand, predict, optimize, and control the real performance of these complex systems. The work carried out is expected to add to the suite of analytical and numerical tools that are essential for the development of highly automated ship systems. We present an accurate dynamic model, perform nonlinear analysis, and develop optimal design and operation for electromechanical valve systems. The mathematical model derived includes electromagnetics, fluid mechanics, and mechanical dynamics. Nondimensionalization has been carried out in order to reduce the large number of parameters to a few critical independent sets to help carry out a parametric analysis. The system stability analysis is then carried out with the aid of the tools from nonlinear dynamic analysis. This reveals that the system is unstable in a certain region of the parameter space. The system is also shown to exhibit crisis and transient chaotic responses. Smart valves are often operated under local power supply (for various mission-critical reasons) and need to consume as little energy as possible in order to ensure continued operability. The Simulated Annealing (SA) algorithm is utilized to optimize the actuation subsystem yielding the most efficient configuration from the point of view of energy consumption for two sets of design variables. The optimization is particularly important when the smart valves are used in a distributed network. Another aspect of optimality is more subtle and concerns optimal operation given a designed system. Optimal operation comes after the optimal design process to explore if there is any particular method of the valve operation that would yield the minimum possible energy used. The results of our model developed are also validated with the aid of an experimental setup
High order multiplication perturbation method for singular perturbation problems
Institute of Scientific and Technical Information of China (English)
张文志; 黄培彦
2013-01-01
This paper presents a high order multiplication perturbation method for sin-gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coeﬃcient dimensional expanding, the non-homogeneous ordinary dif-ferential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.
Optimizing optical nonlinearities in GaInAs/AlInAs quantum cascade lasers
Directory of Open Access Journals (Sweden)
Gajić Aleksandra D.
2014-01-01
Full Text Available Regardless of the huge advances made in the design and fabrication of mid-infrared and terahertz quantum cascade lasers, success in accessing the ~3-4 mm region of the electromagnetic spectrum has remained limited. This fact has brought about the need to exploit resonant intersubband transitions as powerful nonlinear oscillators, consequently enabling the occurrence of large nonlinear optical susceptibilities as a means of reaching desired wavelengths. In this work, we present a computational model developed for the optimization of second-order optical nonlinearities in In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser structures based on the implementation of the Genetic algorithm. The carrier transport and the power output of the structure were calculated by self-consistent solutions to the system of rate equations for carriers and photons. Both stimulated and simultaneous double-photon absorption processes occurring between the second harmonic generation-relevant levels are incorporated into rate equations and the material-dependent effective mass and band non-parabolicity are taken into account, as well. The developed method is quite general and can be applied to any higher order effect which requires the inclusion of the photon density equation. [Projekat Ministarstva nauke Republike Srbije, br. III 45010
Institute of Scientific and Technical Information of China (English)
Zhang Ya-Ni
2013-01-01
A simple type of photonic crystal fiber (PCF) for supercontinuum generation is proposed for the first time.The proposed PCF is composed of a solid silica core and a cladding with square lattice uniform elliptical air holes,which offers not only a large nonlinear coefficient but also a high birefringence and low leakage losses.The PCF with nonlinear coefficient as large as 46 W-1 · km-1 at the wavelength of 1.55 μm and a total dispersion as low as ±2.5 ps.nm-1 · km-1 over an ultra-broad waveband range of the S-C-L band (wavelength from 1.46 μm to 1.625 μm) is optimized by adjusting its structure parameter,such as the lattice constant A,the air-filling fraction f,and the air-hole ellipticity η.The novel PCF with ultra-flattened dispersion,highly nonlinear coefficient,and nearly zero negative dispersion slope will offer a possibility of efficient super-continuum generation in telecommunication windows using a few ps pulses.
Improved nonlinear optimization in the storage ring of the modern synchrotron radiation light source
Institute of Scientific and Technical Information of China (English)
TIAN Shun-Qiang; LIU Gui-Min; HOU Jie; CHEN Guang-Ling; CHEN Sen-Yu
2009-01-01
In the storage ring of the third generation light sources,nonlinear optimization is an indispensable course in order to obtain ample dynamic acceptances and to reach high injection efficiency and long beam lifetime,especially in a low emittance lattice.An improved optimization algorithm based on the single resonance approach,which takes relative weight and initial Harmonic Sextupole Integral Strength (HSIS) as search variables,is discussed in this paper.Applications of the improved method in several test lattices are presented.Detailed analysis of the storage ring of the Shanghai Synchrotron Radiation Facility (SSRF) is particularly emphasized.Furthermore,cancellation of the driving terms is investigated to reveal the physical mechanism of the harmonic sextupole compensation.Sensitivity to the weight and the initial HSIS as well as dependence of the optimum solution on the convergent factor is analyzed.
Institute of Scientific and Technical Information of China (English)
Tao CHENG; Frank L.LEWIS
2007-01-01
In this paper,neural networks are used to approximately solve the finite-horizon constrained input H-infiniy state feedback control problem.The method is based on solving a related Hamilton-Jacobi-Isaacs equation of the corresponding finite-horizon zero-sum game.The game value function is approximated by a neural network wlth timevarying weights.It is shown that the neural network approximation converges uniformly to the game-value function and the resulting almost optimal constrained feedback controller provides closed-loop stability and bounded L2 gain.The result is an almost optimal H-infinity feedback controller with time-varying coefficients that is solved a priori off-line.The effectiveness of the method is shown on the Rotational/Translational Actuator benchmark nonlinear control problem.
Optimal geometry of nonlinear silicon slot waveguides accounting for the effect of waveguide losses.
Ong, Jun Rong; Chen, Valerian H
2015-12-28
The optimal geometry of silicon-organic hybrid slot waveguides is investigated in the context of the efficiency of four-wave mixing (FWM), a χ(3) nonlinear optical process. We study the effect of slot and waveguide widths, as well as waveguide asymmetry on the two-photon absorption (TPA) figure of merit and the roughness scattering loss. The optimal waveguide core width is shown to be 220nm (symmetric) with a slot width of 120nm, at a fixed waveguide height of 220nm. We also show that state-of-the-art slot waveguides can outperform rib waveguides, especially at high powers, due to the high TPA figure-of-merit.
Directory of Open Access Journals (Sweden)
Yutong Liu
2012-01-01
Full Text Available Purpose. To develop a technique to automate landmark selection for point-based interpolating transformations for nonlinear medical image registration. Materials and Methods. Interpolating transformations were calculated from homologous point landmarks on the source (image to be transformed and target (reference image. Point landmarks are placed at regular intervals on contours of anatomical features, and their positions are optimized along the contour surface by a function composed of curvature similarity and displacements of the homologous landmarks. The method was evaluated in two cases (=5 each. In one, MRI was registered to histological sections; in the second, geometric distortions in EPI MRI were corrected. Normalized mutual information and target registration error were calculated to compare the registration accuracy of the automatically and manually generated landmarks. Results. Statistical analyses demonstrated significant improvement (<0.05 in registration accuracy by landmark optimization in most data sets and trends towards improvement (<0.1 in others as compared to manual landmark selection.
Directory of Open Access Journals (Sweden)
Liu Jinkui
2011-01-01
Full Text Available Abstract In this paper, an efficient modified nonlinear conjugate gradient method for solving unconstrained optimization problems is proposed. An attractive property of the modified method is that the generated direction in each step is always descending without any line search. The global convergence result of the modified method is established under the general Wolfe line search condition. Numerical results show that the modified method is efficient and stationary by comparing with the well-known Polak-Ribiére-Polyak method, CG-DESCENT method and DSP-CG method using the unconstrained optimization problems from More and Garbow (ACM Trans Math Softw 7, 17-41, 1981, so it can be widely used in scientific computation. Mathematics Subject Classification (2010 90C26 · 65H10
Directory of Open Access Journals (Sweden)
Bingyong Yan
2015-01-01
Full Text Available A robust fault detection scheme for a class of nonlinear systems with uncertainty is proposed. The proposed approach utilizes robust control theory and parameter optimization algorithm to design the gain matrix of fault tracking approximator (FTA for fault detection. The gain matrix of FTA is designed to minimize the effects of system uncertainty on residual signals while maximizing the effects of system faults on residual signals. The design of the gain matrix of FTA takes into account the robustness of residual signals to system uncertainty and sensitivity of residual signals to system faults simultaneously, which leads to a multiobjective optimization problem. Then, the detectability of system faults is rigorously analyzed by investigating the threshold of residual signals. Finally, simulation results are provided to show the validity and applicability of the proposed approach.