Simplified non-linear time-history analysis based on the Theory of Plasticity
DEFF Research Database (Denmark)
Costa, Joao Domingues
2005-01-01
is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation......This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...
Simplified non-linear time-history analysis based on the Theory of Plasticity
DEFF Research Database (Denmark)
Costa, Joao Domingues
2005-01-01
is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation......This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...
The Seismic Reliability of Offshore Structures Based on Nonlinear Time History Analyses
Hosseini, Mahmood; Karimiyani, Somayyeh; Ghafooripour, Amin; Jabbarzadeh, Mohammad Javad
2008-07-01
Regarding the past earthquakes damages to offshore structures, as vital structures in the oil and gas industries, it is important that their seismic design is performed by very high reliability. Accepting the Nonlinear Time History Analyses (NLTHA) as the most reliable seismic analysis method, in this paper an offshore platform of jacket type with the height of 304 feet, having a deck of 96 feet by 94 feet, and weighing 290 million pounds has been studied. At first, some Push-Over Analyses (POA) have been preformed to recognize the more critical members of the jacket, based on the range of their plastic deformations. Then NLTHA have been performed by using the 3-components accelerograms of 100 earthquakes, covering a wide range of frequency content, and normalized to three Peak Ground Acceleration (PGA) levels of 0.3 g, 0.65 g, and 1.0 g. By using the results of NLTHA the damage and rupture probabilities of critical member have been studied to assess the reliability of the jacket structure. Regarding that different structural members of the jacket have different effects on the stability of the platform, an "importance factor" has been considered for each critical member based on its location and orientation in the structure, and then the reliability of the whole structure has been obtained by combining the reliability of the critical members, each having its specific importance factor.
Teruna, D. R.
2017-03-01
Pushover analysis or also known as nonlinear static procedures (NSP) have been recognized in recent years for practical evaluation of seismic demands and for structural design by estimating a structural building capacities and deformation demands. By comparing these demands and capacities at the performance level interest, the seismic performance of a building can be evaluated. However, the accuracy of NSP for assessment irregular building is not yet a fully satisfactory solution, since irregularities of a building influence the dynamic responses of the building. The objective of the study presented herein is to understand the nonlinear behaviour of six story RC building with mass irregularities at different floors and stiffness irregularity at first story (soft story) using NSP. For the purpose of comparison on the performance level obtained with NSP, nonlinear time history analysis (THA) were also performed under ground motion excitation with compatible to response spectra design. Finally, formation plastic hinges and their progressive development from elastic level to collapse prevention are presented and discussed.
Institute of Scientific and Technical Information of China (English)
黎超敏; 崔荣乐
2013-01-01
This paper researched on energy dissipation - seismic reduction structure (with nonlinear viscous liquid damper) with the nonlinear time history analysis. Authors mainly discussed the research background, current research at home and aboard, the relevant provisions of the current regulation and standards, several problems and difficulties of the theory and its practical applications, social significance and economic benefits of the energy dissipation - seismic reduction. And take a brief introduction to the nonlinear time history analysis. At last, authors made an example of engineering to make a contrast between the original structure and the energy dissipation - seismic reduction focusing mainly on the axial force of the column, top displacement, displacement angle between layers, and get some useful conclusion which can be used in the practical engineering.%本文对减震结构(附设阻尼器的消能减震结构)进行了非线性时程分析的研究.探讨了减震结构的研究背景、国内外的研究现状、现行规范对减震结构的相关规定、减震结构在理论、实际应用上的问题和难点、减震结构的社会意义和经济效益以及对非线性时程分析进行了简要介绍.最后通过一个工程案例,对减震结构和无控结构进行了比较(柱轴力、顶点位移、层间位移角),得出了一些可以用于工程实际的结论.
Directory of Open Access Journals (Sweden)
Michele Betti
2015-05-01
Full Text Available The paper presents a comparison between two numerical modelling approaches employed to investigate the seismic behavior of unreinforced masonry buildings with flexible diaphragms. The comparison is performed analyzing a two-story prototype tested on a shaking table at the CNR-ENEA research center of Casaccia (Italy. The first numerical model was built by using the finite element (FE technique, while the second one was built by a simplified macro-element (ME approach. Both models were employed to perform non-linear dynamic analyses, integrating the equations of motion by step-by-step procedures. The shaking table tests were simulated to analyze the behavior of the prototype from the initial elastic state until the development of extensive damage. The main results of the analyses are discussed and critically compared in terms of engineering parameters, such as accelerations, displacements and base shears. The effectiveness of both models within the investigated typology of buildings is then evaluated in depth.
Time Series with Tailored Nonlinearities
Raeth, C
2015-01-01
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncor- related Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for e.g. turbulence and financial data can thus be explained in terms of phase correlations.
Predicting Nonlinear Time Series
1993-12-01
response becomes R,(k) = f (Y FV,(k)) (2.4) where Wy specifies the weight associated with the output of node i to the input of nodej in the next layer and...interconnections for each of these previous nodes. 18 prr~~~o• wfe :t iam i -- ---- --- --- --- Figure 5: Delay block for ATNN [9] Thus, nodej receives the...computed values, aj(tn), and dj(tn) denotes the desired output of nodej at time in. In this thesis, the weights and time delays update after each input
Edgerton, David
2012-06-01
This essay argues that taking the economy seriously in histories of science could not only extend the range of activities studied but also change--often quite radically--our understanding of well-known cases and instances in twentieth-century science. It shows how scientific intellectuals and historians of science have followed the money as a means of critique of particular forms of science and of particular conceptions of science. It suggests the need to go further, to a much broader implicit definition of what constitutes science--one that implies a criticism of much history of twentieth-century science for defining it implicitly and inappropriately in very restrictive ways.
Gleick, James
2016-01-01
From the acclaimed author of The Information and Chaos, here is a mind-bending exploration of time travel: its subversive origins, its evolution in literature and science, and its influence on our understanding of time itself. The story begins at the turn of the previous century, with the young H. G. Wells writing and rewriting the fantastic tale that became his first book and an international sensation: The Time Machine. It was an era when a host of forces was converging to transmute the human understanding of time, some philosophical and some technological: the electric telegraph, the steam railroad, the discovery of buried civilizations, and the perfection of clocks. James Gleick tracks the evolution of time travel as an idea that becomes part of contemporary culture—from Marcel Proust to Doctor Who, from Jorge Luis Borges to Woody Allen. He investigates the inevitable looping paradoxes and examines the porous boundary between pulp fiction and modern physics. Finally, he delves into a temporal shift that...
Nonlinear time series modelling: an introduction
Simon M. Potter
1999-01-01
Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear models are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of models. Finally, forecasting and impulse response analysis is developed.
Common large innovations across nonlinear time series
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard)
2002-01-01
textabstractWe propose a multivariate nonlinear econometric time series model, which can be used to examine if there is common nonlinearity across economic variables. The model is a multivariate censored latent effects autoregression. The key feature of this model is that nonlinearity appears as sep
Time, history and international law
Craven, Matthew; Vogiatzi, Maria
2006-01-01
This book examines theoretical and practical issues concerning the relationship between international law, time and history. Problems relating to time and history are ever-present in the work of international lawyers, whether understood in terms of the role of historic practice in the doctrine of sources, the application of the principle of inter-temporal law in dispute settlement, or in gaining a coherent insight into the role that was played by international law in past events. But very little has been written about the various different ways in which international lawyers approach or unders
Nonlinearity: The History and Philosophy of the Science
Burke, Kenneth M.
2009-01-01
This article provides for a concise history of nonlinearity from the context of the changing assumptions in science throughout the turn of the twentieth century. Concerned with the development of an ethics of technology in higher education, it establishes a background for ongoing research on quantitative methods in the social sciences. The history…
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
: Discrete-time delay system, Sliding mode control, nonlinear sliding ... The concept of the sliding mode control in recent years has drawn the ...... His area of interest is dc-dc converters, electrical vehicle and distributed generation application.
Discrete time learning control in nonlinear systems
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
Nonlinear Time Series Analysis Since 1990:Some Personal Reflections
Institute of Scientific and Technical Information of China (English)
Howel Tong
2002-01-01
I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.
Some Nonlinear Dynamic Inequalities on Time Scales
Indian Academy of Sciences (India)
Wei Nian Li; Weihong Sheng
2007-11-01
The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl. 251 (2000) 736--751).
Some Nonlinear Integral Inequalities on Time Scales
Directory of Open Access Journals (Sweden)
Li Wei Nian
2007-01-01
Full Text Available The purpose of this paper is to investigate some nonlinear integral inequalities on time scales. Our results unify and extend some continuous inequalities and their corresponding discrete analogues. The theoretical results are illustrated by a simple example at the end of this paper.
Dimensional reduction of nonlinear time delay systems
Directory of Open Access Journals (Sweden)
M. S. Fofana
2005-01-01
infinite-dimensional problem without the assumption of small time delay. This dimensional reduction is illustrated in this paper with the delay versions of the Duffing and van der Pol equations. For both nonlinear delay equations, transcendental characteristic equations of linearized stability are examined through Hopf bifurcation. The infinite-dimensional nonlinear solutions of the delay equations are decomposed into stable and centre subspaces, whose respective dimensions are determined by the linearized stability of the transcendental equations. Linear semigroups, infinitesimal generators, and their adjoint forms with bilinear pairings are the additional candidates for the infinite-dimensional reduction.
Nonlinear Analysis of Physiological Time Series
Institute of Scientific and Technical Information of China (English)
MENG Qing-fang; PENG Yu-hua; XUE Yu-li; HAN Min
2007-01-01
Abstract.The heart rate variability could be explained by a low-dimensional governing mechanism. There has been increasing interest in verifying and understanding the coupling between the respiration and the heart rate. In this paper we use the nonlinear detection method to detect the nonlinear deterministic component in the physiological time series by a single variable series and two variables series respectively, and use the conditional information entropy to analyze the correlation between the heart rate, the respiration and the blood oxygen concentration. The conclusions are that there is the nonlinear deterministic component in the heart rate data and respiration data, and the heart rate and the respiration are two variables originating from the same underlying dynamics.
Nonlinear refraction and reflection travel time tomography
Zhang, Jiahua; ten Brink, U.S.; Toksoz, M.N.
1998-01-01
We develop a rapid nonlinear travel time tomography method that simultaneously inverts refraction and reflection travel times on a regular velocity grid. For travel time and ray path calculations, we apply a wave front method employing graph theory. The first-arrival refraction travel times are calculated on the basis of cell velocities, and the later refraction and reflection travel times are computed using both cell velocities and given interfaces. We solve a regularized nonlinear inverse problem. A Laplacian operator is applied to regularize the model parameters (cell slownesses and reflector geometry) so that the inverse problem is valid for a continuum. The travel times are also regularized such that we invert travel time curves rather than travel time points. A conjugate gradient method is applied to minimize the nonlinear objective function. After obtaining a solution, we perform nonlinear Monte Carlo inversions for uncertainty analysis and compute the posterior model covariance. In numerical experiments, we demonstrate that combining the first arrival refraction travel times with later reflection travel times can better reconstruct the velocity field as well as the reflector geometry. This combination is particularly important for modeling crustal structures where large velocity variations occur in the upper crust. We apply this approach to model the crustal structure of the California Borderland using ocean bottom seismometer and land data collected during the Los Angeles Region Seismic Experiment along two marine survey lines. Details of our image include a high-velocity zone under the Catalina Ridge, but a smooth gradient zone between. Catalina Ridge and San Clemente Ridge. The Moho depth is about 22 km with lateral variations. Copyright 1998 by the American Geophysical Union.
Time Series Forecasting: A Nonlinear Dynamics Approach
Sello, Stefano
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cy...
Dynamics of Nonlinear Time-Delay Systems
Lakshmanan, Muthusamy
2010-01-01
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...
The action operator for continuous time histories
Savvidou, K N
1999-01-01
We define the action operator for the History Projection Operator consistent histories theory, as the quantum analogue of the classical action functional, for the simple harmonic oscillator in one dimention. We conclude that the action operator is the generator of time transformations, and is associated with the two types of time-evolution of the standard quantum theory: the wave-packet reduction and the Heisenberg time-evolution. We construct corresponding classical histories and demonstrate the relevance with the quantum histories. Finally, we show the appearance of the action operator in the expression for the decoherence functional.
Nonlinear Time Series Analysis via Neural Networks
Volná, Eva; Janošek, Michal; Kocian, Václav; Kotyrba, Martin
This article deals with a time series analysis based on neural networks in order to make an effective forex market [Moore and Roche, J. Int. Econ. 58, 387-411 (2002)] pattern recognition. Our goal is to find and recognize important patterns which repeatedly appear in the market history to adapt our trading system behaviour based on them.
Nonlinear time dependent behaviour of epoxy resins
Marotzke, C.; Feldmann, T.
2016-07-01
The nonlinear behaviour of epoxy resins is studied on standard tensile tests. A strain field measurement system is applied (Aramis) in order to monitor local strains. The residual strain is measured by recovering the specimens for up to 68 hours after unloading. The time span the specimen is exposed to load has a large influence on the creeping process and the residual strain after recovering. This is studied by comparison of instantaneous unloading with keeping the specimen under permanent load for thirty minutes. It is shown that moderate differences in the initial strain can lead to large differences in the creep behaviour as well as in the residual strain.
Forecasting with nonlinear time series models
DEFF Research Database (Denmark)
Kock, Anders Bredahl; Teräsvirta, Timo
and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...
Measuring nonlinear behavior in time series data
Wai, Phoong Seuk; Ismail, Mohd Tahir
2014-12-01
Stationary Test is an important test in detect the time series behavior since financial and economic data series always have missing data, structural change as well as jumps or breaks in the data set. Moreover, stationary test is able to transform the nonlinear time series variable to become stationary by taking difference-stationary process or trend-stationary process. Two different types of hypothesis testing of stationary tests that are Augmented Dickey-Fuller (ADF) test and Kwiatkowski-Philips-Schmidt-Shin (KPSS) test are examine in this paper to describe the properties of the time series variables in financial model. Besides, Least Square method is used in Augmented Dickey-Fuller test to detect the changes of the series and Lagrange multiplier is used in Kwiatkowski-Philips-Schmidt-Shin test to examine the properties of oil price, gold price and Malaysia stock market. Moreover, Quandt-Andrews, Bai-Perron and Chow tests are also use to detect the existence of break in the data series. The monthly index data are ranging from December 1989 until May 2012. Result is shown that these three series exhibit nonlinear properties but are able to transform to stationary series after taking first difference process.
Time Series Forecasting A Nonlinear Dynamics Approach
Sello, S
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cycle. Starting from a previous recent work, we checked the reliability and accuracy of a forecasting model based on concepts of nonlinear dynamical systems applied to experimental time series, such as embedding phase space,Lyapunov spectrum,chaotic behaviour. The model is based on a locally hypothesis of the behaviour on the embedding space, utilizing an optimal number k of neighbour vectors to predict the future evolution of the current point with the set of characteristic parameters determined by several previous paramet...
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
History of nonlinear oscillations theory in France (1880-1940)
Ginoux, Jean-Marc
2017-01-01
This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own...
Managing Perishables with Time and temperature History
Ketzenberg, M.; Bloemhof, J.M.; Gaukler, G.
2015-01-01
We address the use and value of time and temperature information to manage perishables in the contextof a retailer that sells a random lifetime product subject to stochastic demand and lost sales. The product’s lifetime is largely determined by the temperature history and the flow time through the s
Managing Perishables with Time and temperature History
Ketzenberg, M.; Bloemhof, J.M.; Gaukler, G.
2015-01-01
We address the use and value of time and temperature information to manage perishables in the contextof a retailer that sells a random lifetime product subject to stochastic demand and lost sales. The product’s lifetime is largely determined by the temperature history and the flow time through the
Managing Perishables with Time and temperature History
Ketzenberg, M.; Bloemhof, J.M.; Gaukler, G.
2015-01-01
We address the use and value of time and temperature information to manage perishables in the contextof a retailer that sells a random lifetime product subject to stochastic demand and lost sales. The product’s lifetime is largely determined by the temperature history and the flow time through the s
History without time: Buffon's natural history as a nonmathematical physique.
Hoquet, Thierry
2010-03-01
While "natural history" is practically synonymous with the name of Buffon, the term itself has been otherwise overlooked by historians of science. This essay attempts to address this omission by investigating the meanings of "physique," "natural philosophy," and "history," among other terms, with the purpose of understanding Buffon's actual objectives. It also shows that Buffon never claimed to be a Newtonian and should not be considered as such; the goal is to provide a historical analysis that resituates Buffon's thought within his own era. This is done, primarily, by eschewing the often-studied question of time in Buffon. Instead, this study examines the nontemporal meanings of the word "history" within the naturalist's theory and method. The title of his Natural History is examined both as an indicator of the kind of science that Buffon was hoping to achieve and as a source of great misinterpretation among his peers. Unlike Buffon, many of his contemporaries actually envisioned the study of nature from a Baconian perspective where history was restricted to the mere collection of facts and where philosophy, which was the implicit and ultimate goal of studying nature, was seen, at least for the present, as unrealizable. Buffon confronts this tendency insofar as his Histoire naturelle claims to be the real physique that, along with describing nature, also sought to identify general laws and provide clear insight into what true knowledge of nature is or should be. According to Buffon, history (both natural and civil) is not analogous to mathematics; it is a nonmathematical method whose scope encompasses both nature and society. This methodological stance gives rise to the "physicization" of certain moral concepts--a gesture that was interpreted by his contemporaries as Epicurean and atheist. In addition, Buffon reduces a number of metaphysically tainted historical concepts (e.g., antediluvian monuments) to objects of physical analysis, thereby confronting the very
Combined forecasts from linear and nonlinear time series models
N. Terui (Nobuhiko); H.K. van Dijk (Herman)
1999-01-01
textabstractCombined forecasts from a linear and a nonlinear model are investigated for time series with possibly nonlinear characteristics. The forecasts are combined by a constant coefficient regression method as well as a time varying method. The time varying method allows for a locally (non)line
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Generation of partially coherent stationary time histories with non-Gaussian distributions
Energy Technology Data Exchange (ETDEWEB)
Smallwood, D.O.
1996-08-27
In a previous paper Smallwood and Paez (1991) showed how to generate realizations of partially coherent stationary normal time histories with a specified cross-spectral density matrix. This procedure is generalized for the case of multiple inputs with a specified cross-spectral density function and a specified marginal probability density function (pdf) for each of the inputs. The specified pdfs are not required to be Gaussian. A zero memory nonlinear (ZMNL) function is developed for each input to transform a Gaussian or normal time history into a time history with a specified non-Gaussian distribution. The transformation functions have the property that a transformed time history will have nearly the same auto spectral density as the original time history. A vector of Gaussian time histories are then generated with the specified cross-spectral density matrix. These waveforms are then transformed into the required time history realizations using the ZMNL function.
Ben-Naim, Arieh
2016-01-01
The aim of this book is to explain in simple language what we know about time and about the history of time. It is shown that the briefest (as well as the lengthiest) history of time can be described in one or two pages. The second purpose of the book is to show that neither entropy, nor the Second Law of Thermodynamics has anything to do with time. The third purpose is to educate the lay reader how to read popular science books, critically. Towards this goal, detailed reviews of four books on time are presented. There are many popular science books on Time, on the beginning of Time and the end of Time. This book is unique in the following two senses: It explains in simple terms what Time is, and why it is not related to entropy. It critically reviews a few popular science books which perpetuate all kinds of unfounded ideas about the relationship between Time and the Second Law. Readership: Interested lay public, students of any of the sciences, scientists, teachers and researchers.
Time-reversed wave mixing in nonlinear optics.
Zheng, Yuanlin; Ren, Huaijin; Wan, Wenjie; Chen, Xianfeng
2013-11-19
Time-reversal symmetry is important to optics. Optical processes can run in a forward or backward direction through time when such symmetry is preserved. In linear optics, a time-reversed process of laser emission can enable total absorption of coherent light fields inside an optical cavity of loss by time-reversing the original gain medium. Nonlinearity, however, can often destroy such symmetry in nonlinear optics, making it difficult to study time-reversal symmetry with nonlinear optical wave mixings. Here we demonstrate time-reversed wave mixings for optical second harmonic generation (SHG) and optical parametric amplification (OPA) by exploring this well-known but underappreciated symmetry in nonlinear optics. This allows us to observe the annihilation of coherent beams. Our study offers new avenues for flexible control in nonlinear optics and has potential applications in efficient wavelength conversion, all-optical computing.
Time Variance of the Suspension Nonlinearity
DEFF Research Database (Denmark)
Agerkvist, Finn T.; Pedersen, Bo Rohde
2008-01-01
. This paper investigates the changes in compliance the driving signal can cause, this includes low level short duration measurements of the resonance frequency as well as high power long duration measurements of the non-linearity of the suspension. It is found that at low levels the suspension softens...
An extended nonlinear state predictor for a class of nonlinear time delay systems
Institute of Scientific and Technical Information of China (English)
WANG Dong; ZHOU Donghua; JIN Yihui
2004-01-01
An extended nonlinear state predictor (ENSP) for a class of nonlinear systems with input time delay is proposed. Based on the extended Kalman filter (EKF), the ENSP first estimates the current states according to the previous estimations and estimation errors, next calculates the future state values via the system model, and then adjusts the values based on the current errors. After a state predictive algorithm for a class of linear systems is presented, it is extended to a class of nonlinear time delay systems and the detailed ENSP algorithm is further proposed. Finally, computer simulations with the nonlinear example are presented, which demonstrates that the proposed ENSP can effectively and accurately predict the future states for a class of nonlinear time-delay systems no matter whether the state variables change quickly or slowly.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: juan.belmonte@uclm.es; Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: gabriel.fernandez@uclm.es
2009-01-19
In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions.
Impulsive control of nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Yu Yong-Bin; Bao Jing-Fu; Zhang Hong-Bin; Zhong Qi-Shui; Liao Xiao-Feng; Yu Jue-Sang
2008-01-01
A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.
Nonlinear time reversal in a wave chaotic system.
Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M
2013-02-01
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.
Nonlinear analysis and prediction of time series in multiphase reactors
Liu, Mingyan
2014-01-01
This book reports on important nonlinear aspects or deterministic chaos issues in the systems of multi-phase reactors. The reactors treated in the book include gas-liquid bubble columns, gas-liquid-solid fluidized beds and gas-liquid-solid magnetized fluidized beds. The authors take pressure fluctuations in the bubble columns as time series for nonlinear analysis, modeling and forecasting. They present qualitative and quantitative non-linear analysis tools which include attractor phase plane plot, correlation dimension, Kolmogorov entropy and largest Lyapunov exponent calculations and local non-linear short-term prediction.
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
Detecting Nonlinearity in Data with Long Coherence Times
Theiler, J; Rubin, D M; Theiler, James; Linsay, Paul S.; Rubin, David M.
1993-01-01
Abstract: We consider the limitations of two techniques for detecting nonlinearity in time series. The first technique compares the original time series to an ensemble of surrogate time series that are constructed to mimic the linear properties of the original. The second technique compares the forecasting error of linear and nonlinear predictors. Both techniques are found to be problematic when the data has a long coherence time; they tend to indicate nonlinearity even for linear time series. We investigate the causes of these difficulties both analytically and with numerical experiments on ``real'' and computer-generated data. In particular, although we do see some initial evidence for nonlinear structure in the SFI dataset E, we are inclined to dismiss this evidence as an artifact of the long coherence time.
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
Losslessness of Nonlinear Stochastic Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Xikui Liu
2015-01-01
Full Text Available This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree 0,…,0 and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.
Nonlinear Time Series Forecast Using Radial Basis Function Neural Networks
Institute of Scientific and Technical Information of China (English)
ZHENGXin; CHENTian-Lun
2003-01-01
In the research of using Radial Basis Function Neural Network (RBF NN) forecasting nonlinear time series, we investigate how the different clusterings affect the process of learning and forecasting. We find that k-means clustering is very suitable. In order to increase the precision we introduce a nonlinear feedback term to escape from the local minima of energy, then we use the model to forecast the nonlinear time series which are produced by Mackey-Glass equation and stocks. By selecting the k-means clustering and the suitable feedback term, much better forecasting results are obtained.
Fatigue damage localization using time-domain features extracted from nonlinear Lamb waves
Hong, Ming; Su, Zhongqing; Lu, Ye; Cheng, Li
2014-03-01
Nonlinear guided waves are sensitive to small-scale fatigue damage that may hardly be identified by traditional techniques. A characterization method for fatigue damage is established based on nonlinear Lamb waves in conjunction with the use of a piezoelectric sensor network. Theories on nonlinear Lamb waves for damage detection are first introduced briefly. Then, the ineffectiveness of using pure frequency-domain information of nonlinear wave signals for locating damage is discussed. With a revisit to traditional gross-damage localization techniques based on the time of flight, the idea of using temporal signal features of nonlinear Lamb waves to locate fatigue damage is introduced. This process involves a time-frequency analysis that enables the damage-induced nonlinear signal features, which are either undiscernible in the original time history or uninformative in the frequency spectrum, to be revealed. Subsequently, a finite element modeling technique is employed, accounting for various sources of nonlinearities in a fatigued medium. A piezoelectric sensor network is configured to actively generate and acquire probing Lamb waves that involve damageinduced nonlinear features. A probability-based diagnostic imaging algorithm is further proposed, presenting results in diagnostic images intuitively. The approach is experimentally verified on a fatigue-damaged aluminum plate, showing reasonably good accuracy. Compared to existing nonlinear ultrasonics-based inspection techniques, this approach uses a permanently attached sensor network that well accommodates automated online health monitoring; more significantly, it utilizes time-domain information of higher-order harmonics from time-frequency analysis, and demonstrates a great potential for quantitative characterization of small-scale damage with improved localization accuracy.
W-Stability of Multistable Nonlinear Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Zhishuai Ding
2012-01-01
Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.
MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES
Institute of Scientific and Technical Information of China (English)
Jean Louis Woukeng; David Dongo
2011-01-01
We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting. We obtain an accurate homogenization result. We also show that as the nonlinear term depends on the microscopic time variable, the global homogenized problem thus obtained is a system consisting of two hyperbolic equations. It is also shown that in spite of the presence of several time scales, the global homogenized problem is not a reiterated one.
Appropriate Algorithms for Nonlinear Time Series Analysis in Psychology
Scheier, Christian; Tschacher, Wolfgang
Chaos theory has a strong appeal for psychology because it allows for the investigation of the dynamics and nonlinearity of psychological systems. Consequently, chaos-theoretic concepts and methods have recently gained increasing attention among psychologists and positive claims for chaos have been published in nearly every field of psychology. Less attention, however, has been paid to the appropriateness of chaos-theoretic algorithms for psychological time series. An appropriate algorithm can deal with short, noisy data sets and yields `objective' results. In the present paper it is argued that most of the classical nonlinear techniques don't satisfy these constraints and thus are not appropriate for psychological data. A methodological approach is introduced that is based on nonlinear forecasting and the method of surrogate data. In artificial data sets and empirical time series we can show that this methodology reliably assesses nonlinearity and chaos in time series even if they are short and contaminated by noise.
Nonlinear Time Series Forecast Using Radial Basis Function Neural Networks
Institute of Scientific and Technical Information of China (English)
ZHENG Xin; CHEN Tian-Lun
2003-01-01
In the research of using Radial Basis Function Neural Network (RBF NN) forecasting nonlinear timeseries, we investigate how the different clusterings affect the process of learning and forecasting. We find that k-meansclustering is very suitable. In order to increase the precision we introduce a nonlinear feedback term to escape from thelocal minima of energy, then we use the model to forecast the nonlinear time series which are produced by Mackey-Glassequation and stocks. By selecting the k-means clustering and the suitable feedback term, much better forecasting resultsare obtained.
ERROR ESTIMATES FOR THE TIME DISCRETIZATION FOR NONLINEAR MAXWELL'S EQUATIONS
Institute of Scientific and Technical Information of China (English)
Marián Slodi(c)ka; Ján Bu(s)a Jr.
2008-01-01
This paper is devoted to the study of a nonlinear evolution eddy current model of the type (б)tB(H) +▽×(▽×H) = 0 subject to homogeneous Dirichlet boundary conditions H×v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B(H). We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B(H).
Multigrid Reduction in Time for Nonlinear Parabolic Problems
Energy Technology Data Exchange (ETDEWEB)
Falgout, R. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Manteuffel, T. A. [Univ. of Colorado, Boulder, CO (United States); O' Neill, B. [Univ. of Colorado, Boulder, CO (United States); Schroder, J. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-04
The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.
Adaptive control method for nonlinear time-delay processes
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Two complex properties,varying time-delay and block-oriented nonlinearity,are very common in chemical engineering processes and not easy to be controlled by routine control methods.Aimed at these two complex properties,a novel adaptive control algorithm the basis of nonlinear OFS(orthonormal functional series) model is proposed.First,the hybrid model which combines OFS and Volterra series is introduced.Then,a stable state feedback strategy is used to construct a nonlinear adaptive control algorithm that can guarantee the closed-loop stability and can track the set point curve without steady-state errors.Finally,control simulations and experiments on a nonlinear process with varying time-delay are presented.A number of experimental results validate the efficiency and superiority of this algorithm.
Finite-time disturbance attenuation of nonlinear systems
Institute of Scientific and Technical Information of China (English)
MO LiPo; JIA YingMin; ZHENG ZhiMing
2009-01-01
This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems.Based on the finite time Lyapunov stability theory,some finite-time H_∞ performance criterions are derived.Then the state-feedback control law is designed and the structure of such a controller is investigated.Furthermore,it is shown that the H_∞ controller can also make the closed-loop system satisfy finite-time H_∞ performance for nonlinear homogeneous systems.An example is provided to demonstrate the effectiveness of the presented results.
Energy Technology Data Exchange (ETDEWEB)
Pousse, G
2005-10-15
This thesis intends to characterize ground motion during earthquake. This work is based on two Japanese networks. It deals with databases of shallow events, depth less than 25 km, with magnitude between 4.0 and 7.3. The analysis of K-net allows to compute a spectral ground motion prediction equation and to review the shape of the Eurocode 8 design spectra. We show the larger amplification at short period for Japanese data and bring in light the soil amplification that takes place at large period. In addition, we develop a new empirical model for simulating synthetic stochastic nonstationary acceleration time histories. By specifying magnitude, distance and site effect, this model allows to produce many time histories, that a seismic event is liable to produce at the place of interest. Furthermore, the study of near-field borehole records of the Kik-net allows to explore the validity domain of predictive equations and to explain what occurs by extrapolating ground motion predictions. Finally, we show that nonlinearity reduces the dispersion of ground motion at the surface. (author)
Nonlinear pulse propagation: a time-transformation approach.
Xiao, Yuzhe; Agrawal, Govind P; Maywar, Drew N
2012-04-01
We present a time-transformation approach for studying the propagation of optical pulses inside a nonlinear medium. Unlike the conventional way of solving for the slowly varying amplitude of an optical pulse, our new approach maps directly the input electric field to the output one, without making the slowly varying envelope approximation. Conceptually, the time-transformation approach shows that the effect of propagation through a nonlinear medium is to change the relative spacing and duration of various temporal slices of the pulse. These temporal changes manifest as self-phase modulation in the spectral domain and self-steepening in the temporal domain. Our approach agrees with the generalized nonlinear Schrödinger equation for 100 fs pulses and the finite-difference time-domain solution of Maxwell's equations for two-cycle pulses, while producing results 20 and 50 times faster, respectively.
Backstepping tracking control for nonlinear time-delay systems
Institute of Scientific and Technical Information of China (English)
Chen Weisheng; Li Junmin
2006-01-01
Two design approaches of state feedback and output feedback tracking controllers are proposed for a class of strict feedback nonlinear time-delay systems by using backstepping technique. When the states of system cannot be observed, the time-delay state observer is designed to estimate the system states. Domination method is used to deal with nonlinear time-delay function under the assumption that the nonlinear time-delay functions of systems satisfy Lipschitz condition. The global asymptotical tracking of the references signal is achieved and the bound of all signals of the resultant closed-loop system is also guaranteed. By constructing a Lyapunov-Krasoviskii functional, the stability of the closed-loop system is proved. The feasibility of the proposed approach is illustrated by a simulation example.
Nonlinear model calibration of a shear wall building using time and frequency data features
Asgarieh, Eliyar; Moaveni, Babak; Barbosa, Andre R.; Chatzi, Eleni
2017-02-01
This paper investigates the effects of different factors on the performance of nonlinear model updating for a seven-story shear wall building model. The accuracy of calibrated models using different data features and modeling assumptions is studied by comparing the time and frequency responses of the models with the exact simulated ones. Simplified nonlinear finite element models of the shear wall building are calibrated so that the misfit between the considered response data features of the models and the structure is minimized. A refined FE model of the test structure, which was calibrated manually to match the shake table test data, is used instead of the real structure for this performance evaluation study. The simplified parsimonious FE models are composed of simple nonlinear beam-column fiber elements with nonlinearity infused in them by assigning generated hysteretic nonlinear material behaviors to uniaxial stress-strain relationship of the fibers. Four different types of data features and their combinations are used for model calibration: (1) time-varying instantaneous modal parameters, (2) displacement time histories, (3) acceleration time histories, and (4) dissipated hysteretic energy. It has been observed that the calibrated simplified FE models can accurately predict the nonlinear structural response in the absence of significant modeling errors. In the last part of this study, the physics-based models are further simplified for casting into state-space formulation and a real-time identification is performed using an Unscented Kalman filter. It has been shown that the performance of calibrated state-space models can be satisfactory when reasonable modeling assumptions are used.
A new differential equations-based model for nonlinear history-dependent magnetic behaviour
Aktaa, J
2000-01-01
The paper presents a new kind of numerical model describing nonlinear magnetic behaviour. The model is formulated as a set of differential equations taking into account history dependence phenomena like the magnetisation hysteresis as well as saturation effects. The capability of the model is demonstrated carrying out comparisons between measurements and calculations.
Nonlinear projective filtering; 1, Application to real time series
Schreiber, T
1998-01-01
We discuss applications of nonlinear filtering of time series by locally linear phase space projections. Noise can be reduced whenever the error due to the manifold approximation is smaller than the noise in the system. Examples include the real time extraction of the fetal electrocardiogram from abdominal recordings.
General expression for linear and nonlinear time series models
Institute of Scientific and Technical Information of China (English)
Ren HUANG; Feiyun XU; Ruwen CHEN
2009-01-01
The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.
Compositional Finite-Time Stability analysis of nonlinear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
for the system but with bounded disturbance. Sufficient conditions for finite-time stability and finite-time boundedness of nonlinear systems as well as a computational method based on sum of squares programming to check the conditions are given. The problem of finite-time stability for a system that consists......This paper, investigates finite-time stability and finite-time boundedness for nonlinear systems with polynomial vector fields. Finite-time stability requires the states of the system to remain a given bounded set in a finite-time interval and finite-time boundedness considers the same problem...... of an interconnection of subsystems is also considered and we show how to decompose the problem into subproblems for each subsystem with coupling constraints. A solution to the problem using sum of squares programming and dual decomposition is presented. The method is demonstrated through some examples....
Statistics of particle time-temperature histories.
Energy Technology Data Exchange (ETDEWEB)
Hewson, John C.; Lignell, David O.; Sun, Guangyuan
2014-10-01
Particles in non - isothermal turbulent flow are subject to a stochastic environment tha t produces a distribution of particle time - temperature histories. This distribution is a function of the dispersion of the non - isothermal (continuous) gas phase and the distribution of particles relative to that gas phase. In this work we extend the one - dimensional turbulence (ODT) model to predict the joint dispersion of a dispersed particle phase and a continuous phase. The ODT model predicts the turbulent evolution of continuous scalar fields with a model for the cascade of fluctuations to smaller sc ales (the 'triplet map') at a rate that is a function of the fully resolved one - dimens ional velocity field . Stochastic triplet maps also drive Lagrangian particle dispersion with finite Stokes number s including inertial and eddy trajectory - crossing effect s included. Two distinct approaches to this coupling between triplet maps and particle dispersion are developed and implemented along with a hybrid approach. An 'instantaneous' particle displacement model matches the tracer particle limit and provide s an accurate description of particle dispersion. A 'continuous' particle displacement m odel translates triplet maps into a continuous velocity field to which particles respond. Particles can alter the turbulence, and modifications to the stochastic rate expr ession are developed for two - way coupling between particles and the continuous phase. Each aspect of model development is evaluated in canonical flows (homogeneous turbulence, free - shear flows and wall - bounded flows) for which quality measurements are ava ilable. ODT simulations of non - isothermal flows provide statistics for particle heating. These simulations show the significance of accurately predicting the joint statistics of particle and fluid dispersion . Inhomogeneous turbulence coupled with the in fluence of the mean flow fields on particles of varying properties
Applied Time Domain Stability Margin Assessment for Nonlinear Time-Varying Systems
Kiefer, J. M.; Johnson, M. D.; Wall, J. H.; Dominguez, A.
2016-01-01
margins. At each time point, the system was linearized about the current operating point using Simulink's built-in solver. Each linearized system in time was evaluated for its rigid-body gain margin (high frequency gain margin), rigid-body phase margin, and aero gain margin (low frequency gain margin) for each control axis. Using the stability margins derived from the baseline linearization approach, the time domain derived stability margins were determined by executing time domain simulations in which axis-specific incremental gain and phase adjustments were made to the nominal system about the expected neutral stability point at specific flight times. The baseline stability margin time histories were used to shift the system gain to various values around the zero margin point such that a precise amount of expected gain margin was maintained throughout flight. When assessing the gain margins, the gain was applied starting at the time point under consideration, thereafter following the variation in the margin found in the linear analysis. When assessing the rigid-body phase margin, a constant time delay was applied to the system starting at the time point under consideration. If the baseline stability margins were correctly determined via the linear analysis, the time domain simulation results should contain unstable behavior at certain gain and phase values. Examples will be shown from repeated simulations with variable added gain and phase lag. Faithfulness of margins calculated from the linear analysis to the nonlinear system will be demonstrated.
Statistics of particle time-temperature histories :
Energy Technology Data Exchange (ETDEWEB)
Hewson, John C.; Gin, Craig; Lignell, David O.; Sun, Guangyuan
2013-10-01
Progress toward predictions of the statistics of particle time-temperature histories is presented. These predictions are to be made using Lagrangian particle models within the one-dimensional turbulence (ODT) model. In the present reporting period we have further characterized the performance, behavior and capabilities of the particle dispersion models that were added to the ODT model in the first period. We have also extended the capabilities in two manners. First we provide alternate implementations of the particle transport process within ODT; within this context the original implementation is referred to as the type-I and the new implementations are referred to as the type-C and type-IC interactions. Second we have developed and implemented models for two-way coupling between the particle and fluid phase. This allows us to predict the reduced rate of turbulent mixing associated with particle dissipation of energy and similar phenomena. Work in characterizing these capabilities has taken place in homogeneous decaying turbulence, in free shear layers, in jets and in channel flow with walls, and selected results are presented.
Time-reversal of nonlinear waves: Applicability and limitations
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
LEARNING GRANGER CAUSALITY GRAPHS FOR MULTIVARIATE NONLINEAR TIME SERIES
Institute of Scientific and Technical Information of China (English)
Wei GAO; Zheng TIAN
2009-01-01
An information theory method is proposed to test the. Granger causality and contemporaneous conditional independence in Granger causality graph models. In the graphs, the vertex set denotes the component series of the multivariate time series, and the directed edges denote causal dependence, while the undirected edges reflect the instantaneous dependence. The presence of the edges is measured by a statistics based on conditional mutual information and tested by a permutation procedure. Furthermore, for the existed relations, a statistics based on the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity. The significance of the nonlinear test statistics is determined by a bootstrap method based on surrogate data. We investigate the finite sample behavior of the procedure through simulation time series with different dependence structures, including linear and nonlinear relations.
Robust stability of discrete-time nonlinear system with time-delay
Institute of Scientific and Technical Information of China (English)
LIU Xin-ge; WU Min
2005-01-01
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
Time shift of pulses due to dispersion slope and nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Marcuse, D.; Menyuk, C.R.; Holzloehner, R.
1999-12-01
The authors show that the time delay of optical pulses traveling in long fibers is influenced by the dispersion slope and the fiber nonlinearity. Consequently, one or more new pulses that are inserted by add-drop operations into a pulse train that has already traveled a long distance may shift relative to the old pulses. This time shift delays the initial pulses more than the newly inserted ones, so that the newly inserted pulses can leave their time frames, leading to errors.
Frozen in Time: The History of Proteins.
Kovacs, Nicholas A; Petrov, Anton S; Lanier, Kathryn A; Williams, Loren Dean
2017-05-01
The ribosome is imprinted with a detailed molecular chronology of the origins and early evolution of proteins. Here we show that when arranged by evolutionary phase of ribosomal evolution, ribosomal protein (rProtein) segments reveal an atomic level history of protein folding. The data support a model in which aboriginal oligomers evolved into globular proteins in a hierarchical step-wise process. Complexity of assembly and folding of polypeptide increased incrementally in concert with expansion of rRNA. (i) Short random coil proto-peptides bound to rRNA, and (ii) lengthened over time and coalesced into β-β secondary elements. These secondary elements (iii) accreted and collapsed, primarily into β-domains. Domains (iv) accumulated and gained complex super-secondary structures composed of mixtures of α-helices and β-strands. Early protein evolution was guided and accelerated by interactions with rRNA. rRNA and proto-peptide provided mutual protection from chemical degradation and disassembly. rRNA stabilized polypeptide assemblies, which evolved in a stepwise process into globular domains, bypassing the immense space of random unproductive sequences. Coded proteins originated as oligomers and polymers created by the ribosome, on the ribosome and for the ribosome. Synthesis of increasingly longer products was iteratively coupled with lengthening and maturation of the ribosomal exit tunnel. Protein catalysis appears to be a late byproduct of selection for sophisticated and finely controlled assembly. © The Author 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.
Global Format for Conservative Time Integration in Nonlinear Dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2014-01-01
The widely used classic collocation-based time integration procedures like Newmark, Generalized-alpha etc. generally work well within a framework of linear problems, but typically may encounter problems, when used in connection with essentially nonlinear structures. These problems are overcome in...
Time-Reversal of Nonlinear Waves - Applicability and Limitations
Ducrozet, G; Chabchoub, A
2016-01-01
Time-reversal (TR) refocusing of waves is one of fundamental principles in wave physics. Using the TR approach, "Time-reversal mirrors" can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backwards. Lately, laboratory experiments proved that this approach can be applied not only in acoustics and electromagnetism but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic TR using a uni-directional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configu...
Probing material nonlinearity at various depths by time reversal mirrors
Payan, C.; Ulrich, T. J.; Le Bas, P. Y.; Griffa, M.; Schuetz, P.; Remillieux, M. C.; Saleh, T. A.
2014-04-01
In this Letter, the time reversal mirror is used to focus elastic energy at a prescribed location and to analyze the amplitude dependence of the focus signal, thus providing the nonlinearity of the medium. By varying the frequency content of the focused waveforms, the technique can be used to probe the surface, by penetrating to a depth defined by the wavelength of the focused waves. The validity of this concept is shown in the presence of gradual and distributed damage in concrete by comparing actual results with a reference nonlinear measurement and X ray tomography images.
Probing material nonlinearity at various depths by time reversal mirrors
Energy Technology Data Exchange (ETDEWEB)
Payan, C. [LMA UPR CNRS 7051, Aix Marseille Université, 31 Chemin Joseph Aiguier, 13402 Marseille (France); Ulrich, T. J.; Le Bas, P. Y.; Remillieux, M. C. [Los Alamos National Laboratory, EES-17, Los Alamos, New Mexico 87545 (United States); Griffa, M.; Schuetz, P. [Swiss Federal Laboratories for Materials Science and Technology (EMPA), Überlandstrasse 129, 8600 Dübendorf (Switzerland); Saleh, T. A. [Los Alamos National Laboratory, MST-16, Los Alamos, New Mexico 87545 (United States)
2014-04-07
In this Letter, the time reversal mirror is used to focus elastic energy at a prescribed location and to analyze the amplitude dependence of the focus signal, thus providing the nonlinearity of the medium. By varying the frequency content of the focused waveforms, the technique can be used to probe the surface, by penetrating to a depth defined by the wavelength of the focused waves. The validity of this concept is shown in the presence of gradual and distributed damage in concrete by comparing actual results with a reference nonlinear measurement and X ray tomography images.
Nonlinear Time Series Prediction Using Chaotic Neural Networks
Institute of Scientific and Technical Information of China (English)
LI KePing; CHEN TianLun
2001-01-01
A nonlinear feedback term is introduced into the evaluation equation of weights of the backpropagation algorithm for neural network, the network becomes a chaotic one. For the purpose of that we can investigate how the different feedback terms affect the process of learning and forecasting, we use the model to forecast the nonlinear time series which is produced by Makey-Glass equation. By selecting the suitable feedback term, the system can escape from the local minima and converge to the global minimum or its approximate solutions, and the forecasting results are better than those of backpropagation algorithm.``
Nonlinear transformation on the transfer entropy of financial time series
Wu, Zhenyu; Shang, Pengjian
2017-09-01
Transfer entropy (TE) now is widely used in the data mining and economic field. However, TE itself demands that time series intend to be stationary and meet Markov condition. Naturally, we are interested in investigating the effect of the nonlinear transformation of the two series on the TE. Therefore, the paper is designed to study the TE of five nonlinear ;volatile; transformations based on the data which are generated by the linear modeling and the logistic maps modeling, as well as the dataset that come from financial markets. With only one of the TE of nonlinear transformations fluctuating around the TE of original series, the TE of others all have increased with different degrees.
Elements of nonlinear time series analysis and forecasting
De Gooijer, Jan G
2017-01-01
This book provides an overview of the current state-of-the-art of nonlinear time series analysis, richly illustrated with examples, pseudocode algorithms and real-world applications. Avoiding a “theorem-proof” format, it shows concrete applications on a variety of empirical time series. The book can be used in graduate courses in nonlinear time series and at the same time also includes interesting material for more advanced readers. Though it is largely self-contained, readers require an understanding of basic linear time series concepts, Markov chains and Monte Carlo simulation methods. The book covers time-domain and frequency-domain methods for the analysis of both univariate and multivariate (vector) time series. It makes a clear distinction between parametric models on the one hand, and semi- and nonparametric models/methods on the other. This offers the reader the option of concentrating exclusively on one of these nonlinear time series analysis methods. To make the book as user friendly as possible...
Nonlinear behaviors of parity-time-symmetric lasers
Yang, Jianke
2016-01-01
We propose a time-dependent partial differential equation model to investigate the dynamical behavior of the parity-time (PT) symmetric laser during the nonlinear stage of its operation. This model incorporates physical effects such as the refractive index distribution, dispersion, material loss, nonlinear gain saturation and self-phase modulation. We show that when the loss is weak, multiple stable steady states and time-periodic states of light exist above the lasing threshold, rendering the laser multi-mode. However, when the loss is strong, only a single stable steady state of broken PT symmetry exists for a wide range of the gain amplitude, rendering the laser single-mode. These results reveal the important role the loss plays in maintaining the single-mode operation of PT lasers.
Design and Control of Nonlinear Mechanical Systems for Minimum Time
Directory of Open Access Journals (Sweden)
J.B. Cardoso
2008-01-01
Full Text Available This paper presents an integrated methodology for optimal design and control of nonlinear flexible mechanical systems, including minimum time problems. This formulation is implemented in an optimum design code and it is applied to the nonlinear behavior dynamic response. Damping and stiffness characteristics plus control driven forces are considered as decision variables. A conceptual separation between time variant and time invariant design parameters is presented, this way including the design space into the control space and considering the design variables as control variables not depending on time. By using time integrals through all the derivations, design and control problems are unified. In the optimization process we can use both types of variables simultaneously or by interdependent levels. For treating minimum time problems, a unit time interval is mapped onto the original time interval, then treating equally time variant and time invariant problems. The dynamic response and its sensitivity are discretized via space-time finite elements, and may be integrated either by at-once integration or step-by-step. Adjoint system approach is used to calculate the sensitivities.
Integrable nonlinear parity-time symmetric optical oscillator
Hassan, Absar U; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N
2016-01-01
The nonlinear dynamics of a balanced parity-time symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain-thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time symmetric systems. Unlike other saturable parity time symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.
Analyzing the Dynamics of Nonlinear Multivariate Time Series Models
Institute of Scientific and Technical Information of China (English)
DenghuaZhong; ZhengfengZhang; DonghaiLiu; StefanMittnik
2004-01-01
This paper analyzes the dynamics of nonlinear multivariate time series models that is represented by generalized impulse response functions and asymmetric functions. We illustrate the measures of shock persistences and asymmetric effects of shocks derived from the generalized impulse response functions and asymmetric function in bivariate smooth transition regression models. The empirical work investigates a bivariate smooth transition model of US GDP and the unemployment rate.
Economic History in Times of Transition
DEFF Research Database (Denmark)
Reckendrees, Alfred
2017-01-01
This issue coincides with my retirement as one of the (co-)editors of the Scandinavian Economic History Review. It has been a great pleasure and a real privilege to work for this journal over the last six years, and I am grateful that Jari Ojala, editor-in-chief since 2015, invited me to reflect...... of all, I am grateful for the enjoyable collaboration with Jacob Weisdorf (we edited SEHR together for four years) and with Janette Rawlings who ran the secretariat and enabled us to focus mainly on content. Copenhagen Business School and the Department for Management, Politics, and Philosophy generously...
A Novel Method for Nonlinear Time Series Forecasting of Time-Delay Neural Network
Institute of Scientific and Technical Information of China (English)
JIANG Weijin; XU Yuhui
2006-01-01
Based on the idea of nonlinear prediction of phase space reconstruction, this paper presented a time delay BP neural network model, whose generalization capability was improved by Bayesian regularization.Furthermore, the model is applied to forecast the import and export trades in one industry.The results showed that the improved model has excellent generalization capabilities, which not only learned the historical curve, but efficiently predicted the trend of business.Comparing with common evaluation of forecasts, we put on a conclusion that nonlinear forecast can not only focus on data combination and precision improvement, it also can vividly reflect the nonlinear characteristic of the forecasting system.While analyzing the forecasting precision of the model, we give a model judgment by calculating the nonlinear characteristic value of the combined serial and original serial, proved that the forecasting model can reasonably catch' the dynamic characteristic of the nonlinear system which produced the origin serial.
Simulation of Broadband Time Histories Combining Deterministic and Stochastic Methodologies
Graves, R. W.; Pitarka, A.
2003-12-01
We present a methodology for generating broadband (0 - 10 Hz) ground motion time histories using a hybrid technique that combines a stochastic approach at high frequencies with a deterministic approach at low frequencies. Currently, the methodology is being developed for moderate and larger crustal earthquakes, although the technique can theoretically be applied to other classes of events as well. The broadband response is obtained by summing the separate responses in the time domain using matched butterworth filters centered at 1 Hz. We use a kinematic description of fault rupture, incorporating spatial heterogeneity in slip, rupture velocity and rise time by discretizing an extended finite-fault into a number of smaller subfaults. The stochastic approach sums the response for each subfault assuming a random phase, an omega-squared source spectrum and simplified Green's functions (Boore, 1983). Gross impedance effects are incorporated using quarter wavelength theory (Boore and Joyner, 1997) to bring the response to a generic baserock level (e.g., Vs = 1000 m/s). The deterministic approach sums the response for many point sources distributed across each subfault. Wave propagation is modeled using a 3D viscoelastic finite difference algorithm with the minimum shear wave velocity set at 620 m/s. Short- and mid-period amplification factors provided by Borcherdt (1994) are used to develop frequency dependent site amplification functions. The amplification functions are applied to the stochastic and determinsitic responses separately since these may have different (computational) reference site velocities. The site velocity is taken as the measured or estimated value of {Vs}30. The use of these amplification factors is attractive because they account for non-linear response by considering the input acceleration level. We note that although these design factors are strictly defined for response spectra, we have applied them to the Fourier amplitude spectra of our
Zabusky, Norman J
2005-03-01
This paper is mostly a history of the early years of nonlinear and computational physics and mathematics. I trace how the counterintuitive result of near-recurrence to an initial condition in the first scientific digital computer simulation led to the discovery of the soliton in a later computer simulation. The 1955 report by Fermi, Pasta, and Ulam (FPU) described their simulation of a one-dimensional nonlinear lattice which did not show energy equipartition. The 1965 paper by Zabusky and Kruskalshowed that the Korteweg-de Vries (KdV) nonlinear partial differential equation, a long wavelength model of the alpha-lattice (or cubic nonlinearity), derived by Kruskal, gave quantitatively the same results obtained by FPU. In 1967, Zabusky and Deem showed that a localized short wavelength initial excitation (then called an "optical" and now a "zone-boundary mode" excitation ) of the alpha-lattice revealed "n-curve" coherent states. If the initial amplitude was sufficiently large energy equipartition followed in a short time. The work of Kruskal and Miura (KM), Gardner and Greene (GG), and myself led to the appreciation of the infinity of denumerable invariants (conservation laws) for Hamiltonian systems and to a procedure by GGKM in 1967 for solving KdV exactly. The nonlinear science field exponentiated in diversity of linkages (as described in Appendix A). Included were pure and applied mathematics and all branches of basic and applied physics, including the first nonhydrodynamic application to optical solitons, as described in a brief essay (Appendix B) by Hasegawa. The growth was also manifest in the number of meetings held and institutes founded, as described briefly in Appendix D. Physicists and mathematicians in Japan, USA, and USSR (in the latter two, people associated with plasma physics) contributed to the diversification of the nonlinear paradigm which continues worldwide to the present. The last part of the paper (and Appendix C) discuss visiometrics: the
Discrete-Time Approximation for Nonlinear Continuous Systems with Time Delays
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Bemri H’mida
2016-05-01
Full Text Available This paper is concerned with the discretization of nonlinear continuous time delay systems. Our approach is based on Taylor-Lie series. The main idea aims to minimize the effect of the delay and neglects the importance of nonlinear parameter by the linearization of the system study in an attempt to make its handling and easier programming as possible. We investigate a new method based on the development of new theoretical methods for the time discretization of nonlinear systems with time delay .The performance of these proposed discretization methods was validated by doing the numerical simulation using a nonlinear system with state delay. Some illustrative examples are given to show the effectiveness of the obtained results.
The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
Pedlosky, J.; Flierl, G. R.
2006-12-01
The nonlinear dynamics of baroclinically unstable waves in a time dependent zonal shear flow is considered in the framework of the two-layer Phillips model on the beta plane. In most cases considered in this study the amplitude of the shear is well below the critical value of the steady shear version of the model. Nevertheless, the time dependent problem in which the shear oscillates periodically is unstable, and the unstable waves grow to substantial amplitudes, in some cases with strongly nonlinear and turbulent characteristics. For very small values of the shear amplitude in the presence of dissipation an analytical, asymptotic theory predicts a self-sustained wave whose amplitude undergoes a nonlinear oscillation whose period is amplitude dependent. There is a sensitive amplitude dependence of the wave on the frequency of the oscillating shear when the shear amplitude is small. This behavior is also found in a truncated model of the dynamics, and that model is used to examine larger shear amplitudes. When there is a mean value of the shear in addition to the oscillating component, but such that the total shear is still subcritical, the resulting nonlinear states exhibit a rectified horizontal buoyancy flux with a nonzero time average as a result of the instability of the oscillating shear. For higher, still subcritical, values of the shear we have detected a symmetry breaking in which a second cross-stream mode is generated through an instability of the unstable wave although this second mode would by itself be stable on the basic time dependent current. For shear values that are substantially subcritical but of order of the critical shear, calculations with a full quasi-geostrophic numerical model reveal a turbulent flow generated by the instability. If the beta effect is disregarded the inviscid, linear problem is formally stable. However, our calculations show that a small degree of nonlinearity is enough to destabilize the flow leading to large amplitude
Nonlinear time-series-based adaptive control applications
Mohler, R. R.; Rajkumar, V.; Zakrzewski, R. R.
1991-01-01
A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.
Blind speech source separation via nonlinear time-frequency masking
Institute of Scientific and Technical Information of China (English)
XU Shun; CHEN Shaorong; LIU Yulin
2008-01-01
Aim at the underdetermined convolutive mixture model, a blind speech source separation method based on nonlinear time-frequency masking was proposed, where the approximate W-disjoint orthogonality (W-DO) property among independent speech signals in time-frequency domain is utilized. In this method, the observation mixture signal from multimicrophones is normalized to be independent of frequency in the time-frequency domain at first, then the dynamic clustering algorithm is adopted to obtain the active source information in each time-frequency slot, a nonlinear function via deflection angle from the cluster center is selected for time-frequency masking, finally the blind separation of mixture speech signals can be achieved by inverse STFT (short-time Fourier transformation). This method can not only solve the problem of frequency permutation which may be met in most classic frequency-domain blind separation techniques, but also suppress the spatial direction diffusion of the separation matrix. The simulation results demonstrate that the proposed separation method is better than the typical BLUES method, the signal-noise-ratio gain (SNRG) increases 1.58 dB averagely.
Nonlinear triple-point problems on time scales
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Douglas R. Anderson
2004-04-01
Full Text Available We establish the existence of multiple positive solutions to the nonlinear second-order triple-point boundary-value problem on time scales, $$displaylines{ u^{Delta abla}(t+h(tf(t,u(t=0, cr u(a=alpha u(b+delta u^Delta(a,quad eta u(c+gamma u^Delta(c=0 }$$ for $tin[a,c]subsetmathbb{T}$, where $mathbb{T}$ is a time scale, $eta, gamma, deltage 0$ with $Beta+gamma>0$, $0
On time-space of nonlinear phenomena with Gompertzian dynamics.
Waliszewski, Przemyslaw; Konarski, Jerzy
2005-04-01
This paper describes a universal relationship between time and space for a nonlinear process with Gompertzian dynamics, such as growth. Gompertzian dynamics implicates a coupling between time and space. Those two categories are related to each other through a linear function of their logarithms. Moreover, we demonstrate that the spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium of regular states, that is, states with dynamics that are predictable for any time-point (e.g., sinusoidal glycolytic oscillations) and chaotic states, that is, states with dynamics that are unpredictable in time, but are characterized by certain regularities (e.g., the existence of strange attractor for any biochemical reaction). We conclude that both this equilibrium and volume of the available complementary Euclidean space determine temporal and spatial expansion of a process with Gompertzian dynamics.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, J [Departamento de Matematicas, E T S de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), Avda Camilo Jose Cela, 3 Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain); Cuevas, J [Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Universitaria Politecnica, C/Virgen de Africa, 7, 41011 Sevilla (Spain)], E-mail: juan.belmonte@uclm.es, E-mail: jcuevas@us.es
2009-04-24
In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic-quintic nonlinear Schroedinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose-Einstein condensates and nonlinear optics.
A brief history of the philosophy of time
Bardon, Adrian
2013-01-01
Adrian Bardon's A Brief History of the Philosophy of Time is a short introduction to the history, philosophy, and science of the study of time-from the pre-Socratic philosophers through Einstein and beyond. A Brief History of the Philosophy of Time covers subjects such as time and change, the experience of time, physical and metaphysical approaches to the nature of time, the direction of time, time travel, time and freedom of the will, and scientific and philosophical approaches to eternity and the beginning of time. Bardon employs helpful illustrations and keeps technical language to a minimum in bringing the resources of over 2500 years of philosophy and science to bear on some of humanity's most fundamental and enduring questions.
Hybrid discretization method for time-delay nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zheng [Xi' an Jiaotong University, Xi' an (China); Zhang, Yuanliang; Kil Chong, To [Chonbuk National University, Jeonju (Korea, Republic of); Kostyukova, Olga [3Institute of Mathematics National Academy of Science of Belarus, Minsk (Belarus)
2010-03-15
A hybrid discretization scheme that combines the virtues of the Taylor series and Matrix exponential integration methods is proposed. In the algorithm, each sampling time interval is divided into two subintervals to be considered according to the time delay and sampling period. The algorithm is not too expensive computationally and lends itself to be easily inserted into large simulation packages. The mathematical structure of the new discretization scheme is explored and described in detail. The performance of the proposed discretization procedure is evaluated by employing case studies. Various input signals, sampling rates, and time-delay values are considered to test the proposed method. The results demonstrate that the proposed discretization scheme is better than previous Taylor series method for nonlinear time-delay systems, especially when a large sampling period is inevitable
Real-Time Implementation of Nonlinear Optical Processing Functions.
1986-09-30
demonstrating that the memory is nonlinear and selective. The recording medium could be replaced with real-time media such as photorefractive crystals. Thicker...recording media Fi4 4. Schematic of experiment that d,.non* trated ,,pera have the added advantage of higher angular selectiv- "" . e e r aity. thus... geometrica snapes in contact ’A,.n a c-:’:ser ’Figure 51a’ ., and a spher:cal 4:verg.ng reference -eam Upion :"um’latlon of t -" c-’gram by the object beam
Reaching a consensus: a discrete nonlinear time-varying case
Saburov, M.; Saburov, K.
2016-07-01
In this paper, we have considered a nonlinear protocol for a structured time-varying and synchronous multi-agent system. By means of cubic triple stochastic matrices, we present an opinion sharing dynamics of the multi-agent system as a trajectory of a non-homogeneous system of cubic triple stochastic matrices. We show that the multi-agent system eventually reaches to a consensus if either of the following two conditions is satisfied: (1) every member of the group people has a positive subjective distribution on the given task after some revision steps or (2) all entries of some cubic triple stochastic matrix are positive.
The illustrated A brief history of time
Hawking, Stephen
1996-01-01
This is Stephen Hawking's updated, expanded and illustrated edition of his celebrated work which includes the most recent developments in the field, many of which were forecast by him. At the same time, he explains his complex theories through a fresh visual dimension. Over one hunded and fifty stunning colour illustrations have been specially commissioned for this purpose to help the reader understand what have become popular mythic images of our century, but which nonetheless remain difficult, abstract ideas to grasp. It includes a new introduction written specially for this edition.
Discrete-Time Nonlinear Control of VSC-HVDC System
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TianTian Qian
2015-01-01
Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.
Cycle slipping in nonlinear circuits under periodic nonlinearities and time delays
Smirnova, Vera; Proskurnikov, Anton; Utina, Natalia V.
2014-01-01
Phase-locked loops (PLL), Costas loops and other synchronizing circuits are featured by the presence of a nonlinear phase detector, described by a periodic nonlinearity. In general, nonlinearities can cause complex behavior of the system such multi-stability and chaos. However, even phase locking ma
Empirical intrinsic geometry for nonlinear modeling and time series filtering.
Talmon, Ronen; Coifman, Ronald R
2013-07-30
In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.
Linear and nonlinear dynamic systems in financial time series prediction
Directory of Open Access Journals (Sweden)
Salim Lahmiri
2012-10-01
Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.
A New Hybrid Methodology for Nonlinear Time Series Forecasting
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Mehdi Khashei
2011-01-01
Full Text Available Artificial neural networks (ANNs are flexible computing frameworks and universal approximators that can be applied to a wide range of forecasting problems with a high degree of accuracy. However, using ANNs to model linear problems have yielded mixed results, and hence; it is not wise to apply them blindly to any type of data. This is the reason that hybrid methodologies combining linear models such as ARIMA and nonlinear models such as ANNs have been proposed in the literature of time series forecasting. Despite of all advantages of the traditional methodologies for combining ARIMA and ANNs, they have some assumptions that will degenerate their performance if the opposite situation occurs. In this paper, a new methodology is proposed in order to combine the ANNs with ARIMA in order to overcome the limitations of traditional hybrid methodologies and yield more general and more accurate hybrid models. Empirical results with Canadian Lynx data set indicate that the proposed methodology can be a more effective way in order to combine linear and nonlinear models together than traditional hybrid methodologies. Therefore, it can be applied as an appropriate alternative methodology for hybridization in time series forecasting field, especially when higher forecasting accuracy is needed.
TIME LINE OF HISTORY OF HYPERTENSION TREATMENT
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Mohammad Golam Saklayen
2016-02-01
Full Text Available It is surprising that only about 50 years ago hypertension was considered an essential malady and not a treatable condition. Introduction of thiazide diuretics in late 50’s made some headway in successful treatment of hypertension and ambitious multicenter VA co-operative study (phase 1 and 2 started in 1964 for diastolic hypertension ranging between 90 to 129 mmHg and completed by 1971 established for the first time that treating diastolic hypertension reduced CV events like stroke and heart failure and improved mortality. In the following decade these results were confirmed for the wider US and Non-US population, including women and goal oriented BP treatment to diastolic 90 became the standard therapy recommendation. But isolated systolic hypertension (accounting for two thirds of the 70 million hypertensive population in USA alone was not considered treatable until 1991 when SHEP study (systolic hypertension in elderly program was completed and showed tremendous benefits of treating systolic BP over 160 mmHg using only a simple regimen using small dose Chlorthalidone with addition of Atenolol if needed. In the next 2 decades ALLHAT and other studies examined the comparability of outcomes with use of different classes and combinations of antihypertensive drugs. While diastolic BP goal was established as 90 in late 70’s and later confirmed by HOT study, the goal BP for systolic hypertension was not settled until very recently with completion of SPRINT study. ACCORD study showed no significant difference in outcome with sys 140 vs 120 in diabetics . But recently completed SPRINT study with somewhat similar protocol as in ACCORD but in nondiabetic, showed almost one quarter reduction in all-cause mortality and one-third reduction of CV events with systolic BP goal 120.
Finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems.
Kanno, Kazutaka; Uchida, Atsushi
2014-03-01
We introduce a method for the calculation of finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems. We apply the method to the Mackey-Glass model with time-delayed feedback. We investigate the standard deviation of the probability distribution of the finite-time Lyapunov exponents when the finite time or the delay time is changed. It is found that the standard deviation decreases in a power-law scaling with the exponent ∼0.5 as the finite time or the delay time is increased. Similar results are obtained for the finite-time Lyapunov spectrum.
Design of Nonlinear Circuits: The Linear Time-Varying Approach
Kuijstermans, F.C.M.
2003-01-01
Over the last years the ever-growing demand for higher performance has led to much interest in using nonlinear circuit concepts for electronic circuit design. For this we have to deal with analysis and synthesis of dynamic nonlinear circuits. This thesis proposes to handle the nonlinear design
Design of Nonlinear Circuits: The Linear Time-Varying Approach
Kuijstermans, F.C.M.
2003-01-01
Over the last years the ever-growing demand for higher performance has led to much interest in using nonlinear circuit concepts for electronic circuit design. For this we have to deal with analysis and synthesis of dynamic nonlinear circuits. This thesis proposes to handle the nonlinear design comp
Directory of Open Access Journals (Sweden)
Fei Chen
2013-01-01
Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.
Nonlinear Time Series Analysis in Earth Sciences - Potentials and Pitfalls
Kurths, Jürgen; Donges, Jonathan F.; Donner, Reik V.; Marwan, Norbert; Zou, Yong
2010-05-01
The application of methods of nonlinear time series analysis has a rich tradition in Earth sciences and has enabled substantially new insights into various complex processes there. However, some approaches and findings have been controversially discussed over the last decades. One reason is that they are often bases on strong restrictions and their violation may lead to pitfalls and misinterpretations. Here, we discuss three general concepts of nonlinear dynamics and statistical physics, synchronization, recurrence and complex networks and explain how to use them for data analysis. We show that the corresponding methods can be applied even to rather short and non-stationary data which are typical in Earth sciences. References Marwan, N., Romano, M., Thiel, M., Kurths, J.: Recurrence plots for the analysis of complex systems, Physics Reports 438, 237-329 (2007) Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks, Physics Reports 469, 93-153 (2008) Marwan, N., Donges, J.F., Zou, Y., Donner, R. and Kurths, J., Phys. Lett. A 373, 4246 (2009) Donges, J.F., Zou, Y., Marwan, N. and Kurths, J. Europhys. Lett. 87, 48007 (2009) Donner, R., Zou, Y., Donges, J.F., Marwan, N. and Kurths, J., Phys. Rev. E 81, 015101(R) (2010)
Nonlinear Aerodynamics-Structure Time Simulation for HALE Aircraft Design/Analysis Project
National Aeronautics and Space Administration — Time simulation of a nonlinear aerodynamics model (NA) developed at Virginia Tech coupled with a nonlinear structure model (NS) is proposed as a design/analysis...
Sahadevan, R.; Prakash, P.
2017-01-01
We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.
Ouari, Kamel; Rekioua, Toufik; Ouhrouche, Mohand
2014-01-01
In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.
Non-linear shape functions over time in the space-time finite element method
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Kacprzyk Zbigniew
2017-01-01
Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.
A time-domain method to generate artificial time history from a given reference response spectrum
Energy Technology Data Exchange (ETDEWEB)
Shin, Gang Sik [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of); Song, Oh Seop [Dept. of Mechanical Engineering, Chungnam National University, Daejeon (Korea, Republic of)
2016-06-15
Seismic qualification by test is widely used as a way to show the integrity and functionality of equipment that is related to the overall safety of nuclear power plants. Another means of seismic qualification is by direct integration analysis. Both approaches require a series of time histories as an input. However, in most cases, the possibility of using real earthquake data is limited. Thus, artificial time histories are widely used instead. In many cases, however, response spectra are given. Thus, most of the artificial time histories are generated from the given response spectra. Obtaining the response spectrum from a given time history is straightforward. However, the procedure for generating artificial time histories from a given response spectrum is difficult and complex to understand. Thus, this paper presents a simple time-domain method for generating a time history from a given response spectrum; the method was shown to satisfy conditions derived from nuclear regulatory guidance.
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
Directory of Open Access Journals (Sweden)
M. Finizio
Full Text Available Starting from a number of observables in the form of time-series of meteorological elements in various areas of the northern hemisphere, a model capable of fitting past records and predicting monthly vorticity time changes in the western Mediterranean is implemented. A new powerful statistical methodology is introduced (MARS in order to capture the non-linear dynamics of time-series representing the available 40-year history of the hemispheric circulation. The developed model is tested on a suitable independent data set. An ensemble forecast exercise is also carried out to check model stability in reference to the uncertainty of input quantities.
Key words. Meteorology and atmospheric dynamics · General circulation ocean-atmosphere interactions · Synoptic-scale meteorology
Global Format for Conservative Time Integration in Nonlinear Dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2014-01-01
equivalent static load steps, easily implemented in existing computer codes. The paper considers two aspects: representation of nonlinear internal forces in a form that implies energy conservation, and the option of an algorithmic damping with the purpose of extracting energy from undesirable high...... over the time step. This explicit formula is exact for structures with internal energy in the form of a polynomial in the displacement components of degree four. A fully general form follows by introducing an additional term based on a secant representation of the internal energy. The option......-frequency parts of the response. The energy conservation property is developed in two steps. First a fourth-order representation of the internal energy increment is obtained in terms of the mean value of the associated internal forces and an additional term containing the increment of the tangent stiffness matrix...
On Hamiltonian realization of time-varying nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper Investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingu-lar, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a nonsingular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.
Nonlinear Time Series Analysis of White Dwarf Light Curves
Jevtic, N.; Zelechoski, S.; Feldman, H.; Peterson, C.; Schweitzer, J.
2001-12-01
We use nonlinear time series analysis methods to examine the light intensity curves of white dwarf PG1351+489 obtained by the Whole Earth Telescope (WET). Though these methods were originally introduced to study chaotic systems, when a clear signature of determinism is found for the process generating an observable and it couples the active degrees of freedom of the system, then the notion of phase space provides a framework for exploring the system dynamics of nonlinear systems in general. With a pronounced single frequency, its harmonics and other frequencies of lower amplitude on a broadband background, the PG1351 light curve lends itself to the use of time delay coordinates. Our phase space reconstruction yields a triangular, toroidal three-dimensional shape. This differs from earlier results of a circular toroidal representation. We find a morphological similarity to a magnetic dynamo model developed for fast rotators that yields a union of both results: the circular phase space structure for the ascending portion of the cycle, and the triangular structure for the declining portion. The rise and fall of the dynamo cycle yield both different phase space representations and different correlation dimensions. Since PG1351 is known to have no significant fields, these results may stimulate the observation of light curves of known magnetic white dwarfs for comparison. Using other data obtained by the WET, we compare the phase space reconstruction of DB white dwarf PG1351 with that of GD 358 which has a more complex power spectrum. We also compare these results with those for PG1159. There is some general similarity between the results of the phase space reconstruction for the DB white dwarfs. As expected, the difference between the results for the DB white dwarfs and PG1159 is great.
A nonlinear correlation function for selecting the delay time in dynamical reconstructions
Aguirre, Luis Antonio
1995-02-01
Numerical results discussed in this paper suggest that a function which detects nonlinear correlations in time series usually indicates shorter correlation times than the linear autocorrelation function which is often used for this purpose. The nonlinear correlation function can also detect changes in the data which cannot be distinguished by the linear counterpart. This affects a number of approaches for the selection of the delay time used in the reconstruction of nonlinear dynamics from a single time series based on time delay coordinates.
Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control
Valenza, Gaetano; Citi, Luca; Garcia, Ronald G.; Taylor, Jessica Noggle; Toschi, Nicola; Barbieri, Riccardo
2017-01-01
The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson’s Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity. PMID:28218249
Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control
Valenza, Gaetano; Citi, Luca; Garcia, Ronald G.; Taylor, Jessica Noggle; Toschi, Nicola; Barbieri, Riccardo
2017-02-01
The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson’s Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity.
Energy Technology Data Exchange (ETDEWEB)
Spears, Robert Edward [Idaho National Lab. (INL), Idaho Falls, ID (United States); Coleman, Justin Leigh [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
methodology will be known as, NonLinear Soil-Structure Interaction (NLSSI). In general NLSSI analysis should provide a more accurate representation of the seismic demands on nuclear facilities their systems and components. INL, in collaboration with a Nuclear Power Plant Vender (NPP-V), will develop a generic Nuclear Power Plant (NPP) structural design to be used in development of the methodology and for comparison with SASSI. This generic NPP design has been evaluated for the INL soil site because of the ease of access and quality of the site specific data. It is now being evaluated for a second site at Vogtle which is located approximately 15 miles East-Northeast of Waynesboro, Georgia and adjacent to Savanna River. The Vogtle site consists of many soil layers spanning down to a depth of 1058 feet. The reason that two soil sites are chosen is to demonstrate the methodology across multiple soil sites. The project will drive the models (soil and structure) using successively increasing acceleration time histories with amplitudes. The models will be run in time domain codes such as ABAQUS, LS-DYNA, and/or ESSI and compared with the same models run in SASSI. The project is focused on developing and documenting a method for performing time domain, non-linear seismic soil structure interaction (SSI) analysis. Development of this method will provide the Department of Energy (DOE) and industry with another tool to perform seismic SSI analysis.
Time, Space and the History of Agricultural Landscapes
DEFF Research Database (Denmark)
Svenningsen, Stig Roar; Christensen, Andreas Aagaard
to the physical structure of landscapes has a fixed temporal nature depicting the landscape at time of record, often at different spatial scales. This creates a challenge for Environmental history of European agricultural landscapes to produce a framework, which can incorporate these differences in temporal...... and spatial scales together with traditional written sources. This paper investigates the potential of sources to the environmental history of the agricultural landscape across different spatial and temporal scales in a small case study of the landscape history of five parishes in Jutland, Denmark. The paper......Agricultural land use constitutes one of the main forces of anthropogenic change in most European countries, especially since the agricultural reforms in the beginning of the 19 th century. Researching the history of these landscapes is an important task in the present European environmental...
Nonlinear time-domain modeling of balanced-armature receivers
DEFF Research Database (Denmark)
Jensen, Joe; Agerkvist, Finn T.; Harte, James
2011-01-01
Nonlinear distortion added by the loudspeaker in a hearing aid lowers the signal-to-noise ratio and may degrade the hearing aid user's ability to understand speech. The balancedarmature- type loudspeakers, predominantly used in hearing aids, are inherently nonlinear devices, as any displacement o...
AUTO-EXTRACTING TECHNIQUE OF DYNAMIC CHAOS FEATURES FOR NONLINEAR TIME SERIES
Institute of Scientific and Technical Information of China (English)
CHEN Guo
2006-01-01
The main purpose of nonlinear time series analysis is based on the rebuilding theory of phase space, and to study how to transform the response signal to rebuilt phase space in order to extract dynamic feature information, and to provide effective approach for nonlinear signal analysis and fault diagnosis of nonlinear dynamic system. Now, it has already formed an important offset of nonlinear science. But, traditional method cannot extract chaos features automatically, and it needs man's participation in the whole process. A new method is put forward, which can implement auto-extracting of chaos features for nonlinear time series. Firstly, to confirm time delay τ by autocorrelation method; Secondly, to compute embedded dimension m and correlation dimension D;Thirdly, to compute the maximum Lyapunov index λmax; Finally, to calculate the chaos degree Dch of features extracting has important meaning to fault diagnosis of nonlinear system based on nonlinear chaos features. Examples show validity of the proposed method.
Carasso, Alfred S
2013-01-01
Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations. In this paper, an iterative procedure originating in spectroscopy in the 1930's, is adapted into a useful tool for solving a wide class of 2D nonlinear backward parabolic equations. In addition, previously unsuspected difficulties are uncovered that may preclude useful backward continuation in parabolic equations deviating too strongly from the linear, autonomous, self adjoint, canonical model. This paper explores backward continuation in selected 2D nonlinear equations, by creating fictitious blurred images obtained by using several sharp images as initial data in these equations, and capturing the corresponding solutions at some positive time T. Successful backward continuation from t=T to t = 0, would recover the original sharp image. Visual recognition provides meaningful evaluation of the degree of success or failure in the reconstructed solutions. Instructive examples are developed, illustrating the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred images are presented, with vastly different deblurring results. These examples indicate that how an image is nonlinearly blurred is critical, in addition to the amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the blurred images may be interpreted as visually expressing the results of novel stochastic processes.
Time Development in the Early History of Social Networks
DEFF Research Database (Denmark)
Bruun, Jesper; Bearden, Ian
2014-01-01
Studies of the time development of empirical networks usually investigate late stages where lasting connections have already stabilized. Empirical data on early network history are rare but needed for a better understanding of how social network topology develops in real life. Studying students w...
Mining the Twentieth Century's History from the Time Magazine Corpus
Kestemont, Mike; Karsdorp, F.B.; Düring, Marten
2014-01-01
In this paper we report on an explorative study of the history of the twentieth cen- tury from a lexical point of view. As data, we use a diachronic collection of 270,000+ English-language articles har- vested from the electronic archive of the well-known Time Magazine (1923–2006). We attempt to aut
Non-linear time series extreme events and integer value problems
Turkman, Kamil Feridun; Zea Bermudez, Patrícia
2014-01-01
This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included. Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basic understanding of nonlinear time ...
Nonlinear dynamics of wind waves: multifractal phase/time effects
Directory of Open Access Journals (Sweden)
R. H. Mellen
1994-01-01
Full Text Available In addition to the bispectral coherence method, phase/time analysis of analytic signals is another promising avenue for the investigation of phase effects in wind waves. Frequency spectra of phase fluctuations obtained from both sea and laboratory experiments follow an F-β power law over several decades, suggesting that a fractal description is appropriate. However, many similar natural phenomena have been shown to be multifractal. Universal multifractals are quantified by two additional parameters: the Lévy index 0 α 2 for the type of multifractal and the co-dimension 0 C1 1 for intermittence. The three parameters are a full statistical measure the nonlinear dynamics. Analysis of laboratory flume data is reported here and the results indicate that the phase fluctuations are 'hard multifractal' (α > 1. The actual estimate is close to the limiting value α = 2, which is consistent with Kolmogorov's lognormal model for turbulent fluctuations. Implications for radar and sonar backscattering from the sea surface are briefly considered.
Assessing Spontaneous Combustion Instability with Nonlinear Time Series Analysis
Eberhart, C. J.; Casiano, M. J.
2015-01-01
Considerable interest lies in the ability to characterize the onset of spontaneous instabilities within liquid propellant rocket engine (LPRE) combustion devices. Linear techniques, such as fast Fourier transforms, various correlation parameters, and critical damping parameters, have been used at great length for over fifty years. Recently, nonlinear time series methods have been applied to deduce information pertaining to instability incipiency hidden in seemingly stochastic combustion noise. A technique commonly used in biological sciences known as the Multifractal Detrended Fluctuation Analysis has been extended to the combustion dynamics field, and is introduced here as a data analysis approach complementary to linear ones. Advancing, a modified technique is leveraged to extract artifacts of impending combustion instability that present themselves a priori growth to limit cycle amplitudes. Analysis is demonstrated on data from J-2X gas generator testing during which a distinct spontaneous instability was observed. Comparisons are made to previous work wherein the data were characterized using linear approaches. Verification of the technique is performed by examining idealized signals and comparing two separate, independently developed tools.
Time-domain seismic reliability of nonlinear structures
Indian Academy of Sciences (India)
Achintya Haldar; Jungwon Huh; Ali Mehrabian
2006-08-01
A novel reliability analysis technique is presented to estimate the reliability of real structural systems. Its unique feature is that the dynamic loadings can be applied in time domain. It is a nonlinear stochastic ﬁnite element logarithm combined with the response surface method (RSM). It generates the response surface around the most probable failure point and incorporates information of the distribution of the random variables in the RSM formulation. It is veriﬁed using the Monte Carlo simulation technique, and is found to be very efﬁcient and accurate. Most sources of nonlinearlity and uncertainty can be explicitly incorporated in the formulation. The ﬂexibility of connections, represented by moment-relative rotation $(M–\\theta )$ curves, is addressed. After the Northridge earthquake of 1994, several improved steel connections were proposed. Structural Sesimic Design Associates (SSDA) tested several full-scale proprietory slotted web beam–column connections. The authors suggested $(M–\\theta )$ curves for this connection using actual test data. Behaviours of steel frames, assuming the connections are fully restrained, partially restrained, consisting of pre- and post-Northridge connections are evaluated and compared. Desirable features of the post-Northridge connections observed during testing are analytically conﬁrmed. Laterally weak steel frame is then strengthened with concrete shear walls. Capabilities and the advanced nature of the method are demonstrated with the help of realistic examples.
Non-linear Imaging using an Experimental Synthetic Aperture Real Time Ultrasound Scanner
DEFF Research Database (Denmark)
Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt
2011-01-01
This paper presents the first non-linear B-mode image of a wire phantom using pulse inversion attained via an experimental synthetic aperture real-time ultrasound scanner (SARUS). The purpose of this study is to implement and validate non-linear imaging on SARUS for the further development of new...... non-linear techniques. This study presents non-linear and linear B-mode images attained via SARUS and an existing ultrasound system as well as a Field II simulation. The non-linear image shows an improved spatial resolution and lower full width half max and -20 dB resolution values compared to linear...
Neural network-based H∞ filtering for nonlinear systems with time-delays
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A novel H∞ design methodology for a neural network-based nonlinear filtering scheme is addressed.Firstly,neural networks are employed to approximate the nonlinearities.Next,the nonlinear dynamic system is represented by the mode-dependent linear difference inclusion (LDI).Finally,based on the LDI model,a neural network-based nonlinear filter (NNBNF) is developed to minimize the upper bound of H∞ gain index of the estimation error under some linear matrix inequality (LMI) constraints.Compared with the existing nonlinear filters,NNBNF is time-invariant and numerically tractable.The validity and applicability of the proposed approach are successfully demonstrated in an illustrative example.
Cosmological history in York time: inflation and perturbations
Roser, Philipp
2016-01-01
The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. We show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more broadly and contrast it with the conventional cosmological timeline.
From Mystics to Modern Times: A History of Craniotomy & Religion.
Newman, W Christopher; Chivukula, Srinivas; Grandhi, Ramesh
2016-08-01
Neurosurgical treatment of diseases dates back to prehistoric times and the trephination of skulls for various maladies. Throughout the evolution of trephination, surgery and religion have been intertwined to varying degrees, a relationship that has caused both stagnation and progress. From its mystical origins in prehistoric times to its scientific progress in ancient Egypt and its resurgence as a well-validated surgical technique in modern times, trephination has been a reflection of the cultural and religious times. Herein we present a brief history of trephination as it relates religion, culture, and the evolution of neurosurgery. Copyright © 2016 Elsevier Inc. All rights reserved.
Cosmological history in York time: inflation and perturbations
Roser, Philipp; Valentini, Antony
2017-02-01
The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. While the physics is, of course, observationally equivalent, we show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more broadly and contrast it with the conventional cosmological timeline.
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS:TIME-FREQUENCY FILTERING AND SKELETON CURVES
Institute of Scientific and Technical Information of China (English)
王丽丽; 张景绘
2001-01-01
The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O . F nonlinear system.A masking operator on definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system ( GSLS ). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. More over, an identification method is proposed through the skeleton curves and the time frequency filtering technique.
Global exponential stabilisation of a class of nonlinear time-delay systems
Benabdallah, Amel; Echi, Nadhem
2016-12-01
This paper deals with the state and output feedback stabilisation problems for a family of nonlinear time-delay systems satisfying some relaxed triangular-type condition. The delay is supposed to be constant. Parameter-dependent control laws are used to compensate for the nonlinearities. Based on the Lyapunov-Krasovskii functionals, global exponential stability of the closed-loop systems is achieved. Finally, an extension to nonlinear time-varying delay systems is given.
van der Male, Pim; van Dalen, Karel N.; Metrikine, Andrei V.
2016-11-01
Existing models for the analysis of offshore wind turbines account for the aerodynamic action on the turbine rotor in detail, requiring a high computational price. When considering the foundation of an offshore wind turbine, however, a reduced rotor model may be sufficient. To define such a model, the significance of the nonlinear velocity and history dependency of the aerodynamic force on a rotating blade should be known. Aerodynamic interaction renders the dynamics of a rotating blade in an ambient wind field nonlinear in terms of the dependency on the wind velocity relative to the structural motion. Moreover, the development in time of the aerodynamic force does not follow the flow velocity instantaneously, implying a history dependency. In addition, both the non-uniform blade geometry and the aerodynamic interaction couple the blade motions in and out of the rotational plane. Therefore, this study presents the Euler-Bernoulli formulation of a twisted rotating blade connected to a rigid hub, excited by either instantaneous or history-dependent aerodynamic forces. On this basis, the importance of the history dependency is determined. Moreover, to assess the nonlinear contributions, both models are linearized. The structural response is computed for a stand-still and a rotating blade, based on the NREL 5-MW turbine. To this end, the model is reduced on the basis of its first three free-vibration mode shapes. Blade tip response predictions, computed from turbulent excitation, correctly account for both modal and directional couplings, and the added damping resulting from the dependency of the aerodynamic force on the structural motion. Considering the deflection of the blade tip, the history-dependent and the instantaneous force models perform equally well, providing a basis for the potential use of the instantaneous model for the rotor reduction. The linearized instantaneous model provides similar results for the rotating blade, indicating its potential
Prandtl-Ishlinskii hysteresis models for complex time dependent hysteresis nonlinearities
Al Janaideh, M.; Krejčí, P
2012-01-01
We introduce a new class of time dependent hysteresis models by combining the time dependent Prandtl–Ishlinskii model with functional nonlinearities. This combination improves the capability of the time dependent Prandtl–Ishlinskii model to characterize a class of complex time dependent hysteresis nonlinearities in smart actuators. The analytical inversion for the proposed time dependent hysteresis model is also presented in order to extend the inversion algorithm of the inverse time dependen...
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched bet
A neural architecture for nonlinear adaptive filtering of time series
DEFF Research Database (Denmark)
Hoffmann, Nils; Larsen, Jan
1991-01-01
A neural architecture for adaptive filtering which incorporates a modularization principle is proposed. It facilitates a sparse parameterization, i.e. fewer parameters have to be estimated in a supervised training procedure. The main idea is to use a preprocessor which determines the dimension...... of the input space and can be designed independently of the subsequent nonlinearity. Two suggestions for the preprocessor are presented: the derivative preprocessor and the principal component analysis. A novel implementation of fixed Volterra nonlinearities is given. It forces the boundedness...
Sir Clive Granger’s contributions to nonlinear time series and econometrics
DEFF Research Database (Denmark)
Terasvirta, Timo
Clive Granger had a wide range of reseach interests and has worked in a number of areas. In this work the focus is on his contributions to nonlinear time series models and modelling. Granger's contributions to a few other aspects of nonlinearity are reviewed as well.......Clive Granger had a wide range of reseach interests and has worked in a number of areas. In this work the focus is on his contributions to nonlinear time series models and modelling. Granger's contributions to a few other aspects of nonlinearity are reviewed as well....
Global adaptive output feedback control for a class of nonlinear time-delay systems.
Zhai, Jun-yong; Zha, Wen-ting
2014-01-01
This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.
System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time
DEFF Research Database (Denmark)
Sun, Zhen; Yang, Zhenyu
2011-01-01
. In order to identify these parameters in an online manner, the considered system is discretized at first. Then, the nonlinear FOPDT identification problem is formulated as a stochastic Mixed Integer Non-Linear Programming problem, and an identification algorithm is proposed by combining the Branch......An on-line iterative method of system identification for a kind of nonlinear FOPDT system is proposed in the paper. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its dead time depends on the input signal and the other parameters are time dependent...
Laurendeau, Aurore; Bonilla, Luis Fabian
2012-01-01
For earthquake-resistant design, engineering seismologists employ time-history analysis for nonlinear simulations. The nonstationary stochastic method previously developed by Pousse et al. (2006) has been updated. This method has the advantage of being both simple, fast and taking into account the basic concepts of seismology (Brune's source, realistic time envelope function, nonstationarity and ground-motion variability). Time-domain simulations are derived from the signal spectrogram and depend on few ground-motion parameters: Arias intensity, significant relative duration and central frequency. These indicators are obtained from empirical attenuation equations that relate them to the magnitude of the event, the source-receiver distance, and the site conditions. We improve the nonstationary stochastic method by using new functional forms (new surface rock dataset, analysis of both intra-event and inter-event residuals, consideration of the scaling relations and VS30), by assessing the central frequency with...
Response time in adults with a history of language difficulties.
Miller, Carol A; Poll, Gerard H
2009-01-01
The purpose of the study was to investigate speed of processing in college students with a history of problems with language. Affected individuals (n=16) were identified through a self-reported history of language and/or reading difficulties, and compared to a group of 16 unaffected individuals. Measures of language ability and a battery of response time tasks were administered. Results showed that the affected group had lower language performance and slower response time than the unaffected group. Better language performance was associated with faster response time, and this relationship was stronger in the affected group. These findings are consistent with the literature showing that language impairment often persists into adulthood. Further investigation of the relation between processing speed and language ability may help describe vulnerabilities for adults with language problems, as well as ways to promote compensation for those vulnerabilities. Readers will (1) increase understanding of associations between processing speed and language in children and adults; (2) become familiar with a method for assessing processing speed; and (3) increase understanding of possible vulnerabilities in adults with a history of language and/or reading problems.
On the ?2-stability of time-varying linear and nonlinear discrete-time MIMO systems
Institute of Scientific and Technical Information of China (English)
Y.V.VENKATESH
2014-01-01
New conditions are derived for the 2-stability of time-varying linear and nonlinear discrete-time multiple-input multiple-output (MIMO) systems, having a linear time time-invariant block with the transfer function Γ(z), in negative feedback with a matrix of periodic/aperiodic gains A(k),k =0,1,2,. . . and a vector of certain classes of non-monotone/monotone nonlinearitiesϕ( · ), without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features: i) They involve the positive definiteness of the real part (as evaluated on |z| = 1) of the product of Γ(z) and a matrix multiplier function of z. ii) For periodic A(k), one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A(k), but for aperiodic A(k), which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of (A(k+1),A(k)),k=1,2,. . . . iii) They are distinct from and less restrictive than recent results in the literature.
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Sachdev, PL
2010-01-01
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions
Grigoryeva, Lyudmila; Henriques, Julie; Larger, Laurent; Ortega, Juan-Pablo
2014-07-01
Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs. Copyright © 2014 Elsevier Ltd. All rights reserved.
Hashemi, Mahnaz; Ghaisari, Jafar; Askari, Javad
2015-07-01
This paper investigates an adaptive controller for a class of Multi Input Multi Output (MIMO) nonlinear systems with unknown parameters, bounded time delays and in the presence of unknown time varying actuator failures. The type of considered actuator failure is one in which some inputs may be stuck at some time varying values where the values, times and patterns of the failures are unknown. The proposed approach is constructed based on a backstepping design method. The boundedness of all the closed-loop signals is guaranteed and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark and a chemical reactor system. The simulation results show the effectiveness of the proposed method.
Nonlinear Analysis of Spur Gear Pair with Time-varying Mesh Stiffness
Rao T. V. V. L. N.; Awang M.; Lias M. R.; Rani A. M. A.
2014-01-01
This study presents nonlinear analysis of single degree of freedom spur gear pair with time-varying mesh stiffness. The backlash is approximated using nonlinear term. The periodic steady-state solutions of the nonlinear system are obtained by closed-form expressions using the method of multiple scales. The stability and forced vibration response of the gear system are analyzed. The effect of mesh stiffness variation on the amplitude parameter of nondimensional dynamic transmission error for p...
Time-Periodic Solution of a 2D Fourth-Order Nonlinear Parabolic Equation
Indian Academy of Sciences (India)
Xiaopeng Zhao; Changchun Liu
2014-08-01
By using the Galerkin method, we study the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a fourth-order nonlinear parabolic equation in 2D case.
Nonlinear Time Reversal Acoustic Method of Friction Stir Weld Assessment Project
National Aeronautics and Space Administration — The goal of the project is demonstration of the feasibility of Friction Stir Weld (FSW) assessment by novel Nonlinear Time Reversal Acoustic (TRA) method. Time...
Time: The Biggest Pattern in Natural History Research
Gontier, Nathalie
2016-10-01
We distinguish between four cosmological transitions in the history of Western intellectual thought, and focus on how these cosmologies differentially define matter, space and time. We demonstrate that how time is conceptualized significantly impacts a cosmology's notion on causality, and hone in on how time is conceptualized differentially in modern physics and evolutionary biology. The former conflates time with space into a single space-time continuum and focuses instead on the movement of matter, while the evolutionary sciences have a tradition to understand time as a given when they cartography how organisms change across generations over or in time, thereby proving the phenomenon of evolution. The gap becomes more fundamental when we take into account that phenomena studied by chrono-biologists demonstrate that numerous organisms, including humans, have evolved a "sense" of time. And micro-evolutionary/genetic, meso-evolutionary/developmental and macro-evolutionary phenomena including speciation and extinction not only occur by different evolutionary modes and at different rates, they are also timely phenomena that follow different periodicities. This article focusses on delineating the problem by finding its historical roots. We conclude that though time might be an obsolete concept for the physical sciences, it is crucial for the evolutionary sciences where evolution is defined as the change that biological individuals undergo in/over or through time.
Time and History in Hegel’s Phenomenology of Spirit
Directory of Open Access Journals (Sweden)
Luis Mariano De La Maza
2007-04-01
Full Text Available Resumen:En este artículo se presenta una interpretación de las tesis fundamentales de Hegel en la Fenomenología del Espíritu acerca de la relación entre tiempo, historia y filosofía especulativa o ciencia. Para Hegel la formación de la conciencia individual hacia la ciencia se conecta con la historia universal y el concepto de la historia es inseparable del concepto del espíritu. Se distinguen los distintos sentidos del tiempo en la Fenomenología para centrar la atención principalmente en uno de ellos, que corresponde a la organización fenomenológico-conceptual de la historia. Finalmente, se ofrece una reflexión sobre la cuestión más general de la relación entre filosofía y temporalidad desde una perspectiva actual.Abstract:This article offers an interpretation of Hegel's fundamental theses in the Phenomenology of spirit concerning the relationship between time, history and speculative philosophy or science. For Hegel, the formation of individual consciousness is connected to world history, and the concept of history is inseparable from the concept of spirit. The different senses of time in the Phenomenology are distinguished, and special attention is given to one of them, the phenomenological-conceptual organization of history. Finally, some thoughts are provided on the more general question of the relationship between philosophy and temporality from a contemporary point of view.
Directory of Open Access Journals (Sweden)
Meng-Meng Jiang
2016-01-01
Full Text Available Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.
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...
Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
Yang, Baiyuan; Hu, QiangLin; Yu, XiaoGuang
2016-01-01
We propose a mechanism for realization of exact control of parity-time (PT) symmetry by using a periodically modulated nonlinear optical coupler with balanced gain and loss. It is shown that for certain appropriately chosen values of the modulation parameters, we can construct a family of exact analytical solutions for the two-mode equations describing the dynamics of such nonlinear couplers. These exact solutions give explicit examples that allow us to precisely manipulate the system from nonlinearity-induced symmetry breaking to PT symmetry, thus providing an analytical approach to the all-optical signal control in nonlinear PT-symmetric structures.
Nonlinear time series theory, methods and applications with R examples
Douc, Randal; Stoffer, David
2014-01-01
FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre
Wideband nonlinear time reversal seismo-acoustic method for landmine detection.
Sutin, Alexander; Libbey, Brad; Fillinger, Laurent; Sarvazyan, Armen
2009-04-01
Acoustic and seismic waves provide a method to localize compliant mines by vibrating the top plate and a thin soil layer above the mine. This vibration is mostly linear, but also includes a small nonlinear deviation. The main goal of this paper is to introduce a method of processing that uses phase-inversion to observe nonlinear effects in a wide frequency band. The method extracts a nonlinear part of surface velocity from two similar broadcast signals of opposite sign by summing and cancelling the linear components and leaving the nonlinear components. This phase-inversion method is combined with time reversal focusing to provide increased seismic vibration and enhance the nonlinear effect. The experiments used six loudspeakers in a wood box placed over sand in which inert landmines were buried. The nonlinear surface velocity of the sand with a mine compared to the sand without a mine was greater as compared to a linear technique.
Conceptualizing time preference: a life-history analysis.
Copping, Lee T; Campbell, Anne; Muncer, Steven
2014-09-29
Life-history theory (LHT) has drawn upon the concept of "time preference" as a psychological mechanism for the development of fast and slow strategies. However, the conceptual and empirical nature of this mechanism is ill-defined. This study compared four traits commonly used as measures of "time preference" (impulsivity, sensation seeking, future orientation and delay discounting) and evaluated their relationship to variables associated with life-history strategies (aggressive behavior and mating attitudes, biological sex, pubertal timing, victimization, and exposure to aggression in the environment). Results indicated that only sensation seeking consistently showed all the predicted associations, although impulsivity, future orientation, and delay discounting showed some significant associations. A unidimensional higher-order factor of "time preference" did not adequately fit the data and lacked structural invariance across age and sex, suggesting that personality traits associated with LHT do not represent a global trait. We discuss the use of personality traits as measures in LHT and suggest that greater caution and clarity is required when conceptualizing this construct in future work.
Directory of Open Access Journals (Sweden)
Mourad Kchaou
2017-01-01
Full Text Available This paper addresses the problem of sliding mode control (SMC design for a class of uncertain switched descriptor systems with state delay and nonlinear input. An integral sliding function is designed and an adaptive sliding mode controller for the reaching motion is then synthesised such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. Moreover, based on a new Lyapunov-Krasovskii functional, a delay-dependent sufficient condition is established such that the admissibility as well as the H∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delay, external disturbances, and nonlinear input which comprises dead-zones and/or sector nonlinearities. The major contributions of this paper of this approach include (i the closed-loop system exhibiting strong robustness against nonlinear dynamics and (ii the control scheme enjoying the chattering-free characteristic. Finally, two representative examples are given to illustrate the theoretical developments.
H∞ Control for Nonlinear Stochastic Systems with Time-Delay and Multiplicative Noise
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Ming Gao
2015-01-01
Full Text Available This paper studies the infinite horizon H∞ control problem for a general class of nonlinear stochastic systems with time-delay and multiplicative noise. The exponential/asymptotic mean square H∞ control design of delayed nonlinear stochastic systems is presented by solving Hamilton-Jacobi inequalities. Two numerical examples are provided to show the effectiveness of the proposed design method.
Analysis of nonlinear systems with time varying inputs and its application to gain scheduling
Directory of Open Access Journals (Sweden)
J.-T. Lim
1996-01-01
Full Text Available An analytical framework for analysis of a class of nonlinear systems with time varying inputs is presented. It is shown that the trajectories of the transformed nonlinear systems are uniformly bounded with an ultimate bound under certain conditions shown in this paper. The result obtained is useful for applications, in particular, analysis and design of gain scheduling.
OSCILLATION FOR NONLINEAR SECOND-ORDER DYNAMIC EQUATIONS ON TIME SCALES
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references.
Design of nonlinear discrete-time controllers using a parameter space sampling procedure
Young, G. E.; Auslander, D. M.
1983-01-01
The design of nonlinear discrete-time controllers is investigated where the control algorithm assumes a special form. State-dependent control actions are obtained from tables whose values are the design parameters. A new design methodology capable of dealing with nonlinear systems containing parameter uncertainty is used to obtain the controller design. Various controller strategies are presented and illustrated through an example.
Absolute stability of nonlinear systems with time delays and applications to neural networks
Directory of Open Access Journals (Sweden)
Xinzhi Liu
2001-01-01
Full Text Available In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.
Long-time asymptotics for the defocusing integrable discrete nonlinear Schr\\"odinger equation
YAMANE, HIDESHI
2011-01-01
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schr\\"odinger equation by means of the Deift-Zhou nonlinear steepest descent method. The leading term is a sum of two terms that oscillate with decay of order $t^{-1/2}$.
Long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation
YAMANE, HIDESHI
2014-01-01
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation of Ablowitz-Ladik by means of the inverse scattering transform and the Deift-Zhou nonlinear steepest descent method. The leading part is a sum of two terms that oscillate with decay of order $t^{-1/2}$.
Finite time blow-up for a wave equation with a nonlocal nonlinearity
Fino, Ahmad; Georgiev, Vladimir
2010-01-01
In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear forcing term.
Analysis of Nonlinear Discrete Time Active Control System with Boring Chatter
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Shujing Wu
2014-03-01
Full Text Available In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS was proposed by Okubo (1985. In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k║&le&alpha+&betaβ║v (k║&gamma, where &alpha&ge0, &beta&ge0, 0&le&gamma&le1. When 0&le&gamma&le1. It is easy to extend the method to discrete time systems. But in the case &gamma = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.
Synthesis of nonlinear discrete control systems via time-delay affine Takagi-Sugeno fuzzy models.
Chang, Wen-Jer; Chang, Wei
2005-04-01
The affine Takagi-Sugeno (TS) fuzzy model played a more important role in nonlinear control because it can be used to approximate the nonlinear systems more than the homogeneous TS fuzzy models. Besides, it is known that the time delays exist in physical systems and the previous works did not consider the time delay effects in the analysis of affine TS fuzzy models. Hence a parallel distributed compensation based fuzzy controller design issue for discrete time-delay affine TS fuzzy models is considered in this paper. The time-delay effect is considered in the discrete affine TS fuzzy models and the stabilization issue is developed for the nonlinear time-delay systems. Finally, a numerical simulation for a time-delayed nonlinear truck-trailer system is given to show the applications of the present approach.
An internally consistent gamma ray burst time history phenomenology
Cline, T. L.
1985-01-01
A phenomenology for gamma ray burst time histories is outlined. Order of their generally chaotic appearance is attempted, based on the speculation that any one burst event can be represented above 150 keV as a superposition of similarly shaped increases of varying intensity. The increases can generally overlap, however, confusing the picture, but a given event must at least exhibit its own limiting characteristic rise and decay times if the measurements are made with instruments having adequate temporal resolution. Most catalogued observations may be of doubtful or marginal utility to test this hypothesis, but some time histories from Helios-2, Pioneer Venus Orbiter and other instruments having one-to several-millisecond capabilities appear to provide consistency. Also, recent studies of temporally resolved Solar Maximum Mission burst energy spectra are entirely compatible with this picture. The phenomenology suggested here, if correct, may assist as an analytic tool for modelling of burst processes and possibly in the definition of burst source populations.
Tower bells and time zones, a history of synchronization
Sigismondi, Costantino
2014-01-01
The Astrarium made by Jacopo Dondi dell'Orologio in Padua in 1344 is one of the first public horologia in the World, their public utility is also shown through the history of the tower bell of Our Lady of Suffragio in Turin, made by the mathematician Francesco Fa\\`a di Bruno in 1866. The tower bell of St. Anthony in Lanciano made by Antonio Cibotti was inaugurated by the Pope Paul VI in 1973 through a radio impulse, and now many tower bells are radio synchronized to the Central European Time within a single second of accuracy.
On history and policy: Time in the age of neoliberalism
Boldizzoni, Francesco
2013-01-01
It is often said that history matters, but these words are often little more than a hollow statement. In the aftermath of the Great Recession, the view that the economy is a mechanical toy that can be fixed using a few simple tools has continued to be held by economists and policy makers and echoed by the media. The paper addresses the origins of this unfortunate belief, inherent to neoliberalism, and what can be done to bring time back into public discourse. Es heißt, dass Geschichte wich...
Real-Time History of the Cosmological Electroweak Phase Transition
Kurki-Suonio, H
1996-01-01
We study numerically the real-time history of the cosmological electrow= eak phase transition, as it may take place in the Standard Model or in MSSM f= or m_H < m_W according to recent lattice results. We follow the nucleated bubble= s from the initial stages of acceleration and rapid growth, through collisions w= ith compression waves resulting in slowing down and reheating to T_c, until t= he final stages of slow growth and evaporation. We find that collisions with compression waves may make the bubble walls oscillate in the radial direc= tion, and that reheating to T_c takes generically place.
Pola, Giordano; Di Benedetto, Maria Domenica
2010-01-01
Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time-varying delay signals and we propose one approach to the control design of such systems, which is based on the construction of symbolic models. Symbolic models are abstract descriptions of dynamical systems in which one symbolic state and one symbolic input correspond to an aggregate of states and an aggregate of inputs. We first introduce the notion of incremental input-delay-to-state stability and characterize it by means of Liapunov-Krasovskii functionals. We then derive sufficient conditions for the existence of symbolic models that are shown to be alternating approximately bisimilar to the original system. Further results are also derived which prove the computability of the proposed symbolic models in a finite number of steps.
Adaptive robust stabilisation for a class of uncertain nonlinear time-delay dynamical systems
Wu, Hansheng
2013-02-01
The problem of adaptive robust stabilisation is considered for a class of uncertain nonlinear dynamical systems with multiple time-varying delays. It is assumed that the upper bounds of the nonlinear delayed state perturbations are unknown and that the time-varying delays are any non-negative continuous and bounded functions which do not require that their derivatives have to be less than one. In particular, it is only required that the nonlinear uncertainties, which can also include time-varying delays, are bounded in any non-negative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain nonlinear time-delay systems, a new method is presented whereby a class of continuous memoryless adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain nonlinear time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. Finally, as an application, an uncertain nonlinear time-delay ecosystem with two competing species is given to demonstrate the validity of the results.
Analytical approximate solution for nonlinear space-time fractional Klein-Gordon equation
Institute of Scientific and Technical Information of China (English)
Khaled A.Gepreel; Mohamed S.Mohamed
2013-01-01
The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space-time fractional derivatives Klein-Gordon equation.The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space-time fractional derivatives KleinGordon equation.This method introduces a promising tool for solving many space-time fractional partial differential equations.This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.
EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
房少梅; 郭柏灵
2003-01-01
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
Faes, Luca; Zhao, He; Chon, Ki H; Nollo, Giandomenico
2009-03-01
We propose a method to extend to time-varying (TV) systems the procedure for generating typical surrogate time series, in order to test the presence of nonlinear dynamics in potentially nonstationary signals. The method is based on fitting a TV autoregressive (AR) model to the original series and then regressing the model coefficients with random replacements of the model residuals to generate TV AR surrogate series. The proposed surrogate series were used in combination with a TV sample entropy (SE) discriminating statistic to assess nonlinearity in both simulated and experimental time series, in comparison with traditional time-invariant (TIV) surrogates combined with the TIV SE discriminating statistic. Analysis of simulated time series showed that using TIV surrogates, linear nonstationary time series may be erroneously regarded as nonlinear and weak TV nonlinearities may remain unrevealed, while the use of TV AR surrogates markedly increases the probability of a correct interpretation. Application to short (500 beats) heart rate variability (HRV) time series recorded at rest (R), after head-up tilt (T), and during paced breathing (PB) showed: 1) modifications of the SE statistic that were well interpretable with the known cardiovascular physiology; 2) significant contribution of nonlinear dynamics to HRV in all conditions, with significant increase during PB at 0.2 Hz respiration rate; and 3) a disagreement between TV AR surrogates and TIV surrogates in about a quarter of the series, suggesting that nonstationarity may affect HRV recordings and bias the outcome of the traditional surrogate-based nonlinearity test.
Nonlinear Time Series Model for Shape Classification Using Neural Networks
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A complex nonlinear exponential autoregressive (CNEAR) model for invariant feature extraction is developed for recognizing arbitrary shapes on a plane. A neural network is used to calculate the CNEAR coefficients. The coefficients, which constitute the feature set, are proven to be invariant to boundary transformations such as translation, rotation, scale and choice of starting point in tracing the boundary. The feature set is then used as the input to a complex multilayer perceptron (C-MLP) network for learning and classification. Experimental results show that complicated shapes can be accurately recognized even with the low-order model and that the classification method has good fault tolerance when noise is present.
Neural-network-based approximate output regulation of discrete-time nonlinear systems.
Lan, Weiyao; Huang, Jie
2007-07-01
The existing approaches to the discrete-time nonlinear output regulation problem rely on the offline solution of a set of mixed nonlinear functional equations known as discrete regulator equations. For complex nonlinear systems, it is difficult to solve the discrete regulator equations even approximately. Moreover, for systems with uncertainty, these approaches cannot offer a reliable solution. By combining the approximation capability of the feedforward neural networks (NNs) with an online parameter optimization mechanism, we develop an approach to solving the discrete nonlinear output regulation problem without solving the discrete regulator equations explicitly. The approach of this paper can be viewed as a discrete counterpart of our previous paper on approximately solving the continuous-time nonlinear output regulation problem.
Institute of Scientific and Technical Information of China (English)
顾成奎; 王正欧; 孙雅明
2003-01-01
A new method for identifying nonlinear time-varying systems with unknown structure is presented. The method extends the application area of basis sequence identification. The essential idea is to utilize the learning and nonlinear approximating ability of neural networks to model the non-linearity of the system, characterize time-varying dynamics of the system by the time-varying parametric vector of the network, then the parametric vector of the network is approximated by a weighted sum of known basis sequences. Because of black-box modeling ability of neural networks, the presented method can identify nonlinear time-varying systems with unknown structure. In order to improve the real-time capability of the algorithm, the neural network is trained by a simple fast learning algorithm based on local least squares presented by the authors. The effectiveness and the performance of the method are demonstrated by some simulation results.
Time-adaptive and history-adaptive multicriterion routing in stochastic, time-dependent networks
DEFF Research Database (Denmark)
Pretolani, Daniele; Nielsen, Lars Relund; Andersen, Kim Allan
2009-01-01
We compare two different models for multicriterion routing in stochastic time-dependent networks: the classic "time-adaptive'' model and the more flexible "history-adaptive'' one. We point out several properties of the sets of efficient solutions found under the two models. We also devise a metho...
El tiempo de la historia The time of history
Directory of Open Access Journals (Sweden)
Montserrat Galceran
2000-01-01
Full Text Available Una indagación a partir de la idea general de historia formulada por Vico sirve de cauce para reinterpretar el modo como Marx trata la noción general de historia, entendiéndola no como continuidad de unos sistemas productivos por otros, sino como génesis de las condiciones de unos en los elementos integrantes de otros. Se señala que Althusser ha sido el primer marxista en comprender esa complejidad y en abordar el carácter compuesto del tiempo histórico en Marx. Se cierra con una pequeña reflexión en torno a la peculiaridad de la "idea de tiempo" y a su construcciónAn inquiry from Vico's formulation of the general idea of history leads to a reinterpretation of the way Marx deals with the general notion of "history", which is not understood as the linear continuity of different production systems, but as the genesis of some systems' conditions from others' integral elements. It is singled out that Althusser has been the first Marxist who fully understood this complexity and the first who undertook the composite character of Marx's historical time. The article closes on some reflections on the singularity of the "Idea of Time" and its construction.
Time Development in the Early History of Social Networks
DEFF Research Database (Denmark)
Bruun, Jesper; Bearden, Ian
2014-01-01
Studies of the time development of empirical networks usually investigate late stages where lasting connections have already stabilized. Empirical data on early network history are rare but needed for a better understanding of how social network topology develops in real life. Studying students who...... are beginning their studies at a university with no or few prior connections to each other offers a unique opportunity to investigate the formation and early development of link patterns and community structure in social networks. During a nine week introductory physics course, first year physics students were...... asked to identify those with whom they communicated about problem solving in physics during the preceding week. We use these students' self reports to produce time dependent student interaction networks. We investigate these networks to elucidate possible effects of different student attributes in early...
Non-linear time series analysis: methods and applications to atrial fibrillation.
Hoekstra, B P; Diks, C G; Allessie, M A; Degoede, J
2001-01-01
We apply methods from non-linear statistical time series analysis to characterize electrograms of atrial fibrillation. These are based on concepts originating from the theory of non-linear dynamical systems and use the empirical reconstruction density in reconstructed phase space. Application of these methods is not restricted to deterministic chaos but is valid in a general time series context. We illustrate this by applying three recently proposed non-linear time series methods to fibrillation electrograms: 1) a test for time reversibility in atrial electrograms during paroxysmal atrial fibrillation in patients; 2) a test to detect differences in the dynamical behaviour during the pharmacological conversion of sustained atrial fibrillation in instrumented conscious goats; 3) a test for general Granger causality to identify couplings and information transport in the atria during fibrillation. We conclude that a characterization of the dynamics via the reconstruction density offers a useful framework for the non-linear analysis of electrograms of atrial fibrillation.
Oscillation Criteria for Fourth-Order Nonlinear Dynamic Equations on Time Scales
Directory of Open Access Journals (Sweden)
Xin Wu
2013-01-01
Full Text Available We establish some new oscillation criteria for nonlinear dynamic equation of the form on an arbitrary time scale with , where are positive rd-continuous functions. An example illustrating the importance of our result is included.
STABILIZATION OF NONLINEAR TIME-VARYING SYSTEMS: A CONTROL LYAPUNOV FUNCTION APPROACH
Institute of Scientific and Technical Information of China (English)
Zhongping JIANG; Yuandan LIN; Yuan WANG
2009-01-01
This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.
Nonlinear system identification NARMAX methods in the time, frequency, and spatio-temporal domains
Billings, Stephen A
2013-01-01
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) modelThe orthogonal least squares algorithm that allows models to be built term by
Directory of Open Access Journals (Sweden)
Yan Che
2012-01-01
Full Text Available The estimation problem is investigated for a class of stochastic nonlinear systems with distributed time-varying delays and missing measurements. The considered distributed time-varying delays, stochastic nonlinearities, and missing measurements are modeled in random ways governed by Bernoulli stochastic variables. The discussed nonlinearities are expressed by the statistical means. By using the linear matrix inequality method, a sufficient condition is established to guarantee the mean-square stability of the estimation error, and then the estimator parameters are characterized by the solution to a set of LMIs. Finally, a simulation example is exploited to show the effectiveness of the proposed design procedures.
Rogue Waves of Nonlinear Schrödinger Equation with Time-Dependent Linear Potential Function
Directory of Open Access Journals (Sweden)
Ni Song
2016-01-01
Full Text Available The rogue waves of the nonlinear Schrödinger equation with time-dependent linear potential function are investigated by using the similarity transformation in this paper. The first-order and second-order rogue waves solutions are obtained and the nonlinear dynamic behaviors of these solutions are discussed in detail. In addition, the amplitudes of the rogue waves under the effect of the gravity field and external magnetic field changing with the time are analyzed by using numerical simulation. The results can be used to study the matter rogue waves in the Bose-Einstein condensates and other fields of nonlinear science.
Determining the input dimension of a neural network for nonlinear time series prediction
Institute of Scientific and Technical Information of China (English)
张胜; 刘红星; 高敦堂; 都思丹
2003-01-01
Determining the input dimension of a feed-forward neural network for nonlinear time series prediction plays an important role in the modelling.The paper first summarizes the current methods for determining the input dimension of the neural network.Then inspired by the fact that the correlation dimension of a nonlinear dynamic system is the mostimportant feature of it,the paper presents a new idea that the input dimension of the neural network for nonlinear time series prediction can be taken as an integer just greater than or equal to the correlation dimension.Finally,some wlidation examples and results are given.
Time-Resolved Nonlinear Absorptive Properties of Phenyleneethynylenes.
Slepkov, A. D.; Hegmann, F. A.; Tykwinski, R. R.; Marsden, J. A.; Miller, J. J.; Haley, M. M.
2004-03-01
Conjugated organic chromophores of varying polar symmetries are attractive candidate materials for two-photon absorption (TPA) applications. Central to the realization of useful TPA chromophores is a combination of optimized functionalization and special geometry. Phenyleneethynylene molecular scaffolds are small but heavily conjugated systems that display strong two-photon absorption. Furthermore, using optimized synthetic routes, the three-dimensional organization of these molecules can be conveniently controlled. The ultrafast two-photon and excited-state absorption of three substituted molecules display complex temporal behaviour. The nonlinear response of these materials depends drastically on the donor-acceptor symmetry about the central core. Understanding these trends impacts both on designing materials with desirable TPA properties and on understanding the electronic landscape in functionalized organic materials.
A polynomial criterion for adaptive stabilizability of discrete-time nonlinear systems
Li, Chanying; Xie, Liang-Liang; Guo, Lei
2006-01-01
In this paper, we will investigate the maximum capability of adaptive feedback in stabilizing a basic class of discrete-time nonlinear systems with both multiple unknown parameters and bounded noises. We will present a complete proof of the polynomial criterion for feedback capability as stated in "Robust stability of discrete-time adaptive nonlinear control" (C. Li, L.-L. Xie. and L. Guo, IFAC World Congress, Prague, July 3-8, 2005), by providing both the necessity and sufficiency analyze...
Discussion of Some Problems About Nonlinear Time Series Prediction Using v-Support Vector Machine
Institute of Scientific and Technical Information of China (English)
GAO Cheng-Feng; CHEN Tian-Lun; NAN Tian-Shi
2007-01-01
Some problems in using v-support vector machine (v-SVM) for the prediction of nonlinear time series are discussed. The problems include selection of various net parameters, which affect the performance of prediction, mixture of kernels, and decomposition cooperation linear programming v-SVM regression, which result in improvements of the algorithm. Computer simulations in the prediction of nonlinear time series produced by Mackey-Glass equation and Lorenz equation provide some improved results.
Estimation in continuous-time stochastic| volatility models using nonlinear filters
DEFF Research Database (Denmark)
Nielsen, Jan Nygaard; Vestergaard, M.; Madsen, Henrik
2000-01-01
Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308.......Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308....
Noise-correlation-time-mediated localization in random nonlinear dynamical systems
Cabrera, J L; De la Rubia, F J; Cabrera, Juan L.
1999-01-01
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic resonancelike behavior with the noise correlation time, there is an effect of optimal localization of the system trajectories in the phase space. This phenomenon is observed in systems with different nonlinearities, suggesting a degree of universality.
An improved impulsive control approach to nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Zhang Hua-Guang; Fu Jie; Ma Tie-Dong; Tong Shao-Cheng
2009-01-01
A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales
Institute of Scientific and Technical Information of China (English)
YANG Jia-shan
2013-01-01
The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article.By using the generalized Riccati technique,integral averaging technique and the time scales theory,some new sufficient conditions for oscillation of the equation are proposed.These results generalize and extend many known results for second order dynamic equations.Some examples are given to illustrate the main results of this article.
Finite-time H∞ filtering for non-linear stochastic systems
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Cosmic update dark puzzles : arrow of time : future history
Adams, Fred; Mersini-Houghton, Laura; Nekoogar, Farzad
2012-01-01
"...The Multiversal book series is equally unique, providing book-length extensions of the lectures with enough additional depth for those who truly want to explore these fields, while also providing the kind of clarity that is appropriate for interested lay people to grasp the general principles involved." - Lawrence M. Krauss Cosmic Update covers: A novel approach to uncover the dark faces of the Standard Model of cosmology. The possibility that Dark Energy and Dark Matter are manifestations of the inhomogeneous geometry of our Universe. The history of cosmological model building and the general architecture of cosmological models. Illustrations of the Large Scale Structure of the Universe. A new perspective on the classical static Einstein Cosmos. Global properties of World Models including their Topology. The Arrow of Time in a Universe with a Positive Cosmological Constant. The exploration of the consequences of a fundamental Cosmological Constant for our Universe. The exploration of why the current ob...
Discrete Space-Time: History and Recent Developments
Crouse, David
2017-01-01
Discussed in this work is the long history and debate of whether space and time are discrete or continuous. Starting from Zeno of Elea and progressing to Heisenberg and others, the issues with discrete space are discussed, including: Lorentz contraction (time dilation) of the ostensibly smallest spatial (temporal) interval, maintaining isotropy, violations of causality, and conservation of energy and momentum. It is shown that there are solutions to all these issues, such that discrete space is a viable model, yet the solution require strict non-absolute space (i.e., Mach's principle) and a re-analysis of the concept of measurement and the foundations of special relativity. In developing these solutions, the long forgotten but important debate between Albert Einstein and Henri Bergson concerning time will be discussed. Also discussed is the resolution to the Weyl tile argument against discrete space; however, the solution involves a modified version of the typical distance formula. One example effect of discrete space is then discussed, namely how it necessarily imposes order upon Wheeler's quantum foam, changing the foam into a gravity crystal and yielding crystalline properties of bandgaps, Brilluoin zones and negative inertial mass for astronomical bodies.
Nonlinear Dynamics of Complex Coevolutionary Systems in Historical Times
Perdigão, Rui A. P.
2016-04-01
A new theoretical paradigm for statistical-dynamical modeling of complex coevolutionary systems is introduced, with the aim to provide historical geoscientists with a practical tool to analyse historical data and its underlying phenomenology. Historical data is assumed to represent the history of dynamical processes of physical and socio-economic nature. If processes and their governing laws are well understood, they are often treated with traditional dynamical equations: deterministic approach. If the governing laws are unknown or impracticable, the process is often treated as if being random (even if it is not): statistical approach. Although single eventful details - such as the exact spatiotemporal structure of a particular hydro-meteorological incident - may often be elusive to a detailed analysis, the overall dynamics exhibit group properties summarized by a simple set of categories or dynamical regimes at multiple scales - from local short-lived convection patterns to large-scale hydro-climatic regimes. The overwhelming microscale complexity is thus conveniently wrapped into a manageable group entity, such as a statistical distribution. In a stationary setting whereby the distribution is assumed to be invariant, alternating regimes are approachable as dynamical intermittence. For instance, in the context of bimodal climatic oscillations such as NAO and ENSO, each mode corresponds to a dynamical regime or phase. However, given external forcings or longer-term internal variability and multiscale coevolution, the structural properties of the system may change. These changes in the dynamical structure bring about a new distribution and associated regimes. The modes of yesteryear may no longer exist as such in the new structural order of the system. In this context, aside from regime intermittence, the system exhibits structural regime change. New oscillations may emerge whilst others fade into the annals of history, e.g. particular climate fluctuations during
Time-domain Adaptive Compensation Algorithm for Distortion of Nonlinear Amplifiers
Ding, Yuanming; Sun, Lianming; Sano, Akira
A new time-domain adaptive predistortion scheme is proposed to compensate nonlinearity of high power amplifiers (HPA) in OFDM systems. A Hammerstein model is adopted to approximate the input-output nonlinear distortion of HPA by using complex power series followed by linear dynamical distortion. According to the Hammerstein model structure, the compensation input to HPA is adaptively given in an on-line manner so that the linearization from the predistorter input to the HPA output can be attained even if the nonlinear input-output relation of HPA is uncertain and changeable. The effectiveness of the proposed adaptive scheme is validated through numerical simulations.
Nonlinear Analysis of Spur Gear Pair with Time-varying Mesh Stiffness
Directory of Open Access Journals (Sweden)
Rao T. V. V. L. N.
2014-07-01
Full Text Available This study presents nonlinear analysis of single degree of freedom spur gear pair with time-varying mesh stiffness. The backlash is approximated using nonlinear term. The periodic steady-state solutions of the nonlinear system are obtained by closed-form expressions using the method of multiple scales. The stability and forced vibration response of the gear system are analyzed. The effect of mesh stiffness variation on the amplitude parameter of nondimensional dynamic transmission error for primary resonance is presented. The closed-form solutions in terms of mesh stiffness variations provide design guidelines for dynamic analysis of spur gear.
Determining the minimum embedding dimension of nonlinear time series based on prediction method
Institute of Scientific and Technical Information of China (English)
Bian Chun-Hua; Ning Xin-Bao
2004-01-01
Determining the embedding dimension of nonlinear time series plays an important role in the reconstruction of nonlinear dynamics. The paper first summarizes the current methods for determining the embedding dimension.Then, inspired by the fact that the optimum modelling dimension of nonlinear autoregressive (NAR) prediction model can characterize the embedding feature of the dynamics, the paper presents a new idea that the optimum modelling dimension of the NAR model can be taken as the minimum embedding dimension. Some validation examples and results are given and the present method shows its advantage for short data series.
Effect of reduction time on third order optical nonlinearity of reduced graphene oxide
Sreeja, V. G.; Vinitha, G.; Reshmi, R.; Anila, E. I.; Jayaraj, M. K.
2017-04-01
We report the influence of reduction time on structural, linear and nonlinear optical properties of reduced graphene oxide (rGO) thin films synthesized by spin coating method. We observed that the structural, linear and nonlinear optical properties can be tuned with reduction time in GO is due to the increased structural ordering because of the restoration of sp2 carbon atoms with the time of reduction. The nonlinear absorption studies by open aperture Z-scan technique exhibited a saturable absorption. The nonlinear refraction studies showed the self de focusing nature of rGO by closed aperture Z scan technique. The nonlinear absorption coefficient and saturation intensity varies with the time for reduction of GO which is attributed to the depletion of valence band and the conduction band filling effect. Our results emphasize duration for reduction of GO dependent optical nonlinearity of rGO thin films to a great extent and explore its applications Q switched mode locking laser systems for generating ultra short laser pulses and in optical sensors. The rGO coated films were characterized by X-Ray diffraction method (XRD), Fourier transform infrared spectroscopy (FTIR), Raman spectroscopy, UV-Vis absorption spectroscopy (UV-Vis), Photoluminescence (PL) and Scanning electron microscope (SEM) measurements.
Nonlinear response to a click in a time-domain model of the mammalian ear.
Meaud, Julien; Lemons, Charlsie
2015-07-01
In this paper, a state-space implementation of a previously developed frequency-domain model of the cochlea is coupled to a lumped parameter model of the middle ear. After validation of the time-domain model by comparison of its steady-state response to results obtained with a frequency-domain formulation, the nonlinear response of the cochlea to clicks is investigated. As observed experimentally, a compressive nonlinearity progressively develops within the first few cycles of the response of the basilar membrane (BM). Furthermore, a time-frequency analysis shows that the instantaneous frequency of the BM response to a click progressively approaches the characteristic frequency. This phenomenon, called glide, is predicted at all stimulus intensities, as in experiments. In typical experiments with sensitive animals, the click response is characterized by a long ringing and the response envelope includes several lobes. In order to achieve similar results, inhomogeneities are introduced in the cochlear model. Simulations demonstrate the strong link between characteristics of the frequency response, such as dispersion and frequency-dependent nonlinearity, and characteristics of the time-domain response, such as the glide and a time-dependent nonlinearity. The progressive buildup of cochlear nonlinearity in response to a click is shown to be a consequence of the glide and of frequency-dependent nonlinearity.
LS-based discrete-time adaptive nonlinear control——Feasibility and limitations
Institute of Scientific and Technical Information of China (English)
郭雷; 魏晨Institute of Systems Science; Chinese Academy of Sciences; Beijing 100080; China
1996-01-01
Global stability and instability of a class of discrete-time adaptive nonlinear control systems are investigated.The systems to be controlled are assumed to be linear in unknown parameters but nonlinear in dynamics which are characterizEd by a nonlinear function f(x).It is shown that in the scalar parameter case,when the standard least-squares (LS) method is used in estimation,the certainty equivalence adaptive control is globally stable whenever f(x) has a growth rate |f(x)| =0(||x||b) with b<8.Moreover,in the case where b≥8,it is also shown that the dosed-loop adaptive control system does not have global stability in general.Both the results found and the new analytical methods introduced may be regarded as a basic step for further study of discrete-time adaptive nonlinear control systems.
Real-Time Onboard Global Nonlinear Aerodynamic Modeling from Flight Data
Brandon, Jay M.; Morelli, Eugene A.
2014-01-01
Flight test and modeling techniques were developed to accurately identify global nonlinear aerodynamic models onboard an aircraft. The techniques were developed and demonstrated during piloted flight testing of an Aermacchi MB-326M Impala jet aircraft. Advanced piloting techniques and nonlinear modeling techniques based on fuzzy logic and multivariate orthogonal function methods were implemented with efficient onboard calculations and flight operations to achieve real-time maneuver monitoring and analysis, and near-real-time global nonlinear aerodynamic modeling and prediction validation testing in flight. Results demonstrated that global nonlinear aerodynamic models for a large portion of the flight envelope were identified rapidly and accurately using piloted flight test maneuvers during a single flight, with the final identified and validated models available before the aircraft landed.
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.
On invariant analysis of some time fractional nonlinear systems of partial differential equations. I
Singla, Komal; Gupta, R. K.
2016-10-01
An investigation of Lie point symmetries for systems of time fractional partial differential equations including Ito system, coupled Burgers equations, coupled Korteweg de Vries equations, Hirota-Satsuma coupled KdV equations, and coupled nonlinear Hirota equations has been done. Using the obtained symmetries, each one of the systems is reduced to the nonlinear system of fractional ordinary differential equations involving Erdélyi-Kober fractional differential operator depending on a parameter α.
Solving Nonlinear Time Delay Control Systems by Fourier series
Directory of Open Access Journals (Sweden)
Mohammad Hadi Farahi
2014-06-01
Full Text Available In this paper we present a method to find the solution of time-delay optimal control systems using Fourier series. The method is based upon expanding various time functions in the system as their truncated Fourier series. Operational matrices of integration and delay are presented and are utilized to reduce the solution of time-delay control systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
Non-smooth finite-time stabilization for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.
Indian Academy of Sciences (India)
Wenjun Liu; Kewang Chen
2013-09-01
In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.
On Robust Stability of a Class of Uncertain Nonlinear Systems with Time-Varying Delay
Institute of Scientific and Technical Information of China (English)
NIAN Xiao-hong
2002-01-01
The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions onrobust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay.Some previous results are improved and a numerical example is given to demonstrate the validity of our results.
Time to tenure in Spanish universities: an event history analysis.
Directory of Open Access Journals (Sweden)
Luis Sanz-Menéndez
Full Text Available Understanding how institutional incentives and mechanisms for assigning recognition shape access to a permanent job is important. This study, based on data from questionnaire survey responses and publications of 1,257 university science, biomedical and engineering faculty in Spain, attempts to understand the timing of getting a permanent position and the relevant factors that account for this transition, in the context of dilemmas between mobility and permanence faced by organizations. Using event history analysis, the paper looks at the time to promotion and the effects of some relevant covariates associated to academic performance, social embeddedness and mobility. We find that research productivity contributes to career acceleration, but that other variables are also significantly associated to a faster transition. Factors associated to the social elements of academic life also play a role in reducing the time from PhD graduation to tenure. However, mobility significantly increases the duration of the non-tenure stage. In contrast with previous findings, the role of sex is minor. The variations in the length of time to promotion across different scientific domains is confirmed, with faster career advancement for those in the Engineering and Technological Sciences compared with academics in the Biological and Biomedical Sciences. Results show clear effects of seniority, and rewards to loyalty, in addition to some measurements of performance and quality of the university granting the PhD, as key elements speeding up career advancement. Findings suggest the existence of a system based on granting early permanent jobs to those that combine social embeddedness and team integration with some good credentials regarding past and potential future performance, rather than high levels of mobility.
Time to tenure in Spanish universities: an event history analysis.
Sanz-Menéndez, Luis; Cruz-Castro, Laura; Alva, Kenedy
2013-01-01
Understanding how institutional incentives and mechanisms for assigning recognition shape access to a permanent job is important. This study, based on data from questionnaire survey responses and publications of 1,257 university science, biomedical and engineering faculty in Spain, attempts to understand the timing of getting a permanent position and the relevant factors that account for this transition, in the context of dilemmas between mobility and permanence faced by organizations. Using event history analysis, the paper looks at the time to promotion and the effects of some relevant covariates associated to academic performance, social embeddedness and mobility. We find that research productivity contributes to career acceleration, but that other variables are also significantly associated to a faster transition. Factors associated to the social elements of academic life also play a role in reducing the time from PhD graduation to tenure. However, mobility significantly increases the duration of the non-tenure stage. In contrast with previous findings, the role of sex is minor. The variations in the length of time to promotion across different scientific domains is confirmed, with faster career advancement for those in the Engineering and Technological Sciences compared with academics in the Biological and Biomedical Sciences. Results show clear effects of seniority, and rewards to loyalty, in addition to some measurements of performance and quality of the university granting the PhD, as key elements speeding up career advancement. Findings suggest the existence of a system based on granting early permanent jobs to those that combine social embeddedness and team integration with some good credentials regarding past and potential future performance, rather than high levels of mobility.
Scheduling jobs with time-resource tradeoff via nonlinear programming
Grigoriev, Alexander; Uetz, Marc
2009-01-01
We consider a scheduling problem where the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. personnel. An amount of $k$ units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its pro
A time stepping method in analysis of nonlinear structural dynamics
Directory of Open Access Journals (Sweden)
Gholampour A. A.
2011-12-01
Full Text Available In this paper a new method is proposed for the direct time integration method for structural dynamics problems. The proposed method assumes second order variations of the acceleration at each time step. Therefore more terms in the Taylor series expansion were used compared to other methods. Because of the increase in order of variations of acceleration, this method has higher accuracy than classical methods. The displacement function is a polynomial with five constants and they are calculated using: two equations for initial conditions (from the end of previous time step, two equations for satisfying the equilibrium at both ends of the time step, and one equation for the weighted residual integration. Proposed method has higher stability and order of accuracy than the other methods.
CYCLE TIMES ASSIGNMENT OF NONLINEAR DISCRETE EVENT DYNAMIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
CHEN Wende
2000-01-01
In this paper, nonautonomous models of Discrete Event Dynamic Systems (DEDS) are established by min-max function, reachability and observability are defined,the problem on cycle times assignment of DEDS, which corresponds with the important problem on poles assignment of linear systems, is studied. By Gunawardena et al.'Duality Theorem following results are obtained: Cycle times of system can be assigned under state feedback(or output feedback) if and only if system is reachable (or reachable and obserbable).
Demographic analysis of continuous-time life-history models
de Roos, A.M.
2008-01-01
I present a computational approach to calculate the population growth rate, its sensitivity to life-history parameters and associated statistics like the stable population distribution and the reproductive value for exponentially growing populations, in which individual life history is described as
Response Time in Adults with a History of Language Difficulties
Miller, Carol A.; Poll, Gerard H.
2009-01-01
The purpose of the study was to investigate speed of processing in college students with a history of problems with language. Affected individuals (n = 16) were identified through a self-reported history of language and/or reading difficulties, and compared to a group of 16 unaffected individuals. Measures of language ability and a battery of…
Demographic analysis of continuous-time life-history models
A.M. de Roos
2008-01-01
I present a computational approach to calculate the population growth rate, its sensitivity to life-history parameters and associated statistics like the stable population distribution and the reproductive value for exponentially growing populations, in which individual life history is described as
Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays
Institute of Scientific and Technical Information of China (English)
Wei-Sheng Chen; Rui-Hong Li; Jing Li
2010-01-01
An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.
Time-Dependent Nonlinear Optical Susceptibility of an Out-of-Equilibrium Soft Material
Ghofraniha, Neda; Conti, Claudio; Ruocco, Giancarlo; Zamponi, Francesco
2009-01-01
We investigate the time-dependent nonlinear optical absorption of a clay dispersion (Laponite) in an organic dye (rhodamine B) water solution displaying liquid-arrested state transition. Specifically, we determine the characteristic time τD of the nonlinear susceptibility buildup due to the Soret effect. By comparing τD with the relaxation time provided by standard dynamic light scattering measurements we report on the decoupling of the two collective diffusion times at the two very different length scales during the aging of the out-of-equilibrium system. With this demonstration experiment we also show the potentiality of nonlinear optics measurements in the study of the late stage of arrest in soft materials.
H {sub {infinity}} analysis of nonlinear stochastic time-delay systems
Energy Technology Data Exchange (ETDEWEB)
Shu Huisheng [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)] e-mail: hsshu@dhu.edu.cn; Wei Guoliang [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)
2005-10-01
In this paper, the H {sub {infinity}} analysis problem is studied for a general class of nonlinear stochastic systems with time-delay. The stochastic systems are described in terms of stochastic functional differential equations. The Razumikhin-type lemma is employed to establish sufficient conditions for the time-delay stochastic systems to be internally stable, and the H {sub {infinity}} analysis problem is studied in order to quantify the disturbance rejection attenuation level of the nonlinear stochastic time-delay system. In particular, the paper obtains the general conditions under which the L {sub 2} gain of the system is less than or equal to a given constant. Some easy-to-test criteria are also given so as to determine whether the nonlinear stochastic time-delay system under investigation is internally stable and whether it achieves certain H {sub {infinity}} performance index. Finally, illustrative examples are provided to show the usefulness of the proposed theory.
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
Institute of Scientific and Technical Information of China (English)
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
Band-phase-randomized Surrogates to assess nonlinearity in non-stationary time series
Guarin, Diego; Orozco, Alvaro
2011-01-01
Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results heavily depends on the stationarity of the time series. Since most physiological signals are non-stationary, it is easy to falsely detect nonlinearity using the linear surrogate data methods. In this document, we propose a methodology to extend the procedure for generating constrained surrogate time series in order to assess nonlinearity in non-stationary data. The method is based on the band-phase-randomized surrogates, which consists (contrary to the linear surrogate data methods) in randomizing only a portion of the Fourier phases in the high frequency band. Analysis of simulated time series showed that in comparison to the linear surrogate data method, our method is able to discriminate between linear stationarity, linear non-stationary and nonlinear time series. When apply...
Real-time solution of nonlinear potential flow equations for lifting rotors
Directory of Open Access Journals (Sweden)
Jianzhe HUANG
2017-06-01
Full Text Available Analysis of rotorcraft dynamics requires solution of the rotor induced flow field. Often, the appropriate model to be used for induced flow is nonlinear potential flow theory (which is the basis of vortex-lattice methods. These nonlinear potential flow equations sometimes must be solved in real time––such as for real-time flight simulation, when observers are needed for controllers, or in preliminary design computations. In this paper, the major effects of nonlinearities on induced flow are studied for lifting rotors in low-speed flight and hover. The approach is to use a nonlinear state-space model of the induced flow based on a Galerkin treatment of the potential flow equations.
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.
Naro, Daniel; Rummel, Christian; Schindler, Kaspar; Andrzejak, Ralph G.
2014-09-01
The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).
Stability analysis of a general family of nonlinear positive discrete time-delay systems
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
Finite-time stabilization for a class of stochastic nonlinear systems via output feedback.
Zha, Wenting; Zhai, Junyong; Fei, Shumin; Wang, Yunji
2014-05-01
This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.
Adaptive neural network tracking control for a class of unknown nonlinear time-delay systems
Institute of Scientific and Technical Information of China (English)
Chen Weisheng; Li Junmin
2006-01-01
For a class of unknown nonlinear time-delay systems, an adaptive neural network (NN) control design approach is proposed. Backstepping, domination and adaptive bounding design technique are combined to construct a robust memoryless adaptive NN tracking controller. Unknown time-delay functions are approximated by NNs, such that the requirement on the nonlinear time-delay functions is relaxed. Based on Lyapunov-Krasoviskii functional, the sem-global uniformly ultimately boundedness (UUB) of all the signals in the closed-loop system is proved. The arbitrary output tracking accuracy is achieved by tuning the design parameters. The feasibility is investigated by an illustrative simulation example.
Multiple time scale based reduction scheme for nonlinear chemical dynamics
Das, D.; Ray, D. S.
2013-07-01
A chemical reaction is often characterized by multiple time scales governing the kinetics of reactants, products and intermediates. We eliminate the fast relaxing intermediates in autocatalytic reaction by transforming the original system into a new one in which the linearized part is diagonal. This allows us to reduce the dynamical system by identifying the associated time scales and subsequent adiabatic elimination of the fast modes. It has been shown that the reduced system sustains the robust qualitative signatures of the original system and at times the generic form of the return map for the chaotic system from which complex dynamics stems out in the original system can be identified. We illustrate the scheme for a three-variable cubic autocatalytic reaction and four-variable peroxidase-oxidase reaction.
Nonlinear scale space with spatially varying stopping time.
Gilboa, Guy
2008-12-01
A general scale space algorithm is presented for denoising signals and images with spatially varying dominant scales. The process is formulated as a partial differential equation with spatially varying time. The proposed adaptivity is semi-local and is in conjunction with the classical gradient-based diffusion coefficient, designed to preserve edges. The new algorithm aims at maximizing a local SNR measure of the denoised image. It is based on a generalization of a global stopping time criterion presented recently by the author and colleagues. Most notably, the method works well also for partially textured images and outperforms any selection of a global stopping time. Given an estimate of the noise variance, the procedure is automatic and can be applied well to most natural images.
Hybrid time/frequency domain modeling of nonlinear components
DEFF Research Database (Denmark)
Wiechowski, Wojciech Tomasz; Lykkegaard, Jan; Bak, Claus Leth
2007-01-01
model is used as a basis for its implementation. First, the linear network part is replaced with an ideal voltage source and a time domain (EMT) simulation is performed. During the initial oscillations, harmonic content of the converter currents is calculated at every period by a fast Fourier transform...... and the periodic steady state is identified. Obtained harmonic currents are assigned to current sources and used in the frequency domain calculation in the linear network. The obtained three-phase bus voltage is then inverse Fourier transformed and assigned to the voltage source and the time domain simulation...... is performed again. This process is repeated until the change in the magnitudes and phase angles of the fundamental and low order characteristic harmonics of the bus voltage is smaller then predefined precision indexes. The method is verified against precise time domain simulation. The convergence properties...
Sasanpour, Pezhman; Shahmansouri, Afsaneh; Rashidian, Bizhan
2010-11-01
Third order nonlinear effects and its enhancement in gold nanostructures has been numerically studied. Analysis method is based on computationally solving nonlinear Maxwell's equations, considering dispersion behavior of permittivity described by Drude model and third order nonlinear susceptibility. Simulation is done by method of nonlinear finite difference time domain method, in which nonlinear equations of electric field are solved by Newton-Raphshon method. As the main outcomes of third order nonlinear susceptibility, four wave mixing and third harmonic generation terms are produced around gold nanostructures. Results of analysis on different geometries and structures show that third order nonlinearity products are more enhanced in places where electric field enhancement is occurred due to surface plasmons. Results indicates that enhancement of nonlinearities is strongly occurred in structures whose interface is dielectric. According to analysis results, nonlinear effects are highly concentrated in the vicinity of nanostructures. Hence this approach can be used in applications where localized ultraviolet light is required.
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.
Time-dependent exact solutions of the nonlinear Kompaneets equation
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H, E-mail: nib@bth.s [Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 Karlskrona (Sweden)
2010-12-17
Time-dependent exact solutions of the Kompaneets photon diffusion equation are obtained for several approximations of this equation. One of the approximations describes the case when the induced scattering is dominant. In this case, the Kompaneets equation has an additional symmetry which is used for constructing some exact solutions as group invariant solutions. (fast track communication)
Time-varying Combinations of Predictive Densities using Nonlinear Filtering
M. Billio (Monica); R. Casarin (Roberto); F. Ravazzolo (Francesco); H.K. van Dijk (Herman)
2012-01-01
textabstractWe propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics
A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers
Bagci, Hakan
2015-01-07
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representaton. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation...
Teren, F.
1977-01-01
Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.
Multivariate nonlinear time series modeling of exposure and risk in road safety research
Bijleveld, F.; Commandeur, J.; Montfort, van K.; Koopman, S.J.
2010-01-01
A multivariate non-linear time series model for road safety data is presented. The model is applied in a case-study into the development of a yearly time series of numbers of fatal accidents (inside and outside urban areas) and numbers of kilometres driven by motor vehicles in the Netherlands betwee
Stability of quantized time-delay nonlinear systems : A Lyapunov-Krasowskii-functional approach
Persis, Claudio De; Mazenc, Frédéric
2009-01-01
Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of time-invariant constant delays in the input. The quantized control law is implemented via hysteresis to avoid chattering. Under appropriate conditions, our analysis appl
Fsheikh, Ahmed H.
2013-01-01
A nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of reservoir models is presented. Sparse calibration is a challenging problem as the unknowns are both the non-zero components of the solution and their associated weights. NOMP is a greedy algorithm that discovers at each iteration the most correlated components of the basis functions with the residual. The discovered basis (aka support) is augmented across the nonlinear iterations. Once the basis functions are selected from the dictionary, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on approximate gradient estimation using an iterative stochastic ensemble method (ISEM). ISEM utilizes an ensemble of directional derivatives to efficiently approximate gradients. In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm.
Regular nonlinear response of the driven Duffing oscillator to chaotic time series
Institute of Scientific and Technical Information of China (English)
YuanYe; Li Yue; Danilo P. Mandic; Yang Bao-Jun
2009-01-01
Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated.
Tang, You-Fu; Liu, Shu-Lin; Jiang, Rui-Hong; Liu, Ying-Hui
2013-03-01
We study the correlation between detrended fluctuation analysis (DFA) and the Lempel-Ziv complexity (LZC) in nonlinear time series analysis in this paper. Typical dynamic systems including a logistic map and a Duffing model are investigated. Moreover, the influence of Gaussian random noise on both the DFA and LZC are analyzed. The results show a high correlation between the DFA and LZC, which can quantify the non-stationarity and the nonlinearity of the time series, respectively. With the enhancement of the random component, the exponent a and the normalized complexity index C show increasing trends. In addition, C is found to be more sensitive to the fluctuation in the nonlinear time series than α. Finally, the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve, and an effective fault diagnosis result is obtained.
Sequential Monte Carlo methods for nonlinear discrete-time filtering
Bruno, Marcelo GS
2013-01-01
In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable.We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in line
Ulku, Huseyin Arda
2014-07-06
Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half
Return to Old Times: Rural Romanticism in American Education History.
Warren, Donald
1984-01-01
Discusses the rural-urban dichotomy that regularly surfaces in educational history and argues that a full understanding of the role of cities is needed to overcome a rural romanticism that ill-serves public education policy. (CMG)
Return to Old Times: Rural Romanticism in American Education History.
Warren, Donald
1984-01-01
Discusses the rural-urban dichotomy that regularly surfaces in educational history and argues that a full understanding of the role of cities is needed to overcome a rural romanticism that ill-serves public education policy. (CMG)
A unified nonlinear stochastic time series analysis for climate science
Moon, Woosok; Wettlaufer, John S.
2017-03-01
Earth’s orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability.
A unified nonlinear stochastic time series analysis for climate science
Moon, Woosok; Wettlaufer, John S.
2017-01-01
Earth’s orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability. PMID:28287128
The effect and design of time delay in feedback control for a nonlinear isolation system
Sun, Xiuting; Xu, Jian; Fu, Jiangsong
2017-03-01
The optimum value of time delay of active control used in a nonlinear isolation system for different types of external excitation is studied in this paper. Based on the mathematical model of the nonlinear isolator with time-delayed active control, the stability, response and displacement transmissibility of the system are analyzed to obtain the standards for appropriate values of time delay and control strengths. The effects of nonlinearity and time delay on the stability and vibration response are discussed in details. For impact excitation and random excitation, the optimal value of time delay is obtained based on the vibration dissipation time via eigenvalues analysis, while for harmonic excitation, the optimal values are determined based on multiple vibration properties including natural frequency, amplitude death region and effective isolation region by the Averaging Method. This paper establishes the relationship between the parameters and vibration properties of a nonlinear isolation system which provides the guidance for optimizing time-delayed active control for different types of excitation in engineering practices.
Li, Dongfang; Zhang, Jiwei
2016-10-01
Anomalous diffusion behavior in many practical problems can be described by the nonlinear time-fractional parabolic problems on unbounded domain. The numerical simulation is a challenging problem due to the dependence of global information from time fractional operators, the nonlinearity of the problem and the unboundedness of the spacial domain. To overcome the unboundedness, conventional computational methods lead to extremely expensive costs, especially in high dimensions with a simple treatment of boundary conditions by making the computational domain large enough. In this paper, based on unified approach proposed in [25], we derive the efficient nonlinear absorbing boundary conditions (ABCs), which reformulates the problem on unbounded domain to an initial boundary value problem on bounded domain. To overcome nonlinearity, we construct a linearized finite difference scheme to solve the reduced nonlinear problem such that iterative methods become dispensable. And the stability and convergence of our linearized scheme are proved. Most important, we prove that the numerical solutions are bounded by the initial values with a constant coefficient, i.e., the constant coefficient is independent of the time. Overall, the computational cost can be significantly reduced comparing with the usual implicit schemes and a simple treatment of boundary conditions. Finally, numerical examples are given to demonstrate the efficiency of the artificial boundary conditions and theoretical results of the schemes.
Finite time extinction for nonlinear fractional evolution equations and related properties.
Jesus Ildefonso Diaz; Teresa Pierantozzi; Luis Vazquez
2016-01-01
The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly,...
Finite-time Consensus for Nonlinear Multi-agent Systems with Fixed Topologies
Shang, Yilun
2009-01-01
In this paper, we study finite-time state consensus problems for continuous nonlinear multi-agent systems. Building on the theory of finite-time Lyapunov stability, we propose sufficient criteria which guarantee the system to reach a consensus in finite time, provided that the underlying directed network contains a spanning tree. Novel finite-time consensus protocols are introduced as examples for applying the criteria. Simulations are also presented to illustrate our theoretical results.
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragón, J. L.
2012-08-08
We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems. © 2012 American Physical Society.
Integral sliding mode control for a class of nonlinear neutral systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Lou Xu-Yang; Cui Bao-Tong
2008-01-01
This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feasibility of the proposed technique.
Wei, Song; Chen, Wen; Hon, Y. C.
2016-11-01
This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.
Observability of nonlinear dynamics: Normalized results and a time-series approach
Aguirre, Luis A.; Bastos, Saulo B.; Alves, Marcela A.; Letellier, Christophe
2008-03-01
This paper investigates the observability of nonlinear dynamical systems. Two difficulties associated with previous studies are dealt with. First, a normalized degree observability is defined. This permits the comparison of different systems, which was not generally possible before. Second, a time-series approach is proposed based on omnidirectional nonlinear correlation functions to rank a set of time series of a system in terms of their potential use to reconstruct the original dynamics without requiring the knowledge of the system equations. The two approaches proposed in this paper and a former method were applied to five benchmark systems and an overall agreement of over 92% was found.
Anderson, Kristin K.; LaGasse, Michael J.; Haus, Hermann A.; Fujimoto, James G.
1990-05-01
We describe the application of a new femtosecond measurement technique, time division interferometry, for investigating the transient nonlinear index in waveguides. This technique performs an interferometric measurement using a time division multiplexed reference pulse and achieves high sensitivity with increased immunity to acoustic and thermal parasitics. Using a tunable femtosecond laser source, direct measurements of the wavelength dependent nonresonant nonlinear index have been performed in A1GaAs waveguides. In addition, conventional pump and probe absorption measurements permit the investigation of carrier dynamics, band filling, and two photon absorption effects. Two photon absorption is found to be a potentially serious limiting effect for obtaining all optical switching.
Finite-time Consensus of Heterogeneous Multi-agent Systems with Linear and Nonlinear Dynamics
Institute of Scientific and Technical Information of China (English)
ZHU Ya-Kun; GUAN Xin-Ping; LUO Xiao-Yuan
2014-01-01
In this paper, the finite-time consensus problems of heterogeneous multi-agent systems composed of both linear and nonlinear dynamics agents are investigated. Nonlinear consensus protocols are proposed for the heterogeneous multi-agent systems. Some suﬃcient conditions for the finite-time consensus are established in the leaderless and leader-following cases. The results are also extended to the case where the communication topology is directed and satisfies a detailed balance condition on coupling weights. At last, some simulation results are given to illustrate the effectiveness of the obtained theoretical results.
Linear and Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects
2017-02-22
AFRL-AFOSR-UK-TR-2017-0023 Linear and Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects Marco Martorella... UNIVERSITY DI PISA, DEPARTMENT DI INGEGNERIA Final Report 02/22/2017 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research...Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-14-1-0183 5c. PROGRAM
Energy Technology Data Exchange (ETDEWEB)
Burr, T.L.
1994-04-01
This report is a primer on the analysis of both linear and nonlinear time series with applications in nuclear safeguards and nonproliferation. We analyze eight simulated and two real time series using both linear and nonlinear modeling techniques. The theoretical treatment is brief but references to pertinent theory are provided. Forecasting is our main goal. However, because our most common approach is to fit models to the data, we also emphasize checking model adequacy by analyzing forecast errors for serial correlation or nonconstant variance.
Adaptive Leader-Following Consensus for Second-Order Time-Varying Nonlinear Multiagent Systems.
Hua, Changchun; You, Xiu; Guan, Xinping
2017-06-01
The leader-following consensus problem is investigated for second-order time-varying nonlinear multiagent systems with unmodeled dynamics and unknown parameters over directed communication topology. Under the assumption that the unknown nonlinearities satisfy Lipschitz conditions with time-varying gains, a local adaptive law is introduced for the design of consensus protocol that enable all followers' state variables to consensus with that of leader asymptotically. The proposed protocols are independent of system parameters and only require the relative state information of its neighbors, and hence they are fully distributed. Simulation examples are given to illustrate the effectiveness of the theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Burr, T.L.
1994-04-01
This report is a primer on the analysis of both linear and nonlinear time series with applications in nuclear safeguards and nonproliferation. We analyze eight simulated and two real time series using both linear and nonlinear modeling techniques. The theoretical treatment is brief but references to pertinent theory are provided. Forecasting is our main goal. However, because our most common approach is to fit models to the data, we also emphasize checking model adequacy by analyzing forecast errors for serial correlation or nonconstant variance.
Practical stabilization of a class of uncertain time-varying nonlinear delay systems
Institute of Scientific and Technical Information of China (English)
Bassem Ben HAMED; Mohamed Ali HAMMAMI
2009-01-01
In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.
A history of spike-timing-dependent plasticity
Directory of Open Access Journals (Sweden)
Henry eMarkram
2011-08-01
Full Text Available How learning and memory is achieved in the brain is a central question in neuroscience research. Key to today’s research into information storage in the brain is the concept of synaptic plasticity, a notion that has been heavily influenced by Donald Hebb’s 1949 postulate. Hebb conjectured that repeatedly and persistently coactive cells should increase connective strength among populations of interconnected neurons as a means of storing a memory trace, also known as an engram. Hebb certainly was not the first to make such a conjecture, as we show in this history. Nevertheless, literally thousands of studies into the classical frequency-dependent paradigm of cellular learning rules were directly inspired by the Hebbian postulate. But in more recent years, a novel concept in cellular learning has emerged, where temporal order instead of frequency is emphasized. This new learning paradigm — known as Spike-Timing-Dependent Plasticity, or STDP — has rapidly gained tremendous interest, perhaps because of its combination of elegant simplicity, biological plausibility, and computational power. But what are the roots of today’s STDP concept? Here, we discuss several centuries of diverse thinking, beginning with philosophers such as Aristotle, Locke and Ribot, traversing e.g. Lugaro’s plasticità and Rosenblatt’s Perceptron, and culminating with the discovery of STDP. We highlight interactions between theoretical and experimental fields, showing how discoveries sometimes occurred in parallel, seemingly without much knowledge of the other field, and sometimes via concrete back-and-forth communication. We point out where the future directions may lie, which includes interneuron STDP, the functional impact of STDP, its mechanisms and its neuromodulatory regulation, and the linking of STDP to the developmental formation and continuous plasticity of neuronal networks.
Frequency-domain L2-stability conditions for time-varying linear and nonlinear MIMO systems
Institute of Scientific and Technical Information of China (English)
Zhihong HUANG; Y. V. VENKATESH; Cheng XIANG; Tong Heng LEE
2014-01-01
The paper deals with the L2-stability analysis of multi-input-multi-output (MIMO) systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin-earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general L2-stability conditions in the frequency domain. These conditions have the following features:i) They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block. ii) For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.
Bifurcation and nonlinear analysis of a time-delayed thermoacoustic system
Yang, Xiaochuan; Turan, Ali; Lei, Shenghui
2017-03-01
In this paper, of primary concern is a time-delayed thermoacoustic system, viz. a horizontal Rijke tube. A continuation approach is employed to capture the nonlinear behaviour inherent to the system. Unlike the conventional approach by the Galerkin method, a dynamic system is naturally built up by discretizing the acoustic momentum and energy equations incorporating appropriate boundary conditions using a finite difference method. In addition, the interaction of Rijke tube velocity with oscillatory heat release is modeled using a modified form of King's law. A comparison of the numerical results with experimental data and the calculations reported reveals that the current approach can yield very good predictions. Moreover, subcritical Hopf bifurcations and fold bifurcations are captured with the evolution of dimensionless heat release coefficient, generic damping coefficient and time delay. Linear stability boundary, nonlinear stability boundary, bistable region and limit cycles are thus determined to gain an understanding of the intrinsic nonlinear behaviours.
H∞ output tracking control of discrete-time nonlinear systems via standard neural network models.
Liu, Meiqin; Zhang, Senlin; Chen, Haiyang; Sheng, Weihua
2014-10-01
This brief proposes an output tracking control for a class of discrete-time nonlinear systems with disturbances. A standard neural network model is used to represent discrete-time nonlinear systems whose nonlinearity satisfies the sector conditions. H∞ control performance for the closed-loop system including the standard neural network model, the reference model, and state feedback controller is analyzed using Lyapunov-Krasovskii stability theorem and linear matrix inequality (LMI) approach. The H∞ controller, of which the parameters are obtained by solving LMIs, guarantees that the output of the closed-loop system closely tracks the output of a given reference model well, and reduces the influence of disturbances on the tracking error. Three numerical examples are provided to show the effectiveness of the proposed H∞ output tracking design approach.
Using missing ordinal patterns to detect nonlinearity in time series data
Kulp, Christopher W.; Zunino, Luciano; Osborne, Thomas; Zawadzki, Brianna
2017-08-01
The number of missing ordinal patterns (NMP) is the number of ordinal patterns that do not appear in a series after it has been symbolized using the Bandt and Pompe methodology. In this paper, the NMP is demonstrated as a test for nonlinearity using a surrogate framework in order to see if the NMP for a series is statistically different from the NMP of iterative amplitude adjusted Fourier transform (IAAFT) surrogates. It is found that the NMP works well as a test statistic for nonlinearity, even in the cases of very short time series. Both model and experimental time series are used to demonstrate the efficacy of the NMP as a test for nonlinearity.
Real-Time Monitoring of Non-linear Suicidal Dynamics: Methodology and a Demonstrative Case Report.
Fartacek, Clemens; Schiepek, Günter; Kunrath, Sabine; Fartacek, Reinhold; Plöderl, Martin
2016-01-01
In recent years, a number of different authors have stressed the usefulness of non-linear dynamic systems approach in suicide research and suicide prevention. This approach applies specific methods of time series analysis and, consequently, it requires a continuous and fine-meshed assessment of the processes under consideration. The technical means for this kind of process assessment and process analysis are now available. This paper outlines how suicidal dynamics can be monitored in high-risk patients by an Internet-based application for continuous self-assessment with integrated tools of non-linear time series analysis: the Synergetic Navigation System. This procedure is illustrated by data from a patient who attempted suicide at the end of a 90-day monitoring period. Additionally, future research topics and clinical applications of a non-linear dynamic systems approach in suicidology are discussed.
A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics
Wang, Xuechuan; Atluri, Satya N.
2017-05-01
A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions and Dirac-Delta functions as the test functions over the finite time interval, the three algorithms are developed into three different discrete time-integrators through the collocation method. These time integrators are labeled as Chebyshev local iterative collocation methods. Through examples of the forced Duffing oscillator, the Lorenz system, and the multiple coupled Duffing equations (which arise as semi-discrete equations for beams, plates and shells undergoing large deformations), it is shown that the new algorithms are far superior to the 4th order Runge-Kutta and ODE45 of MATLAB, in predicting the chaotic responses of strongly nonlinear dynamical systems.
A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics
Wang, Xuechuan; Atluri, Satya N.
2017-01-01
A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions and Dirac-Delta functions as the test functions over the finite time interval, the three algorithms are developed into three different discrete time-integrators through the collocation method. These time integrators are labeled as Chebyshev local iterative collocation methods. Through examples of the forced Duffing oscillator, the Lorenz system, and the multiple coupled Duffing equations (which arise as semi-discrete equations for beams, plates and shells undergoing large deformations), it is shown that the new algorithms are far superior to the 4th order Runge-Kutta and ODE45 of MATLAB, in predicting the chaotic responses of strongly nonlinear dynamical systems.
Zamani, Iman; Shafiee, Masoud; Ibeas, Asier
2014-05-01
The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.
Delay-Dependent Observers for Uncertain Nonlinear Time-Delay Systems
Directory of Open Access Journals (Sweden)
Dongmei Yan
2013-05-01
Full Text Available This paper is concerned with the observer design problem for a class of discrete-time uncertain nonlinear systems with time-varying delay. The nonlinearities are assumed to satisfy global Lipschitz conditions which appear in both the state and measurement equations. The uncertainties are assumed to be time-varying but norm-bounded. Two Luenberger-like observers are proposed. One is delay observer and the other is delay-free observer. The delay observer which has an internal time delay is applicable when the time delay is known. The delay-free observer which does not use delayed information is especially applicable when the time delay is not known explicitly. Delay-dependent conditions for the existences of these two observers are derived based on Lyapunpv functional approach. Based on these conditions, the observer gains are obtained using the cone complementarity linearization algorithm. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
DEFF Research Database (Denmark)
Poulsen, Jens Aage
Historie i serien handler om læreplaner og læremidler og deres brug i skolefaget historie. Bogen indeholder nyttige redskaber til at analysere og vurdere læremidler......Historie i serien handler om læreplaner og læremidler og deres brug i skolefaget historie. Bogen indeholder nyttige redskaber til at analysere og vurdere læremidler...
The effect of nonlinear decompression history on H2O/CO2 vesiculation in rhyolitic magmas
Su, Yanqing; Huber, Christian
2017-04-01
Magma ascent rate is one of the key parameters that control volcanic eruption style, tephra dispersion, and volcanic atmospheric impact. Many methods have been employed to investigate the magma ascent rate in volcanic eruptions, and most rely on equilibrium thermodynamics. Combining the mixed H2O-CO2 solubility model with the diffusivities of both H2O and CO2 for normal rhyolitic melt, we model the kinetics of H2O and CO2 in rhyolitic eruptions that involve nonlinear decompression rates. Our study focuses on the effects of the total magma ascent time, the nonlinearity of decompression paths, and the influence of different initial CO2/H2O content on the posteruptive H2O and CO2 concentration profiles around bubbles within the melt. Our results show that, under most circumstances, volatile diffusion profiles do not constrain a unique solution for the decompression rate of magmas during an eruption, but, instead, provide a family of decompression paths with a well-defined trade-off between ascent time and nonlinearity. An important consequence of our analysis is that the common assumption of a constant decompression rate (averaged value) tends to underestimate the actual magma ascent time.
Time-varying interaction leads to amplitude death in coupled nonlinear oscillators
Indian Academy of Sciences (India)
Awadhesh Prasad
2013-09-01
A new form of time-varying interaction in coupled oscillators is introduced. In this interaction, each individual oscillator has always time-independent self-feedback while its interaction with other oscillators are modulated with time-varying function. This interaction gives rise to a phenomenon called amplitude death even in diffusively coupled identical oscillators. The nonlinear variation of the locus of bifurcation point is shown. Results are illustrated with Landau–Stuart (LS) and Rössler oscillators.
The (G'/G)-expansion method for the nonlinear time fractional differential equations
Unsal, Omer; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.
2017-01-01
In this paper, we obtain exact solutions of two time fractional differential equations using Jumarie's modified Riemann-Liouville derivative which is encountered in mathematical physics and applied mathematics; namely (3 + 1)-dimensional time fractional KdV-ZK equation and time fractional ADR equation by using fractional complex transform and (G/'G )-expansion method. It is shown that the considered transform and method are very useful in solving nonlinear fractional differential equations.
Nonlinear Maps for Design of Discrete-Time Models of Neuronal Network Dynamics
2016-03-31
responsive tiring patterns . We propose to use modern DSP ideas to develop new efficient approaches to the design of such discrete-time models for...2016 Performance/Technic~ 03-01-2016- 03-31-2016 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Nonlinear Maps for Design of Discrete-Time Models of...simulations is to design a neuronal model in the form of difference equations that generates neuronal states in discrete moments of time. In this
Wei, H. L.; Balikhin, M.; S. A. Billings
2003-01-01
Identification techniques for nonlinear time-varying systems are investigated based on the NARMAX model and multiresolution wavelet expansions. It is shown that a NARMAX model with time-varying coefficients can be reduced to a time-invariant linear-in-the-parameters analysis problem by then adapted to estimate the parameters. An application data relating to magnetic storms is used to illustrate the realistic application of the new identification technique.
Third-order nonlinear and linear time-dependent dynamical diffraction of X-rays in crystals.
Balyan, Minas K
2016-07-01
For the first time the third-order nonlinear time-dependent Takagi's equations of X-rays in crystals are obtained and investigated. The third-order nonlinear and linear time-dependent dynamical diffraction of X-rays spatially restricted in the diffraction plane pulses in crystals is investigated theoretically. A method of solving the linear and the third-order nonlinear time-dependent Takagi's equations is proposed. Based on this method, results of analytical and numerical calculations for both linear and nonlinear diffraction cases are presented and compared.
Facilitating Conversations across Time: Using Simulations in Living History Training
Seig, Mary Theresa
2008-01-01
This article describes the use of a simulation as a crucial part of a larger training program at a living history museum. The simulation provided an experiential, emotional base from which museum staff could re-envision their interactions with visitors and effect cultural and organizational change from within those interactions. (Contains 1 note.)
Tiempos Pasados (Past Times). Grass-Roots Oral History.
Hunsaker, Alan, Ed.
Compiled with learning objectives, suggested lesson plans, learning center activities, and selected teacher and student bibliographies for use at the elementary level, transcripts of oral history interviews with 11 Mexican Americans in San Bernardino County's West End provide understanding of the mass movement of Mexicans to the United States in…
Estimating marginal properties of quantitative real-time PCR data using nonlinear mixed models
DEFF Research Database (Denmark)
Gerhard, Daniel; Bremer, Melanie; Ritz, Christian
2014-01-01
A unified modeling framework based on a set of nonlinear mixed models is proposed for flexible modeling of gene expression in real-time PCR experiments. Focus is on estimating the marginal or population-based derived parameters: cycle thresholds and ΔΔc(t), but retaining the conditional mixed mod...
ON THE PARTIAL EQUIASYMPTOTIC STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
JianJigui; JiangMinghui; ShenYanjun
2005-01-01
In this paper, the problem of partial equiasymptotic stability for nonlinear time-varying differential equations are analyzed. A sufficient condition of partial stability and a set of sufficient conditions of partial equiasymptotic stability are given. Some of these conditions allow the derivative of Lyapunov function to be positive. Finally, several numerical examples are also given to illustrate the main results.
Stability of quantized time-delay nonlinear systems : a Lyapunov–Krasowskii-functional approach
Persis, Claudio De; Mazenc, Frédéric
2010-01-01
Lyapunov–Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to avoid chattering. Under appropriate conditions, our analysis applies to stabiliz
MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Yufan
2005-01-01
The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
Institute of Scientific and Technical Information of China (English)
Yepeng Xing; Qiong Wang; Valery G. Romanovski
2009-01-01
We prove several new comparison results and develop the monotone iterative tech-nique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E.; Vegt, van der J.J.W.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is cont
Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system
Kahraman, A.; Singh, R.
1991-04-01
Frequency response characteristics of a non-linear geared rotor-bearing system with time-varying mesh stiffness k h( overlinet) are examined in this paper. First, the single-degree-of-freedom spur gear pair model with backlash is extended to include sinusoidal or periodic mesh stiffness k h( overlinet) . Second, a three-degree-of-freedom model with k h( overlinet) and clearance non-lineariries associated with gear backlash and rolling element bearings, as excited by the static transmission error overlinee( overlinet) under a mean torque load, is developed. The governing equations are solved using digital simulation technique and only the primary resonances are studied. Resonances of the corresponding linear time-varying system associated with parametric and external excitations are identified using the method of multiple scales and digital simulation. Interactions between the mesh stiffness variation and clearance non-linearities have been investigated; a strong interaction between time-varying mesh stiffness k h( overlinet) and gear backlash is found, whereas the coupling between k h( overlinet) and bearing non-linearities is weak. Finally, our time-varying non-linear formulations yield reasonably good predictions when compared with the benchmark experimental results available in the literature.
Directory of Open Access Journals (Sweden)
Il Young Song
2015-01-01
Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.
Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales
Directory of Open Access Journals (Sweden)
Topal SGulsan
2009-01-01
Full Text Available We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for -Laplacian boundary value problem is also given by the monotone method.
Nonlinearity, Breaks, and Long-Range Dependence in Time-Series Models
DEFF Research Database (Denmark)
Hillebrand, Eric Tobias; Medeiros, Marcelo C.
We study the simultaneous occurrence of long memory and nonlinear effects, such as parameter changes and threshold effects, in ARMA time series models and apply our modeling framework to daily realized volatility. Asymptotic theory for parameter estimation is developed and two model building...
Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time
Institute of Scientific and Technical Information of China (English)
YAN Jun
2005-01-01
The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.
Yan, Xuehua
2014-01-01
This paper is the further investigation of work of Yan and Liu, 2011, and considers the global practical tracking problem by output feedback for a class of uncertain nonlinear systems with not only unmeasured states dependent growth but also time-varying time delay. Compared with the closely related works, the remarkableness of the paper is that the time-varying time delay and unmeasurable states are permitted in the system nonlinear growth. Motivated by the related tracking results and flexibly using the ideas and techniques of universal control and dead zone, an adaptive output-feedback tracking controller is explicitly designed with the help of a new Lyapunov-Krasovskii functional, to make the tracking error prescribed arbitrarily small after a finite time while keeping all the closed-loop signals bounded. A numerical example demonstrates the effectiveness of the results. PMID:25276859
Design of robust fault detection filter for nonlinear time-delay systems
Institute of Scientific and Technical Information of China (English)
BAI Lei-shi; HE Li-ming; TIAN Zuo-hua; SHI Song-jiao
2006-01-01
In this paper, the robust fault detection filter (RFDF) design problems are studied for nonlinear time-delay systems with unknown inputs. First, a reference residual model is introduced to formulate the RFDF design problem as an H∞model-matching problem. Then appropriate input/output selection matrices are introduced to extend a performance index to the time-delay systems in time domain. The reference residual model designed according to the performance index is an optimal residual generator, which takes into account the robustness against disturbances and sensitivity to faults simultaneously. Applying robust H∞ optimization control technique, the existence conditions of the RFDF for nonlinear time-delay systems with unknown inputs are presented in terms of linear matrix inequality (LMI) formulation, independently of time delay. An illustrative design example is used to demonstrate the validity and applicability of the proposed approach.
Semistability of Nonlinear Systems Having a Continuum of Equilibria and Time-Varying Delays
Hui, Qing
2010-01-01
In this paper, we develop a semistability analysis framework for nonlinear systems with time-varying delays with applications to stability analysis of multiagent dynamic networks with consensus protocols in the presence of unknown heterogeneous time-varying delays along the communication links. We show that for such a nonlinear system having a continuum of equilibria, if the system asymptotically converges to a constant time-delay system and this new system is semistable, then the original time-varying delay system is semistable, provided that the delays are just bounded, not necessarily differentiable. In proving our results, we extend the limiting equation approach to the time-varying delay systems and also develop some new convergence results for functional differential equations.
STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES
Institute of Scientific and Technical Information of China (English)
马军海; 陈予恕; 辛宝贵
2004-01-01
The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions.By combining neural networks and wavelet theories,the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given.Based on wavelet networks,a new method for parameter identification was suggested,which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series.Through pre-treatment and comparison of results before and after the treatment,several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.
New adaptive quasi-sliding mode control for nonlinear discrete-time systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A new adaptive quasi-sliding mode control algorithm is developed for a class of nonlinear diecrete-time systems,which is especially useful for nonlinear systems with vaguely known dynamics.This design is model-free,and is based directly on pseudo-partial-derivatives derived on-line from the input and output information of the system using an improved recursive projection type of identification algorithm.The theoretical analysis and simulation results show that the adaptive quasi-sliding mode control system is stable and convergent.
Dimensional Reduction for Filters of Nonlinear Systems with Time-Scale Separation
2013-03-01
Rapp, Edwin Kreuzer and N. Sri Namachchivaya, “Reduced Nor- mal Forms for Nonlinear Control of Underactuated Hoisting Systems ,” Archive of Applied Mechanics , Vol.82, 2012, pp. 297 - 315. 7 ... Mechanics , Vol. 78(6), 2011, pp. 61001-1 - 61001-10. 8. Lee DeVille, N. Sri Namachchivaya and Zoi Rapti, “Noisy Two Dimensional Non-Hamiltonian System ...AFRL-OSR-VA-TR-2013-0009 Dimensional Reduction for Filters of Nonlinear Systems with Time- Scale Separation Namachchivaya, N
Adaptive neural control for a class of nonlinearly parametric time-delay systems.
Ho, Daniel W C; Li, Junmin; Niu, Yugang
2005-05-01
In this paper, an adaptive neural controller for a class of time-delay nonlinear systems with unknown nonlinearities is proposed. Based on a wavelet neural network (WNN) online approximation model, a state feedback adaptive controller is obtained by constructing a novel integral-type Lyapunov-Krasovskii functional, which also efficiently overcomes the controller singularity problem. It is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed-loop systems. An example is provided to illustrate the application of the approach.
Energy Technology Data Exchange (ETDEWEB)
Leolukman, Melvina; Paoprasert, Peerasak; Wang, Yao; Makhija, Varun; McGee, David J.; Gopalan, Padma (UW)
2008-10-02
Factors affecting the electric-field-induced poling of nonlinear optical chromophores in block copolymer domains were investigated by encapsulating the chromophores in a linear-diblock copolymer [poly(styrene-b-4-vinylpyridine)] and linear-dendritic (poly(methyl methacrylate)-dendron) block copolymer via hydrogen bonding. Temperature-dependent Fourier transform infrared spectroscopy and morphology evaluation by X-ray scattering and transmission electron microscopy were used with in situ second harmonic generation to correlate domain architectures, processing conditions such as thermal history, and chromophore concentrations with poling efficiency. Poling of chromophores encapsulated in the minority domain (spheres or cylinders) of a linear-diblock copolymer was inhibited by the increasing chromophore concentration within the domain and the chemical nature of the majority domain. Chromophore encapsulation in the majority domain produced the most favorable conditions for poling as measured by in situ second harmonic generation. Thermal annealing of the linear-diblock copolymer/chromophore composites resulted in chromophore aggregation with a corresponding decrease in nonlinear optical activity. The linear-dendron/chromophore system presented the most effective architecture for spatially dispersing chromophores. These findings suggest that while well-ordered phase-separated systems such as block copolymers enhance chromophore isolation over homopolymer systems, a more effective approach is to explore polymer chains end functionalized with chromophores.
Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
Nixon, Sean
2016-01-01
Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light's amplitude evolution. This ODE predicts that the first class of these non-PT-symmetric waveguides support continuous families of solitons and robust amplitude-oscillating solutions both above and below phase transition, in close analogy with PT-symmetric systems. For the other classes of waveguides, the light's intensity always amplifies under the effect of nonlinearity even if the waveguide is below phase transition. These analytical predictions are confirmed by direct computations of the full system.
Saturations-based nonlinear controllers with integral term: validation in real-time
Alatorre, A. G.; Castillo, P.; Mondié, S.
2016-05-01
Popular saturations-based nonlinear controller usually include proportional and derivative components of the state or output. The fact that in many applications, these components do not suffice to insure the convergence to the desired output values, motivate the addition of an integral term. In this paper, three configurations of nonlinear controllers based on saturation functions are improved with an integral component. The stability of the three algorithms is analysed using the Lyapunov theory. Simulation results validate the proposed control laws when they are applied to nonlinear systems with constant and unknown perturbations. Real-time experiments realised with a quad-rotor aerial vehicle and a hovercraft vehicle show that the proposed scheme can follow autonomously some trajectories, and that it could be robust with respect to delays.
Energy Technology Data Exchange (ETDEWEB)
Han, Dong Ki; Chang, Pyung Hun [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of)
2010-08-15
We propose an enhanced controller to improve the robustness of Time Delay Control (TDC) for a robot manipulator in the presence of nonlinear friction, such as Coulomb friction. The problem of TDC is first analyzed with TDC as a trajectory control for a robot manipulator in the presence of nonlinear friction. Gradient estimation is used to solve this problem. The proposed controller is called TDC with Gradient Estimator (TDCGE). Comparing with a prior research to improve the robustness of TDC, named TDCSA, the TDCGE is much simpler to design. Through 1 DOF linear motor experiment, it is verified that the TDCGE is more robust against nonlinear friction than TDC and the TDCGE has a similar robustness to the TDCSA. In addition, it is confirmed that the TDCGE is easily implemented in the multi degree-of-freedom robot manipulator through a 3 DOF spatial robot manipulator experiment
Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity.
Tang, Guangxin; Jacobs, Laurence J; Qu, Jianmin
2012-04-01
This paper considers the scattering of a plane, time-harmonic wave by an inclusion with heterogeneous nonlinear elastic properties embedded in an otherwise homogeneous linear elastic solid. When the inclusion and the surrounding matrix are both isotropic, the scattered second harmonic fields are obtained in terms of the Green's function of the surrounding medium. It is found that the second harmonic fields depend on two independent acoustic nonlinearity parameters related to the third order elastic constants. Solutions are also obtained when these two acoustic nonlinearity parameters are given as spatially random functions. An inverse procedure is developed to obtain the statistics of these two random functions from the measured forward and backscattered second harmonic fields.
Directory of Open Access Journals (Sweden)
Saul Hazledine
Full Text Available Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia, with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.
Stability Analysis of Fixed points in a Parity-time symmetric coupler with Kerr nonlinearity
Deka, Jyoti Prasad
2016-01-01
We report our study on nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. In the linear regime, the differential equations governing the dynamics of the coupler, under some parametric changes, can be solved exactly. But with the inclusion of nonlinearity, analytical solution of the system is a rather complicated job. And the sensitiveness of the system on the initial conditions is yet another critical issue. To circumvent the situation, we have employed the mathematical framework of nonlinear dynamics. Considering the parity-time threshold of the linear PT-coupler as the reference point, we find that in nonlinear coupler the parity-time symmetric threshold governs the existence of fixed points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. In the unbroken PT regime, we find that the instabilities in the initial launch conditions can trigger an exponential growth and dec...
Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay
Chunodkar, Apurva A.; Akella, Maruthi R.
2013-12-01
This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.
Time delay in thin slabs with self-focusing Kerr-type nonlinearity
Isić, G.; Milanović, V.; Radovanović, J.; Ikonić, Z.; Indjin, D.; Harrison, P.
2008-03-01
Time delays for an intense transverse electric (TE) wave propagating through a Kerr-type nonlinear slab are investigated. The relation between the bidirectional group delay and the dwell time is derived and it is shown that the difference between them can be separated into three terms. The first one is the familiar self-interference time, due to the dispersion of the medium surrounding the slab. The other two terms are caused by the nonlinearity and oblique incidence of the TE wave. It is shown that the electric field distribution along the slab may be expressed in terms of Jacobi elliptic functions while the phase difference introduced by the slab is given in terms of incomplete elliptic integrals. The expressions for the field-intensity-dependent complex reflection and transmission coefficients are derived and the multivalued oscillatory behavior of the delay times for the case of a thin slab is demonstrated.
Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density
Directory of Open Access Journals (Sweden)
David O. Smallwood
1997-01-01
Full Text Available The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general case of matching a target probability density function using a zero memory nonlinear (ZMNL function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.
Institute of Scientific and Technical Information of China (English)
ZHANG JIA-SHU; XIAO XIAN-CI
2001-01-01
A multistage adaptive higher-order nonlinear finite impulse response (MAHONFIR) filter is proposed to predict chaotic time series. Using this approach, we may readily derive the decoupled parallel algorithm for the adaptation of the coefficients of the MAHONFIR filter, to guarantee a more rapid convergence of the adaptive weights to their optimal values. Numerical simulation results show that the MAHONFIR filters proposed here illustrate a very good performance for making an adaptive prediction of chaotic time series.
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E; Vegt, van der, N.F.A.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is continuous in space and discontinuous in time. The key features of this formulation are: (i) a discrete variational approach that gives rise to conservation of discrete energy and phase space and prese...
From Continuous-Time Design to Sampled-Data Design of Nonlinear Observers
Karafyllis, Iasson; Kravaris, Costas
2008-01-01
In this work, a sampled-data nonlinear observer is designed using a continuous-time design coupled with an inter-sample output predictor. The proposed sampled-data observer is a hybrid system. It is shown that under certain conditions, the robustness properties of the continuous-time design are inherited by the sampled-data design, as long as the sampling period is not too large. The approach is applied to linear systems and to triangular globally Lipschitz systems.
Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps
Directory of Open Access Journals (Sweden)
Minsong Zhang
2014-01-01
Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.
A Kernel Time Structure Independent Component Analysis Method for Nonlinear Process Monitoring☆
Institute of Scientific and Technical Information of China (English)
Lianfang Cai; Xuemin Tian; Ni Zhang
2014-01-01
Kernel independent component analysis (KICA) is a newly emerging nonlinear process monitoring method, which can extract mutually independent latent variables cal ed independent components (ICs) from process var-iables. However, when more than one IC have Gaussian distribution, it cannot extract the IC feature effectively and thus its monitoring performance will be degraded drastical y. To solve such a problem, a kernel time struc-ture independent component analysis (KTSICA) method is proposed for monitoring nonlinear process in this paper. The original process data are mapped into a feature space nonlinearly and then the whitened data are calculated in the feature space by the kernel trick. Subsequently, a time structure independent component analysis algorithm, which has no requirement for the distribution of ICs, is proposed to extract the IC feature. Finally, two monitoring statistics are built to detect process faults. When some fault is detected, a nonlinear fault identification method is developed to identify fault variables based on sensitivity analysis. The proposed monitoring method is applied in the Tennessee Eastman benchmark process. Applications demonstrate the superiority of KTSICA over KICA.
Set-membership fuzzy filtering for nonlinear discrete-time systems.
Yang, Fuwen; Li, Yongmin
2010-02-01
This paper is concerned with the set-membership filtering (SMF) problem for discrete-time nonlinear systems. We employ the Takagi-Sugeno (T-S) fuzzy model to approximate the nonlinear systems over the true value of state and to overcome the difficulty with the linearization over a state estimate set rather than a state estimate point in the set-membership framework. Based on the T-S fuzzy model, we develop a new nonlinear SMF estimation method by using the fuzzy modeling approach and the S-procedure technique to determine a state estimation ellipsoid that is a set of states compatible with the measurements, the unknown-but-bounded process and measurement noises, and the modeling approximation errors. A recursive algorithm is derived for computing the ellipsoid that guarantees to contain the true state. A smallest possible estimate set is recursively computed by solving the semidefinite programming problem. An illustrative example shows the effectiveness of the proposed method for a class of discrete-time nonlinear systems via fuzzy switch.
Uniform approach to linear and nonlinear interrelation patterns in multivariate time series
Rummel, Christian; Abela, Eugenio; Müller, Markus; Hauf, Martinus; Scheidegger, Olivier; Wiest, Roland; Schindler, Kaspar
2011-06-01
Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.
Wen, Guoguang; Yu, Yongguang; Peng, Zhaoxia; Rahmani, Ahmed
2016-06-01
This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.
Afeyan, Bedros; Crouseilles, Nicolas; Dodhy, Adila; Faou, Erwan; Mehrenberger, Michel; Sonnendrücker, Eric
2014-01-01
KEEN waves are nonlinear, non-stationary, self-organized asymptotic states in Vlasov plasmas outside the scope or purview of linear theory constructs such as electron plasma waves or ion acoustic waves. Nonlinear stationary mode theories such as those leading to BGK modes also do not apply. The range in velocity that is strongly perturbed by KEEN waves depends on the amplitude and duration of the ponderomotive force used to drive them. Smaller amplitude drives create highly localized structures attempting to coalesce into KEEN waves. These cases have much more chaotic and intricate time histories than strongly driven ones. The narrow range in which one must maintain adequate velocity resolution in the weakly driven cases challenges xed grid numerical schemes. What is missing there is the capability of resolving locally in velocity while maintaining a coarse grid outside the highly perturbed region of phase space. We here report on a new Semi-Lagrangian Vlasov-Poisson solver based on conservative non-uniform c...
Donges, Jonathan F; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V; Marwan, Norbert; Dijkstra, Henk A; Kurths, Jürgen
2015-01-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence qua...
Nonlinear continuous-time generalized predictive control of solar power plant
Directory of Open Access Journals (Sweden)
Khoukhi Billal
2015-01-01
Full Text Available This paper presents an application of nonlinear continuous-time generalized predictive control (GPC to the distributed collector field of a solar power plant. The major characteristic of a solar power plant is that the primary energy source, solar radiation, cannot be manipulated. Solar radiation varies throughout the day, causing changes in plant dynamics and strong perturbations in the process. A brief description of the solar power plant and its simulator is given. After that, basic concepts of predictive control and continuous-time generalized predictive control are introduced. A new control strategy, named nonlinear continuous-time generalized predictive control (NCGPC, is then derived to control the process. The simulation results show that the NCGPC gives a greater flexibility to achieve performance goals and better perturbation rejection than classical control.
Institute of Scientific and Technical Information of China (English)
唐圣金; 郭晓松; 于传强; 周志杰; 周召发; 张邦成
2014-01-01
Real time remaining useful life (RUL) prediction based on condition monitoring is an essential part in condition based maintenance (CBM). In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item’s individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.
Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series.
Gao, Zhong-Ke; Cai, Qing; Yang, Yu-Xuan; Dang, Wei-Dong; Zhang, Shan-Shan
2016-10-19
Visibility graph has established itself as a powerful tool for analyzing time series. We in this paper develop a novel multiscale limited penetrable horizontal visibility graph (MLPHVG). We use nonlinear time series from two typical complex systems, i.e., EEG signals and two-phase flow signals, to demonstrate the effectiveness of our method. Combining MLPHVG and support vector machine, we detect epileptic seizures from the EEG signals recorded from healthy subjects and epilepsy patients and the classification accuracy is 100%. In addition, we derive MLPHVGs from oil-water two-phase flow signals and find that the average clustering coefficient at different scales allows faithfully identifying and characterizing three typical oil-water flow patterns. These findings render our MLPHVG method particularly useful for analyzing nonlinear time series from the perspective of multiscale network analysis.
Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series
Gao, Zhong-Ke; Cai, Qing; Yang, Yu-Xuan; Dang, Wei-Dong; Zhang, Shan-Shan
2016-10-01
Visibility graph has established itself as a powerful tool for analyzing time series. We in this paper develop a novel multiscale limited penetrable horizontal visibility graph (MLPHVG). We use nonlinear time series from two typical complex systems, i.e., EEG signals and two-phase flow signals, to demonstrate the effectiveness of our method. Combining MLPHVG and support vector machine, we detect epileptic seizures from the EEG signals recorded from healthy subjects and epilepsy patients and the classification accuracy is 100%. In addition, we derive MLPHVGs from oil-water two-phase flow signals and find that the average clustering coefficient at different scales allows faithfully identifying and characterizing three typical oil-water flow patterns. These findings render our MLPHVG method particularly useful for analyzing nonlinear time series from the perspective of multiscale network analysis.
Krasilenko, Vladimir G.; Nikolsky, Alexander I.; Lazarev, Alexander A.; Lazareva, Maria V.
2008-03-01
In the paper the actuality of neurophysiologically motivated neuron arrays with flexibly programmable functions and operations with possibility to select required accuracy and type of nonlinear transformation and learning are shown. We consider neurons design and simulation results of multichannel spatio-time algebraic accumulation - integration of optical signals. Advantages for nonlinear transformation and summation - integration are shown. The offered circuits are simple and can have intellectual properties such as learning and adaptation. The integrator-neuron is based on CMOS current mirrors and comparators. The performance: consumable power - 100...500 μW, signal period- 0.1...1ms, input optical signals power - 0.2...20 μW time delays - less 1μs, the number of optical signals - 2...10, integration time - 10...100 of signal periods, accuracy or integration error - about 1%. Various modifications of the neuron-integrators with improved performance and for different applications are considered in the paper.
Comparison of different nonlinear solvers for 2D time-implicit stellar hydrodynamics
Viallet, Maxime; Walder, Rolf
2013-01-01
Time-implicit schemes are attractive since they allow numerical time steps that are much larger than those permitted by the Courant-Friedrich-Lewy criterion characterizing time-explicit methods. This advantage comes, however, with a cost: the solution of a system of nonlinear equations is required at each time step. In this work, the nonlinear system results from the discretization of the hydrodynamical equations with the Crank-Nicholson scheme. We compare the cost of different methods, based on Newton-Raphson iterations, to solve this nonlinear system, and benchmark their performances against time-explicit schemes. Since our general scientific objective is to model stellar interiors, we use as test cases two realistic models for the convective envelope of a red giant and a young Sun. Focusing on 2D simulations, we show that the best performances are obtained with the quasi-Newton method proposed by Broyden. Another important concern is the accuracy of implicit calculations. Based on the study of an idealized...
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
In safety critical systems, the control system is composed of a core control system with a fault detection and isolation scheme together with a repair or a recovery strategy. The time that it takes to detect, isolate, and recover from the fault (fault recovery time) is a critical factor in safety...... of a system. It must be guaranteed that the trajectory of a system subject to fault remains in the region of attraction (ROA) of the post-fault system during this time. This paper proposes a new algorithm to compute the critical fault recovery time for nonlinear systems with polynomial vector elds using sum...
Time-ordering effects in the generation of entangled photons using nonlinear optical processes.
Quesada, Nicolás; Sipe, J E
2015-03-06
We study the effects of time ordering in photon generation processes such as spontaneous parametric down-conversion (SPDC) and four wave mixing (SFWM). The results presented here are used to construct an intuitive picture that allows us to predict when time-ordering effects significantly modify the joint spectral amplitude (JSA) of the photons generated in SPDC and SFWM. These effects become important only when the photons being generated lie with the pump beam that travels through the nonlinear material for a significant amount of time. Thus sources of spectrally separable photons are ideal candidates for the observation of modifications of the JSA due to time ordering.
Effects of Nonlinear Time-Delay on a Stochastic Asymmetric System
Institute of Scientific and Technical Information of China (English)
WANG Jiu-Yun; ZHU Chun-Lian; JIA Ya; LI Jia-Rong
2006-01-01
We numerically investigate the effects of nonlinear time-delay on the stochastic system. With the delay time increasing, it is found that the peak of probability distribution in low steady states is decreased, and the peak of probability distribution in high steady states is increased. The mean of state variable, the normalized variance, and the normalized autocorrelation function which quantifies the concentrated degree are slowly varied for small delay time. However, the mean of state variable is rapidly increased, and the normalized variance and the normalized autocorrelation function is rapidJy decreased for large delay time.
Abdel-Salam, Emad A-B; Hassan, Gmal F
2015-01-01
In this paper, the fractional projective Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Burgers equation, the space-time fractional mKdV equation and time fractional biological population model. The solutions are expressed in terms of fractional hyperbolic functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The fractal index for the obtained results is equal to one. Counter examples to compute the fractal index are introduced in appendix.
Time-Domain Volume Integral Equation for TM-Case Scattering from Nonlinear Penetrable Objects
Institute of Scientific and Technical Information of China (English)
WANG Jianguo; Eric Michielssen
2001-01-01
This paper presents the time-domainvolume integral equation (TDVIE) method to analyzescattering from nonlinear penetrable objects, whichare illuminated by the transverse magnetic (TM) in-cident pulse. The time-domain volume integral equa-tion is formulated in terms of two-dimensional (2D)Green's function, and solved by using the march-on-in time (MOT) technique. Some numerical results aregiven to validate this method, and comparisons aremade with the results obtained by using the finite-difference time-domain (FDTD) method.
Technology and the End of History : From Time Capsules to Time Machines
Munnik, René
2016-01-01
The introduction of writing, especially the alphabet, marked the transition from (oral, mythical) pre-history to history, because it allowed the past to leave its own articulated messages. So, history – consisting of ‘historical facts’, both ‘absent’ and ‘objectively real’ – had a beginning. Contemp
The Fourier decomposition method for nonlinear and non-stationary time series analysis.
Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik
2017-03-01
for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
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.
Neural-network predictive control for nonlinear dynamic systems with time-delay.
Huang, Jin-Quan; Lewis, F L
2003-01-01
A new recurrent neural-network predictive feedback control structure for a class of uncertain nonlinear dynamic time-delay systems in canonical form is developed and analyzed. The dynamic system has constant input and feedback time delays due to a communications channel. The proposed control structure consists of a linearized subsystem local to the controlled plant and a remote predictive controller located at the master command station. In the local linearized subsystem, a recurrent neural network with on-line weight tuning algorithm is employed to approximate the dynamics of the time-delay-free nonlinear plant. No linearity in the unknown parameters is required. No preliminary off-line weight learning is needed. The remote controller is a modified Smith predictor that provides prediction and maintains the desired tracking performance; an extra robustifying term is needed to guarantee stability. Rigorous stability proofs are given using Lyapunov analysis. The result is an adaptive neural net compensation scheme for unknown nonlinear systems with time delays. A simulation example is provided to demonstrate the effectiveness of the proposed control strategy.
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.
Some results of a nodal method for nonlinear space-time reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Le, T.T. (Westinghouse Savannah River Co., Aiken, SC (United States)); Grossman, L.M. (California Univ., Berkeley, CA (United States). Dept. of Nuclear Engineering)
1991-01-01
There are many reports about nodal methods for static and dynamic problems, but not many for the nonlinear feedback cases. In this paper, a class of nodal methods called mathematical nodal method'' (MNM) is studied with the temperature feedback problems. The spatially complex domain of the problem is represented as a collection of geometrically simple subdomains of the size of fuel assemblies called nodes. Over each node, the time dependent coefficients of the neutron flux, precursor concentrations, fuel and coolant temperatures are the surface and volume weighted average (moment) values of the unknown solutions; the space dependent basis functions are a combination of Legendre polynomials. If the material parameters are a linear function of fuel and coolant temperatures, the coupled equations can be put in a dimensionless form and a system of time dependent ordinary differential equations containing nonlinear feedback terms is obtained. These nonlinear feedback terms are updated at each time step during the time iteration process. Results of some benchmark problems are included in this report.
Some results of a nodal method for nonlinear space-time reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Le, T.T. [Westinghouse Savannah River Co., Aiken, SC (United States); Grossman, L.M. [California Univ., Berkeley, CA (United States). Dept. of Nuclear Engineering
1991-12-31
There are many reports about nodal methods for static and dynamic problems, but not many for the nonlinear feedback cases. In this paper, a class of nodal methods called ``mathematical nodal method`` (MNM) is studied with the temperature feedback problems. The spatially complex domain of the problem is represented as a collection of geometrically simple subdomains of the size of fuel assemblies called nodes. Over each node, the time dependent coefficients of the neutron flux, precursor concentrations, fuel and coolant temperatures are the surface and volume weighted average (moment) values of the unknown solutions; the space dependent basis functions are a combination of Legendre polynomials. If the material parameters are a linear function of fuel and coolant temperatures, the coupled equations can be put in a dimensionless form and a system of time dependent ordinary differential equations containing nonlinear feedback terms is obtained. These nonlinear feedback terms are updated at each time step during the time iteration process. Results of some benchmark problems are included in this report.
Nonlinear shot noise, memory systems, and all-time hit parades
Eliazar, Iddo; Klafter, Joseph
2006-07-01
Consider the evolution of a memory system ‘fed’ by an external event-process. New memories are continuously recorded by the system. Simultaneously, the recollection of old memories continuously fades away. Thus, at a given time epoch the memory system ranks all past events according to present importance-magnitudes attributed to them. Illustratively, the memory system is an all-time hit parade run continuously in time. Motivated by a recently-introduced nonlinear shot noise system-model [I. Eliazar, J. Klafter, Physica A, in press (titled: non-linear shot noise: Lévy, Noah, & Joseph).], we explore a memory system-model in which: (i) the external events follow an arbitrary time-homogeneous Poisson point process; and (ii) the ‘fading’ of memories is governed by an arbitrary nonlinear differential-equation dynamics. A Poissonian analysis of the model is conducted, addressing questions such as: How do memories get constructed and degraded? How does the memory process evolve? What is its stationary structure? What is its correlation structure? In addition, a Poissonian eigenvalue problem, arising in this context, is studied.
Dyja, Robert; van der Zee, Kristoffer G
2016-01-01
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...
Liang, Fayun; Chen, Haibing; Huang, Maosong
2017-07-01
To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.
H∞ reference tracking control design for a class of nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Mei-qin LIU; Hai-yang CHEN; Sen-lin ZHANG
2015-01-01
This paper investigates the H∞ trajectory tracking control for a class of nonlinear systems with time-varying delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. A unifi ed model consisting of a linear delayed dynamic system and a bounded static nonlinear operator is introduced, which covers most of the nonlinear systems with bounded nonlinear terms, such as the one-link robotic manipulator, chaotic systems, complex networks, the continuous stirred tank reactor (CSTR), and the standard genetic regulatory network (SGRN). First, the defi nition of the tracking control is given. Second, the H∞ performance analysis of the closed-loop system including this unifi ed model, reference model, and state feedback controller is presented. Then criteria on the tracking controller design are derived in terms of LMIs such that the output of the closed-loop system tracks the given reference signal in the H∞ sense. The reference model adopted here is modifi ed to be more fl exible. A scaling factor is introduced to deal with the disturbance such that the control precision is improved. Finally, a CSTR system is provided to demonstrate the effectiveness of the established control laws.
Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative
Płociniczak, Łukasz; Okrasińska, Hanna
2013-10-01
In this paper, we consider a fractional nonlinear problem for anomalous diffusion. The diffusion coefficient we use is of power type, and hence the investigated problem generalizes the porous-medium equation. A generalization is made by introducing a fractional time derivative. We look for self-similar solutions for which the fractional setting introduces other than classical space-time scaling. The resulting similarity equations are of nonlinear integro-differential type. We approximate these equations by an expansion of the integral operator and by looking for solutions in a power function form. Our method can be easily adapted to solve various problems in self-similar diffusion. The approximations obtained give very good results in numerical analysis. Their simplicity allows for easy use in applications, as our fitting with experimental data shows. Moreover, our derivation justifies theoretically some previously used empirical models for anomalous diffusion.
Global format for energy-momentum based time integration in nonlinear dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2014-01-01
A global format is developed for momentum and energy consistent time integration of second‐order dynamic systems with general nonlinear stiffness. The algorithm is formulated by integrating the state‐space equations of motion over the time increment. The internal force is first represented...... in fourth‐order form consisting of the end‐point mean value plus a term containing the stiffness matrix increment. This form gives energy conservation for systems with internal energy as a quartic function of the displacement components. This representation is then extended to general energy conservation...... of mean value products at the element level or explicit use of a geometric stiffness matrix. An optional monotonic algorithmic damping, increasing with response frequency, is developed in terms of a single damping parameter. In the solution procedure, the velocity is eliminated and the nonlinear...
Adaptive Fuzzy Control of Strict-Feedback Nonlinear Time-Delay Systems With Unmodeled Dynamics.
Yin, Shen; Shi, Peng; Yang, Hongyan
2016-08-01
In this paper, an approximated-based adaptive fuzzy control approach with only one adaptive parameter is presented for a class of single input single output strict-feedback nonlinear systems in order to deal with phenomena like nonlinear uncertainties, unmodeled dynamics, dynamic disturbances, and unknown time delays. Lyapunov-Krasovskii function approach is employed to compensate the unknown time delays in the design procedure. By combining the advances of the hyperbolic tangent function with adaptive fuzzy backstepping technique, the proposed controller guarantees the semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system from the mean square point of view. Two simulation examples are finally provided to show the superior effectiveness of the proposed scheme.
Nonlinear H{sub {infinity}} control of stochastic time-delay systems with Markovian switching
Energy Technology Data Exchange (ETDEWEB)
Wei Guoliang [School of Information Sciences and Technology, Donghua University, Shanghai 200051 (China); Wang Zidong [School of Information Sciences and Technology, Donghua University, Shanghai 200051 (China); Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH (United Kingdom)], E-mail: Zidong.Wang@brunel.ac.uk; Shu Huisheng [Department of Applied Mathematics, Donghua University, Shanghai 200051 (China)
2008-02-15
In this paper, the stabilization and H{sub {infinity}} control problems are investigated for a class of stochastic time-delay systems with both nonlinear disturbances and Markovian jumping parameters. The purpose of the stochastic stabilization problem is to design a memoryless state feedback controller such that, for the addressed nonlinear disturbances as well as Markovian jumping parameters, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. In the H{sub {infinity}} control problem, in addition to the mean-square exponential stability requirement, a prescribed H{sub {infinity}} performance index is required to be achieved. By using Ito's differential formula and the Lyapunov stability theory, sufficient conditions for the solvability of these problems are derived in term of linear matrix inequalities, which can be easily checked by resorting to available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed results.
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.
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.
Explicit finite-difference time domain for nonlinear analysis of waveguide modes
Barakat, N. M.; Shabat, M. M.; El-Azab, S.; Jaeger, Dieter
2003-07-01
The Finite Difference Time Domain Technique is at present the most widely used tool employed in the study of light propagation in various photonic waveguide structure. In this paper we derived an explicit finite-difference time-domain (FDTD) method for solving the wave equation in a four optical waveguiding rectangular structure. We derive the stability condition to achieve the stability in nonlinear media region, we also check that the wave equation used is consistence and convergent with the approximate finite difference equation. Our method is tested against some previous problems and we find a high degree of accuracy, moreover it is easy for programming. Numerical results are illustrated for a rectangular waveguide with four layers, where one of these layers is a nonlinear medium.
Escape time from potential wells of strongly nonlinear oscillators with slowly varying parameters
Directory of Open Access Journals (Sweden)
Cai Jianping
2005-01-01
Full Text Available The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well of quadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear oscillators with slowly varying parameters, and secondly the character of modulus of Jacobian elliptic function is applied to derive the equations governing the escape time. The approximate potential method, instead of Taylor series expansion, is used to approximate the potential of an oscillation system such that the asymptotic solution can be expressed in terms of Jacobian elliptic function. Numerical examples verify the efficiency of the present method.
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.
An approach to design semi-global finite-time observers for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
DENG XiuCheng; SHEN YanJun
2009-01-01
In this paper, the problem of designing semi-global finite-time observers for a class of nonlinear systems is investigated. Based on the theories of finite-time stability, an approach to designing semi-global finite-time observers for the nonlinear systems is presented. It has been shown that, after the finite time, the designed finite-time observer realizes the accurate reconstruction of the states of the nonlinear system. A numerical example is given to illustrate the effectiveness and validity of the method.
History and Point in Time in Enterprise Applications
Directory of Open Access Journals (Sweden)
Constantin Gelu APOSTOL
2006-01-01
Full Text Available First part points out the main differences between temporal and non-temporal databases. In the second part, based on identification of the three main categories of time involved in database applications: user-defined time, valid time and transaction time, some relevant solutions for their implementation are discussed, mainly from the point of view of database organization and data access level of enterprise applications. The final part is dedicated to the influences of historical data in the business logic and presentation levels of enterprise applications and in application services, as security, workflow, reporting.
The history of time a very short introduction
Holford-Strevens, Leofranc
2005-01-01
Leofranc Holford-Strevens explores time measurement and the organisation of time into hours, days, months and years using a range of fascinating examples from Ancient Rome and Julius Caesar's Leap Year, to the 1920s' project for a fixed Easter. - ;Why do we measure time in the way that we do? Why is a week seven days long? At what point did minutes and seconds come into being? Why are some calendars lunar and some solar? The organisation of time into hours, days, months and years seems immutable and universal, but is actually far more artificial than most people realise. The French Revolution
LARGE TIME BEHAVIOR OF SOLUTIONS TO NONLINEAR VISCOELASTIC MODEL WITH FADING MEMORY
Institute of Scientific and Technical Information of China (English)
Yanni Zeng
2012-01-01
We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system of balance laws.When it is a perturbation of a constant state,the solution is shown time asymptotically approaching to predetermined diffusion waves.Pointwise estimates on the convergence details are obtained.
An Inhomogeneous Space-Time Patching Model Based on a Nonlocal and Nonlinear Schrodinger Equation
Dantas, Christine C
2016-01-01
We consider an integrable, nonlocal and nonlinear, Schr\\"odinger equation (NNSE) as a model for building space-time patchings in inhomogeneous loop quantum cosmology (LQC). We briefly review exact solutions of the NNSE, specially those obtained through "geometric equivalence" methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.
Interconnected delay and state observer for nonlinear systems with time-varying input delay
Léchappé, V; Moulay, Emmanuel; Plestan, F; Glumineau, A.
2016-01-01
International audience; This work presents a general framework to estimate both state and delay thanks to two interconnected observers. This scheme can be applied to a large class of nonlinear systems with time-varying input delay. In order to illustrate this approach, a new delay observer based on an optimization technique is proposed. Theoretical results are illustrated and compared with existing works in simulation.
Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping
Directory of Open Access Journals (Sweden)
Jieqiong Wu
2015-09-01
Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.
Numerical Simulations for the Space-Time Variable Order Nonlinear Fractional Wave Equation
Directory of Open Access Journals (Sweden)
Nasser Hassan Sweilam
2013-01-01
Full Text Available The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered. The concept of variable order fractional derivative is considered in the sense of Caputo. The stability analysis and the truncation error of the method are discussed. To demonstrate the effectiveness of the method, some numerical test examples are presented.
A nonlinear ordinary differential equation associated with the quantum sojourn time
Energy Technology Data Exchange (ETDEWEB)
Benguria, Rafael D [Facultad de Fisica, Pontificia Universidad Catolica de Chile, Santiago (Chile); Duclos, Pierre [Universite de Toulon, CPT-CNRS (France); Fernandez, Claudio [Anestoc-Facultad de Matematicas, Pontificia Universidad Catolica de Chile, Santiago (Chile); Sing-Long, Carlos, E-mail: rbenguri@fis.puc.c, E-mail: cfernand@mat.puc.c, E-mail: casinglo@gmail.co [Centro de Imagenes Biomedicas, Pontificia Universidad Catolica de Chile, Santiago (Chile)
2010-11-26
We study a nonlinear ordinary differential equation on the half-line, with the Dirichlet boundary condition at the origin. This equation arises when studying the local maxima of the sojourn time for a free quantum particle whose states belong to an adequate subspace of the unit sphere of the corresponding Hilbert space. We establish several results concerning the existence and asymptotic behavior of the solutions.
Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
Indian Academy of Sciences (India)
Hitender Kumar; Anand Malik; Fakir Chand
2013-02-01
In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.
Estimates for solutions to a class of nonlinear time-delay systems of neutral type
Directory of Open Access Journals (Sweden)
Gennadii V. Demidenko
2015-02-01
Full Text Available We consider nonlinear time-delay systems of neutral type with constant coefficients in the linear terms, $$ \\frac{d}{dt}\\big(y(t + D y(t-\\tau\\big = A y(t + B y(t-\\tau + F(t, y(t, y(t-\\tau. $$ We obtain estimates characterizing the exponential decay of solutions at infinity, and dependending on the norms of the powers of D.
A Nonlinear Small-Gain Theorem for Large-Scale Time Delay Systems
Tiwari, Shanaz; Jiang, Zhong-Ping
2009-01-01
This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain theorem for operators is examined. The result developed for operators allows applications to a wide class of systems, including state space systems with delays.
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.
Nonlinear techniques for forecasting solar activity directly from its time series
Ashrafi, S.; Roszman, L.; Cooley, J.
1993-01-01
This paper presents numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series. This approach makes it possible to extract dynamical in variants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), give a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.
Adaptive Neural Control for a Class of Outputs Time-Delay Nonlinear Systems
Directory of Open Access Journals (Sweden)
Ruliang Wang
2012-01-01
Full Text Available This paper considers an adaptive neural control for a class of outputs time-delay nonlinear systems with perturbed or no. Based on RBF neural networks, the radius basis function (RBF neural networks is employed to estimate the unknown continuous functions. The proposed control guarantees that all closed-loop signals remain bounded. The simulation results demonstrate the effectiveness of the proposed control scheme.
Discussion About Nonlinear Time Series Prediction Using Least Squares Support Vector Machine
Institute of Scientific and Technical Information of China (English)
XU Rui-Rui; BIAN Guo-Xing; GAO Chen-Feng; CHEN Tian-Lun
2005-01-01
The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction.First, the parameter γ and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.
Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan
2017-01-01
The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.
Adaptive Neural Control Design For a Class of Nonlinear Time-delay Systems
Institute of Scientific and Technical Information of China (English)
FENG Ling-ling; ZHANG Wei
2014-01-01
This paper proposes an indirect adaptive neural control scheme for a class of nonlinear systems with time delays. Based on the backstepping technique and Lyapunov–Krasovskii functional method are combined to construct the indirect adaptive neural controller. The proposed indirect adaptive neural controller guarantees that the state variables converge to a small neighborhood of the origin and all the signals of the closed-loop system are bounded. Finally, an example is used to show the effectiveness of the proposed control strategy.
Universal fuzzy models and universal fuzzy controllers for discrete-time nonlinear systems.
Gao, Qing; Feng, Gang; Dong, Daoyi; Liu, Lu
2015-05-01
This paper investigates the problems of universal fuzzy model and universal fuzzy controller for discrete-time nonaffine nonlinear systems (NNSs). It is shown that a kind of generalized T-S fuzzy model is the universal fuzzy model for discrete-time NNSs satisfying a sufficient condition. The results on universal fuzzy controllers are presented for two classes of discrete-time stabilizable NNSs. Constructive procedures are provided to construct the model reference fuzzy controllers. The simulation example of an inverted pendulum is presented to illustrate the effectiveness and advantages of the proposed method. These results significantly extend the approach for potential applications in solving complex engineering problems.
Directory of Open Access Journals (Sweden)
Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
Goos-Haenchen shift and time delay in dispersive nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Ilic, I. [Vinca Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade (Serbia); Belicev, P.P., E-mail: petrab@vinca.r [Vinca Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade (Serbia); Milanovic, V.; Radovanovic, J. [Faculty of Electrical Engineering, University of Belgrade, Bul. kralja Aleksandra 73, 11120 Belgrade (Serbia); Hadzievski, Lj. [Vinca Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade (Serbia)
2011-03-07
We present an analysis of the influence of the Goos-Haenchen effect on tunneling times, group delay and dwell time, of electromagnetic waves propagating through an obstacle made of left-handed metamaterial embedded in a dielectric which exhibits saturable type of nonlinearity. The derived equations show that only the group delay, is affected by the Goos-Haenchen shift without any impact on the dwell time. Besides the reduction of the group delay, the most remarkable result is the possibility for total reduction of the Goos-Haenchen shift for finite incident angles. These phenomena are observable in the frequency region for which metamaterial exhibits negative index of refraction.
Zhang, Huaguang; Song, Ruizhuo; Wei, Qinglai; Zhang, Tieyan
2011-12-01
In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.
Damage Detection of Closed Crack in a Metallic Plate Using Nonlinear Ultrasonic Time Reversal Method
Directory of Open Access Journals (Sweden)
Wang Zhang
2013-01-01
Full Text Available Initial cracks in metallic structures incline to be closed at rest. Such incipient damage generally fails to be detected and located with traditional linear ultrasonic techniques because ultrasonic waves penetrate the contact area of the closed crack. In this paper, an imaging algorithm based on nonlinear ultrasonic time reversal method is proposed to detect closed cracks in aluminum plates. Two surface-bonded piezoelectric transducer arrays are used to generate, receive, and reemit ultrasonic wave signals. The closed crack is simulated by tightening a bolt on the aluminum plate. By applying large amplitude excitation voltage on the PZT transducers, the closed crack could be opened and closed. The transmitted waves recorded by PZT array contain nonlinear components, the signals are time reversed and emitted back, and the tone burst reconstructions are achieved. The linear reciprocity and the time reversibility break down due to the presence of the nonlinear components. The correlation coefficient between the original excitation signal and the reconstructed signal is calculated to define the damage index for individual sensing path and is used to develop an imaging algorithm to locate the closed crack on the plate. The experimental results demonstrate that incident wave signals and their reconstructed signals can be used to accurately detect and locate closed cracks.
Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems.
Liu, Derong; Wei, Qinglai
2014-03-01
This paper is concerned with a new discrete-time policy iteration adaptive dynamic programming (ADP) method for solving the infinite horizon optimal control problem of nonlinear systems. The idea is to use an iterative ADP technique to obtain the iterative control law, which optimizes the iterative performance index function. The main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete-time nonlinear systems for the first time. It shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the Hamilton-Jacobi-Bellman equation. It is also proven that any of the iterative control laws can stabilize the nonlinear systems. Neural networks are used to approximate the performance index function and compute the optimal control law, respectively, for facilitating the implementation of the iterative ADP algorithm, where the convergence of the weight matrices is analyzed. Finally, the numerical results and analysis are presented to illustrate the performance of the developed method.
Development of distributed time-variant gain model for nonlinear hydrological systems
Institute of Scientific and Technical Information of China (English)
XIA; Jun; WANG; Gangsheng; TAN; Ge; YE; Aizhong; G.; H.; Hua
2005-01-01
In this paper, a rainfall-runoff modeling system is developed based on a nonlinear Volterra functional series and a hydrological conceptual modeling approach. Two models, i.e. the time-variant gain model (TVGM) and the distributed time-variant gain model (DTVGM) that are built on the platform of Digital Elevation Model (DEM), Remote Sensing (RS) and Unit Hydrological Process were proposed. The developed DTVGM model was applied to two cases in the Heihe River Basin that is located in the arid and semiarid region of northwestern China and the Chaobai River basin located in the semihumid region of northern China. The results indicate that, in addition to the classic dynamic differential approach to describe nonlinear processes in hydrological systems, it is possible to study such complex processes through the proposed systematic approach to identify prominent hydrological relations. The DTVGM, coupling the advantages of both nonlinear and distributed hydrological models, can simulate variant hydrological processes under different environment conditions. Satisfactory results were obtained in forecasting the time-space variations of hydrological processes and the relationships between land use/cover change and surface runoff variation.
Boiler-turbine control system design using continuous-time nonlinear model predictive control
Institute of Scientific and Technical Information of China (English)
ZHUO Xu-sheng; ZHOU Huai-chun
2008-01-01
A continuous-time nonlinear model predictive controller (NMPC) was designed for a boiler-turbine unit. The controller was designed by optimizing a receding-horizon performance index, with the nonlinear system approximated by its Taylor series expansion with a certain order, the magnitude saturation constraints on the inputs satisfied by increasing the predictive time, and the rate saturation conditions on the actuators satisfied by tuning the time constant of the reference trajectories in a reference governor. Simulation results showed that the controller can drive the drum pressure and output power of the nonlinear boiler-turbine unit to follow their respective reference trajectories throughout a varying operation range and keep the water level deviation within tolerances. Comparison of the NMPC scheme with the generic model control (GMC) scheme indicated that the responses are slower and there are more oscillations in the responses of the water level, fuel flow input and feed water flow input in the GMC scheme when the boiler-turbine unit is operating over a wide range.
Time reversal invariance for a one-dimensional model of contact acoustic nonlinearity
Blanloeuil, Philippe; Francis Rose, L. R.; Veidt, Martin; Wang, Chun H.
2017-04-01
The interaction of a one-dimensional (1D) wave packet with a contact interface characterized by a unilateral contact law is investigated analytically and through a finite difference model. It is shown that this interaction leads to the generation of higher harmonic, sub-harmonic and zero-frequency components in the reflected wave, resulting in a pulse distortion that is attributable to contact acoustic nonlinearity. However, the results also show that the re-emission of a time reversed version of this distorted first reflection results in a healing of the distortions and a perfect recovery of the original pulse shape, thereby demonstrating time reversal invariance for this type of contact acoustic nonlinearity. A step-by-step analysis of the contact interaction provides insights into both the distortion arising from the first interaction and the subsequent healing during the second interaction. These findings suggest that time reversal invariance should also apply more generally for scatterers exhibiting non-dissipative contact acoustic nonlinearity.
Multivariate time delay analysis based local KPCA fault prognosis approach for nonlinear processes☆
Institute of Scientific and Technical Information of China (English)
Yuan Xu; Ying Liu; Qunxiong Zhu
2016-01-01
Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in-cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal com-ponent analysis. In this approach, mutual information estimation and Bayesian information criterion (BIC) are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation (BP) network is applied whose input is multivar-iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis (LKPCA) model for incipient fault prognosis. The new method has been exemplified in a sim-ple nonlinear process and the complicated Tennessee Eastman (TE) benchmark process. The results indicate that the new method has superiority in the fault prognosis sensitivity over other traditional fault prognosis methods. © 2016 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. Al rights reserved.
Fluid resuscitation in human sepsis: Time to rewrite history?
Byrne, Liam; Van Haren, Frank
2017-12-01
Fluid resuscitation continues to be recommended as the first-line resuscitative therapy for all patients with severe sepsis and septic shock. The current acceptance of the therapy is based in part on long history and familiarity with its use in the resuscitation of other forms of shock, as well as on an incomplete and incorrect understanding of the pathophysiology of sepsis. Recently, the safety of intravenous fluids in patients with sepsis has been called into question with both prospective and observational data suggesting improved outcomes with less fluid or no fluid. The current evidence for the continued use of fluid resuscitation for sepsis remains contentious with no prospective evidence demonstrating benefit to fluid resuscitation as a therapy in isolation. This article reviews the historical and physiological rationale for the introduction of fluid resuscitation as treatment for sepsis and highlights a number of significant concerns based on current experimental and clinical evidence. The research agenda should focus on the development of hyperdynamic animal sepsis models which more closely mimic human sepsis and on experimental and clinical studies designed to evaluate minimal or no fluid strategies in the resuscitation phase of sepsis.
Müller, Markus; Meztler, Holger; Glatt, Anna; Sierra, Carlos
2016-04-01
We present theoretical methods to compute dynamic residence and transit time distributions for non-autonomous systems of pools governed by coupled nonlinear differential equations. Although transit time and age distributions have been used to describe reservoir models for a long time, a closer look to their assumptions reveals two major restrictions of generality in previous studies. First, the systems are assumed to be in equilibrium; and second, the equations under consideration are assumed to be linear. While both these assumptions greatly ease the computation and interpretation of transit time and age distributions they are not applicable to a wide range of problems. Moreover, the transfer of previous results learned from linear systems in steady state to the more complex nonlinear non-autonomous systems that do not even need to have equilibria, can be dangerously misleading. Fortunately the topic of time dependent age and transit time distributions has received some attention recently in hydrology, we aim to compute these distributions for systems of multiple reservoirs. We will discuss how storage selection functions can augment the information represented in an ODE system describing a system of reservoirs. We will present analytical and numerical algorithms and a Monte Carlo simulator to compute solutions for system transit time and age distributions for system-wide storage selection functions including the most simple, but important case of well mixed pools.
Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad
2014-11-01
This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
G. P. Pavlos
1999-01-01
Full Text Available A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper and dynamical characteristics (Part II, which is the work a separate paper, and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.
Reservoir computing and extreme learning machines for non-linear time-series data analysis.
Butcher, J B; Verstraeten, D; Schrauwen, B; Day, C R; Haycock, P W
2013-02-01
Random projection architectures such as Echo state networks (ESNs) and Extreme Learning Machines (ELMs) use a network containing a randomly connected hidden layer and train only the output weights, overcoming the problems associated with the complex and computationally demanding training algorithms traditionally used to train neural networks, particularly recurrent neural networks. In this study an ESN is shown to contain an antagonistic trade-off between the amount of non-linear mapping and short-term memory it can exhibit when applied to time-series data which are highly non-linear. To overcome this trade-off a new architecture, Reservoir with Random Static Projections (R(2)SP) is investigated, that is shown to offer a significant improvement in performance. A similar approach using an ELM whose input is presented through a time delay (TD-ELM) is shown to further enhance performance where it significantly outperformed the ESN and R(2)SP as well other architectures when applied to a novel task which allows the short-term memory and non-linearity to be varied. The hard-limiting memory of the TD-ELM appears to be best suited for the data investigated in this study, although ESN-based approaches may offer improved performance when processing data which require a longer fading memory.
Marzuola, Jeremy L
2009-01-01
We consider a class nonlinear Schr\\"odinger / Gross-Pitaevskii equations (NLS/GP) with a focusing (attractive) nonlinear potential and symmetric double well linear potential. NLS/GP plays a central role in the modeling of nonlinear optical and mean-field quantum many-body phenomena. It is known that there is a critical $L^2$ norm (optical power / particle number) at which there is a symmetry breaking bifurcation of the ground state. We study the rich dynamical behavior near the symmetry breaking point. The source of this behavior in the full Hamiltonian PDE is related to the dynamics of a finite-dimensional Hamiltonian reduction. We derive this reduction, analyze a part of its phase space and prove a {\\it shadowing theorem} on the persistence of solutions, with oscillating mass-transport between wells, on very long, but finite, time scales within the full NLS/GP. The infinite time dynamics for NLS/GP are expected to depart, from the finite dimensional reduction, due to resonant coupling of discrete and contin...
Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay
Institute of Scientific and Technical Information of China (English)
Zhang Aiqing; Fang Huajing
2008-01-01
To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems,the Takagi-Sugeno(T-S)fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay.Based on the linear matrix inequality(LMI)techniques and stability theory of stochastic differential equations,a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller.The resulting closed-loop fuzzy system is robustly reliable stochastically stable,and the corresponding quadratic cost function is guarauteed to be no more than a certain upper bound for all admissible uncertainties,as well as different actuator fault cases.A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented.Finally,a numerical simulation is given to illustrate the effectiveness of the proposed method.
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.
Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation.
Joldes, Grand Roman; Wittek, Adam; Miller, Karol
2010-12-15
Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom. In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.
Time-Frequency (Wigner Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers
Directory of Open Access Journals (Sweden)
José Azaña
2005-06-01
Full Text Available Time-frequency analysis, and, in particular, Wigner analysis, is applied to the study of picosecond pulse propagation through optical fibers in both the linear and nonlinear regimes. The effects of first- and second-order group velocity dispersion (GVD and self-phase modulation (SPM are first analyzed separately. The phenomena resulting from the interplay between GVD and SPM in fibers (e.g., soliton formation or optical wave breaking are also investigated in detail. Wigner analysis is demonstrated to be an extremely powerful tool for investigating pulse propagation dynamics in nonlinear dispersive systems (e.g., optical fibers, providing a clearer and deeper insight into the physical phenomena that determine the behavior of these systems.
Direct adaptive control for a class of MIMO nonlinear discrete-time systems
Institute of Scientific and Technical Information of China (English)
Lei Li; Zhizhong Mao
2014-01-01
This paper considers the problem of adaptive con-trol for a class of multiple input multiple output (MIMO) nonlinear discrete-time systems based on input-output model with unknown interconnections between subsystems. Based on the Taylor ex-pand technology, an equivalent model in affine-like form is derived for the original nonaffine nonlinear system. Then a direct adap-tive neural network (NN) control er is implemented based on the affine-like model. By finding an orthogonal matrix to tune the NN weights, the closed-loop system is proven to be semiglobal y uni-formly ultimately bounded. The σ-modification technique is used to remove the requirement of persistence excitation during the adaptation. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.
Efendiev, Y.
2009-11-01
The Markov chain Monte Carlo (MCMC) is a rigorous sampling method to quantify uncertainty in subsurface characterization. However, the MCMC usually requires many flow and transport simulations in evaluating the posterior distribution and can be computationally expensive for fine-scale geological models. We propose a methodology that combines coarse- and fine-scale information to improve the efficiency of MCMC methods. The proposed method employs off-line computations for modeling the relation between coarse- and fine-scale error responses. This relation is modeled using nonlinear functions with prescribed error precisions which are used in efficient sampling within the MCMC framework. We propose a two-stage MCMC where inexpensive coarse-scale simulations are performed to determine whether or not to run the fine-scale (resolved) simulations. The latter is determined on the basis of a statistical model developed off line. The proposed method is an extension of the approaches considered earlier where linear relations are used for modeling the response between coarse-scale and fine-scale models. The approach considered here does not rely on the proximity of approximate and resolved models and can employ much coarser and more inexpensive models to guide the fine-scale simulations. Numerical results for three-phase flow and transport demonstrate the advantages, efficiency, and utility of the method for uncertainty assessment in the history matching. Copyright 2009 by the American Geophysical Union.
Space-time clusters of breast cancer using residential histories
DEFF Research Database (Denmark)
Nordsborg, Rikke Baastrup; Meliker, Jaymie R; Ersbøll, Annette Kjær
2014-01-01
selected from the Civil Registration System. Residential addresses of cases and controls from 1971 to 2003 were collected from the Civil Registration System and geo-coded. Q-statistics were used to identify space-time clusters of breast cancer. All analyses were carried out with both control groups...
Plotting a History: Black and Postcolonial Feminisms in "New Times"
Mirza, Heidi Safia
2009-01-01
Black feminist thought is grounded in an understanding of the nature of power and the way black/othered difference women's is systematically organised through social relations. Postcolonial feminist approaches enable us to situate the silent "spectral" power of colonial times as it appears in the production and reproduction of marginalised,…
UC Berkeley Seismic Guidelines, Appendix II: Ground Motion Time Histories for the UC Berkeley Campus
Energy Technology Data Exchange (ETDEWEB)
Authors, Various
2003-06-03
Three sets of ten time histories each were developed to represent the ground motions for each of the three return periods. All of the time histories are provided as pairs of fault-normal and fault-parallel components. The ground motion time histories are provided in two forms: unmodified, and spectrally modified to match the probabilistic response spectra. The unmodified time histories can be scaled to match the probabilistic response spectra at a specified period, such as the first mode period of the structure being analyzed, while leaving the shape of the response spectrum unmodified. This approach preserves the particular characteristics of the individual time history, together with the peaks and troughs of its response spectrum. These individual characteristics are modified in the spectrally matched time histories, resulting in a suite of ten time histories (for a given return period) that all have the same response spectrum for a given component (fault normal or fault parallel) that follows the smooth shape of the probabilistic response spectrum.
UC Berkeley Seismic Guidelines, Appendix II: Ground Motion TimeHistories for the UC Berkeley Campus
Energy Technology Data Exchange (ETDEWEB)
Various
2003-06-03
Three sets of ten time histories each were developed to represent the ground motions for each of the three return periods. All of the time histories are provided as pairs of fault-normal and fault-parallel components. The ground motion time histories are provided in two forms: unmodified, and spectrally modified to match the probabilistic response spectra. The unmodified time histories can be scaled to match the probabilistic response spectra at a specified period, such as the first mode period of the structure being analyzed, while leaving the shape of the response spectrum unmodified. This approach preserves the particular characteristics of the individual time history, together with the peaks and troughs of its response spectrum. These individual characteristics are modified in the spectrally matched time histories, resulting in a suite of ten time histories (for a given return period) that all have the same response spectrum for a given component (fault normal or fault parallel) that follows the smooth shape of the probabilistic response spectrum.
Finite time extinction for nonlinear fractional evolution equations and related properties
Directory of Open Access Journals (Sweden)
Jesus Ildefonso Diaz
2016-08-01
Full Text Available The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time.
Conservative fourth-order time integration of non-linear dynamic systems
DEFF Research Database (Denmark)
Krenk, Steen
2015-01-01
An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating the re...... integration of oscillatory systems with only a few integration points per period. Three numerical examples demonstrate the high accuracy of the algorithm. (C) 2015 Elsevier B.V. All rights reserved.......An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...
Variable structure control with sliding mode prediction for discrete-time nonlinear systems
Institute of Scientific and Technical Information of China (English)
Lingfei XIAO; Hongye SU; Xiaoyu ZHANG; Jian CHU
2006-01-01
A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2013-01-01
Full Text Available The fractional Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, space-time fractional Korteweg-de Vries equation, regularized long-wave equation, Boussinesq equation, and Klein-Gordon equation are considered. As a result, abundant types of exact analytical solutions are obtained. These solutions include generalized trigonometric and hyperbolic functions solutions which may be useful for further understanding of the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The periodic and kink solutions are founded as special case.
Nonlinear System Identification via Basis Functions Based Time Domain Volterra Model
Directory of Open Access Journals (Sweden)
Yazid Edwar
2014-07-01
Full Text Available This paper proposes basis functions based time domain Volterra model for nonlinear system identification. The Volterra kernels are expanded by using complex exponential basis functions and estimated via genetic algorithm (GA. The accuracy and practicability of the proposed method are then assessed experimentally from a scaled 1:100 model of a prototype truss spar platform. Identification results in time and frequency domain are presented and coherent functions are performed to check the quality of the identification results. It is shown that results between experimental data and proposed method are in good agreement.
Improved adaptive fuzzy control for MIMO nonlinear time-delay systems
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper presents an improved observer-based indirect adaptive fuzzy control scheme for multiinput-multioutput (MIMO) nonlinear time-delay systems.The control scheme synthesizes adaptive fuzzy control with adaptive fuzzy identification.An observer is designed to observe the system state,and an identifier is developed to identify the unknown parts of the system.The update laws for parameters utilize two types of errors in the adaptive time-delay fuzzy logic systems,the observation error and the identificat...
Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients.
Ge, Shuzhi Sam; Hong, Fan; Lee, Tong Heng
2004-02-01
In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop. In addition, the output of the system is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.
Institute of Scientific and Technical Information of China (English)
Weihai ZHANG; Xuezhen LIU; Shulan KONG; Qinghua LI
2006-01-01
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
Adaptive output feedback control of a class of uncertain nonlinear systems with unknown time delays
Guan, Wei
2012-04-01
This article studies the adaptive output feedback control problem of a class of uncertain nonlinear systems with unknown time delays. The systems considered are dominated by a triangular system without zero dynamics satisfying linear growth in the unmeasurable states. The novelty of this article is that a universal-type adaptive output feedback controller is presented to time-delay systems, which can globally regulate all the states of the uncertain systems without knowing the growth rate. An illustrative example is provided to show the applicability of the developed control strategy.
Nonlinear ion dynamics in Hall thruster plasma source by ion transit-time instability
Lim, Youbong; Choe, Wonho; Mazouffre, Stéphane; Park, Jae Sun; Kim, Holak; Seon, Jongho; Garrigues, L.
2017-03-01
High-energy tail formation in an ion energy distribution function (IEDF) is explained in a Hall thruster plasma with the stationary crossed electric and magnetic fields whose discharge current is oscillated at the ion transit-time scale with a frequency of 360 kHz. Among ions in different charge states, singly charged Xe ions (Xe+) have an IEDF that is significantly broadened and shifted toward the high-energy side, which contributes to tail formation in the entire IEDF. Analytical and numerical investigations confirm that the IEDF tail is due to nonlinear ion dynamics in the ion transit-time oscillation.
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.
Generation of squeezed-state superpositions via time-dependent Kerr nonlinearities
León-Montiel, R de J
2015-01-01
We put forward an experimental scheme for direct generation of optical squeezed coherent-state superpositions. The proposed setup makes use of an optical cavity, filled with a nonlinear Kerr medium, whose frequency is allowed to change during time evolution. By exactly solving the corresponding time-dependent anharmonic-oscillator Hamiltonian, we demonstrate that squeezed-state superpositions can be generated in an optical cavity. Furthermore, we show that the squeezing degree of the produced states can be tuned by properly controlling the frequency shift of the cavity, a feature that could be useful in many quantum information protocols, such as quantum teleportation and quantum computing.
Non-linear wave loads and ship responses by a time-domain strip theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representation. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation. ...... and are systematically compared with the experimental results given by Watanabe et al. (1989, J. Soc. Naval Architects Japan, 166) and O’Dea et al. (1992, Proc. 19th Symp. on Naval Hydrodynamics). The agreement between the present predictions and the experiments is very encouraging....
A short history of time and space in immune discrimination.
Langman, R E; Cohn, M
1996-12-01
The destructive effector functions of the immune system pose a problem that has aptly been described as 'horror autotoxicus'. This problem demands a solution that offers an effective self-nonself discrimination mechanism. Unlike all other defence mechanisms, the immune system makes the self-nonself discrimination somatically, and not at the germline level. This discrimination requires a way of separating self from nonself. Two proposals to accomplish this are based on separation in time or in space. In this paper the authors show that separation in time remains the only viable solution. A generally accepted solution to the mechanism of the self-nonself discrimination is overdue as it strongly influences the way in which much of immune regulation is interpreted.
Donges, Jonathan; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik; Marwan, Norbert; Dijkstra, Henk; Kurths, Jürgen
2016-04-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. pyunicorn is available online at https://github.com/pik-copan/pyunicorn. Reference: J.F. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q.-Y. Feng, L. Tupikina, V. Stolbova, R.V. Donner, N. Marwan, H.A. Dijkstra, and J. Kurths, Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos 25, 113101 (2015), DOI: 10.1063/1.4934554, Preprint: arxiv.org:1507.01571 [physics.data-an].
The Treatment of Geological Time & the History of Life on Earth in High School Biology Textbooks
Summers, Gerald; Decker, Todd; Barrow, Lloyd
2007-01-01
In spite of the importance of geological time in evolutionary biology, misconceptions about historical events in the history of life on Earth are common. Glenn (1990) has documented a decline from 1960 to 1989 in the amount of space devoted to the history of life in high school earth science textbooks, but we are aware of no similar study in…
Testing for nonlinearity in time series: The method of surrogate data
Energy Technology Data Exchange (ETDEWEB)
Theiler, J.; Galdrikian, B.; Longtin, A. (Los Alamos National Lab., NM (United States)); Eubank, S.; Farmer, J.D. (Los Alamos National Lab., NM (United States) Santa Fe Inst., NM (United States))
1991-01-01
We describe a statistical approach for identifying nonlinearity in time series; in particular, we want to avoid claims of chaos when simpler models (such as linearly correlated noise) can explain the data. The method requires a careful statement of the null hypothesis which characterizes a candidate linear process, the generation of an ensemble of surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. We present algorithms for generating surrogate data under various null hypotheses, and we show the results of numerical experiments on artificial data using correlation dimension, Lyapunov exponent, and forecasting error as discriminating statistics. Finally, we consider a number of experimental time series -- including sunspots, electroencephalogram (EEG) signals, and fluid convection -- and evaluate the statistical significance of the evidence for nonlinear structure in each case. 56 refs., 8 figs.
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2002-01-01
Spatiotemporal instability in nonlinear dispersive media is investigated on the basis of the nonlinear envelope equation. A general expression for instability gain which includes the effects of space-time focusing, arbitrarily higher-order dispersions and self-steepening is obtained. It is found that, for both normal and anomalous group-velocity dispersions, space-time focusing may lead to the appearance of new instability regions and influence the original instability gain spectra mainly by shrinking their regions. The region of the original instability gain spectrum shrinks much more in normal dispersion case than in anomalous one. In the former case, space-time focusing completely suppresses the growing of higher frequency components. In addition, we find that all the oddth-order dispersions contribute none to instability, while all the eventh-order dispersions influence instability region and do not influence the maximum instability gain, therein the fourth-order dispersion plays the same role as space-time focusing in spatiotemporal instability. The main role played by self-steepening in spatiotemporal instability is that it reduces the instability gain and exerts much more significant influence on the new instability regions resulting from space-time focusing.
Short-time Lv transform and its application for non-linear FM signal detection
Institute of Scientific and Technical Information of China (English)
Shan Luo; Xiumei Li; Guoan Bi
2015-01-01
A new time-frequency transform, known as short-time Lv transform (STLVT), is proposed by applying the inverse Lv dis-tribution to process consecutive segments of long data sequence. Compared with other time-frequency representations, the STLVT is able to achieve better energy concentration in the time-frequency domain for signals containing multiple linear and/or non-linear frequency modulated components. The merits of the STLVT are demonstrated in terms of the effects of window length and overlap length between adjacent segments on signal energy concentra-tion in the time-frequency domain, and the required computational complexity. An application on the spectrum sensing for cognitive ratio (CR) by using a joint use of the STLVT and Hough transform (HT) is proposed and simulated.
Directory of Open Access Journals (Sweden)
Xiaohui Mo
2017-01-01
Full Text Available In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.
Ganjefar, Soheil; Rezaei, Sara; Hashemzadeh, Farzad
2017-03-01
In this paper, a new bounded force feedback control law is proposed to guarantee position and force tracking in nonlinear teleoperation systems in the presence of passive and nonpassive input interaction forces, time varying delay in their communication channels and sandwich linearity in their actuators. The proposed control is a nonlinear-proportional plus nonlinear damping (nP+nD) controller with the addition of a nonlinear function of the environment force on the slave side and nonlinear function of the human force and force error on the master side, the transparency of the proposed scheme will be improved. The controller prevents the inputs from reaching their usual actuator bounds. Using a novel Lyapunov-Krasovskii functional, the asymptotic stability and tracking performance of the teleoperation system are established under some conditions on the controller parameters, actuator saturation characteristics and maximum allowable time delays.
Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations
Energy Technology Data Exchange (ETDEWEB)
Mikaelian, K O
2009-09-28
We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub L}). The model is found to be in very good agreement with direct numerical simulations. Bubble amplitudes for a variety of accelerations are seen to scale with s defined by s = {integral} {radical}g(t)dt, while spike amplitudes prefer scaling with displacement {Delta}x = {integral}[{integral}g(t)dt]dt.
Energy Technology Data Exchange (ETDEWEB)
Wang, Hailing [Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong); Chung, Kwok-wai, E-mail: makchung@cityu.edu.hk [Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)
2012-02-27
The analytical solutions of nonlinear oscillators obtained from most perturbation or approximate methods usually have poor accuracy near homoclinic/heteroclinic (HH) orbits. In this Letter, we propose a nonlinear time transformation method to overcome such difficulty. In particular, we apply such method with Padé approximation to find analytical solutions of a generalized Duffing-harmonic oscillator having a rational form for the potential energy. For some parametric ranges, HH orbits exist in such an oscillator. For analytical approximation of periodic solution obtained from the present method, it is shown that the relative error of period with respect to the exact period tends to zero when the amplitude of periodic solution tends to either zero or infinity. The relative error is still very small even near to HH orbits. Furthermore, analytical approximate of HH orbits can also be obtained. From the illustrative examples, the phase portraits are in excellent agreement with the exact HH orbits. The results from the present method are compared with the exact solutions and that from the cubication method. -- Highlights: ► A nonlinear transformation is proposed for a generalized Duffing-harmonic oscillator. ► The relative error of period with respect to the exact one is always very small. ► Approximate solution of homoclinic/heteroclinic orbits can be obtained. ► Phase portraits are in excellent agreement even at homoclinic/heteroclinic orbits.
Cao, Jiguo
2012-01-01
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
A time integral formulation and algorithm for structural dynamics with nonlinear stiffness
Institute of Scientific and Technical Information of China (English)
Kaiping Yu; Jie Zhao
2006-01-01
A newly-developed numerical algorithm, which is called the new Generalized-α(G-α)method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zerostable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.
Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof.
Al-Tamimi, Asma; Lewis, Frank L; Abu-Khalaf, Murad
2008-08-01
Convergence of the value-iteration-based heuristic dynamic programming (HDP) algorithm is proven in the case of general nonlinear systems. That is, it is shown that HDP converges to the optimal control and the optimal value function that solves the Hamilton-Jacobi-Bellman equation appearing in infinite-horizon discrete-time (DT) nonlinear optimal control. It is assumed that, at each iteration, the value and action update equations can be exactly solved. The following two standard neural networks (NN) are used: a critic NN is used to approximate the value function, whereas an action network is used to approximate the optimal control policy. It is stressed that this approach allows the implementation of HDP without knowing the internal dynamics of the system. The exact solution assumption holds for some classes of nonlinear systems and, specifically, in the specific case of the DT linear quadratic regulator (LQR), where the action is linear and the value quadratic in the states and NNs have zero approximation error. It is stressed that, for the LQR, HDP may be implemented without knowing the system A matrix by using two NNs. This fact is not generally appreciated in the folklore of HDP for the DT LQR, where only one critic NN is generally used.
Cao, Jiguo; Huang, Jianhua Z; Wu, Hulin
2012-01-01
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
Optimum Control for Nonlinear Dynamic Radial Deformation of Turbine Casing with Time-Varying LSSVM
Directory of Open Access Journals (Sweden)
Cheng-Wei Fei
2015-01-01
Full Text Available With the development of the high performance and high reliability of aeroengine, the blade-tip radial running clearance (BTRRC of high pressure turbine seriously influences the reliability and performance of aeroengine, wherein the radial deformation control of turbine casing has to be concerned in BTRRC design. To improve BTRRC design, the optimum control-based probabilistic optimization of turbine casing radial deformation was implemented using time-varying least square support vector machine (T-LSSVM by considering nonlinear material properties and dynamic thermal load. First the T-LSSVM method was proposed and its mathematical model was established. And then the nonlinear dynamic optimal control model of casing radial deformation was constructed with T-LSSVM. Thirdly, through the numerical experiments, the T-LSSVM method is demonstrated to be a promising approach in reducing additional design samples and improving computational efficiency with acceptable computational precision. Through the optimum control-based probabilistic optimization for nonlinear dynamic radial turbine casing deformation, the optimum radial deformation is 7.865 × 10−4 m with acceptable reliability degree 0.995 6, which is reduced by 7.86 × 10−5 m relative to that before optimization. These results validate the effectiveness and feasibility of the proposed T-LSSVM method, which provides a useful insight into casing radial deformation, BTRRC control, and the development of gas turbine with high performance and high reliability.
Case histories show real-time information reduces uncertainty
Energy Technology Data Exchange (ETDEWEB)
Meehan, R. [Schlumberger Cambridge Research, Cambridge, MA (United States); Nutt, L. [Schlumberger Wireline and Testing, Houston, TX (United States); Dutta, N. [BP Exploration, Houston, TX (United States); Menzies, J. [Lasmo plc, London (United Kingdom)
1998-05-18
Drill-bit seismic technology provides useful real-time information that reduces uncertainty for the driller. This second part of a two-part series provides real examples, describes the current state of technology and experience, and discusses techniques that will add value through the incorporation of additional information sources. To date, this technology has been used on more than 50 wells in all areas of the world, including a deepwater job in 1,200 m of water. As of March 1998, there were five ongoing jobs in Oman, Indonesia, Malaysia, Gulf of Mexico, and South America. The following examples of oil and gas wells demonstrate the application of the drill-bit seismic technique and show benefits that can be brought to the drilling process.
Nonlinear model of space manipulator joint considering time-variant stiffness and backlash
Yang, Tianfu; Yan, Shaoze; Han, Zengyao
2015-04-01
Modeling of space manipulator joints has been studied for years but accurate positioning control is still unsatisfactory. One of the primary reasons is that, in the past researches, effects of the high-ratio reducers in the joints have usually been neglected. In this paper, a nonlinear dynamic model of the manipulator joint with planetary gear train transmission is developed by considering time-variant joint stiffness, backlash and reduction ratio. Based on the gear parameters and meshing phase relationship, the stiffness of the joint model is presented, in which the time-variant stiffness of 2K-H planetary gear train and the backlash are taken into consideration. The backlash effect is modeled as an alternate engagement mechanism, and the transmitted torque is defined as a dead zone function. This model is simulated on a two-link space manipulator system. The results show that the time-variant stiffness effect can be simplified as a constant value in most cases when other shafting parts are flexible, while if the total stiffness is approximate to the nonlinear stiffness, the positioning accuracy is reduced if neglecting the time-variant part. On the other hand, the backlash is the main source of positioning error and impact. Minimizing backlash is the most effective way to improve positioning accuracy and avoid the impact in the gearing system.
Non-Linear Dynamic Analysis of Inter-Word Time Intervals in Psychotic Speech.
Todder, Doron; Avissar, Sofia; Schreiber, Gabriel
2013-01-01
"Language is a form and not a substance" - Ferdinand de Saussure Objective: Analyses of speech processes in schizophrenia are invariably focused on words as vocal signals. The results of such analyses are, however, strongly related to content, and may be language- and culture-dependent. Little attention has been paid to a pure measure of the form of speech, unrelated to its content: inter-words time intervals. 15 patients with schizophrenia and 15 healthy volunteers are recorded spontaneously speaking for 10-15 min. Recordings are analyzed for inter-words time intervals using the following non-linear dynamical methods: unstable periodic orbits, correlation dimension, bi-spectral analysis, and symbolic dynamics. The series of inter-word time intervals in normal speech have the characteristics of a low-dimensional chaotic attractor with a correlation dimension of [Formula: see text]. Deconstruction of the attractor appears in psychosis with re-establishment after anti-psychotic treatment. Shannon entropy, a measure of the complexity in the time series, calculated from symbolic dynamics, is higher for psychotic speech, which is also characterized by higher levels of phase coupling: higher bicoherence, obtained using bi-spectral analysis. Non-linear dynamical methods applied to ITIs thus enable a content-independent, pure measure of the form of normal thought, its distortion in psychosis, and its restoration under treatment.
Donges, Jonathan F; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V; Marwan, Norbert; Dijkstra, Henk A; Kurths, Jürgen
2015-11-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.
Conservative fourth-order time integration of non-linear dynamic systems
DEFF Research Database (Denmark)
Krenk, Steen
2015-01-01
An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating the re...... integration of oscillatory systems with only a few integration points per period. Three numerical examples demonstrate the high accuracy of the algorithm. (C) 2015 Elsevier B.V. All rights reserved.......An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...
Variational space-time (dis)continuous Galerkin method for nonlinear free surface water waves
Gagarina, E.; Ambati, V. R.; van der Vegt, J. J. W.; Bokhove, O.
2014-10-01
A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a finite element discretization that is continuous in space and discontinuous in time. One novel feature of this variational finite element approach is that the free surface evolution is variationally dependent on the mesh deformation vis-à-vis the mesh deformation being geometrically dependent on free surface evolution. Another key feature is the use of a variational (dis)continuous Galerkin finite element discretization in time. Moreover, in the absence of a wave maker, it is shown to be equivalent to the second order symplectic Störmer-Verlet time stepping scheme for the free-surface degrees of freedom. These key features add to the stability of the numerical method. Finally, the resulting numerical scheme is verified against nonlinear analytical solutions with long time simulations and validated against experimental measurements of driven wave solutions in a wave basin of the Maritime Research Institute Netherlands.
Moradi, Hojjatullah; Majd, Vahid Johari
2016-05-01
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.
The quantile spectral density and comparison based tests for nonlinear time series
Lee, Junbum
2011-01-01
In this paper we consider tests for nonlinear time series, which are motivated by the notion of serial dependence. The proposed tests are based on comparisons with the quantile spectral density, which can be considered as a quantile version of the usual spectral density function. The quantile spectral density 'measures' sequential dependence structure of a time series, and is well defined under relatively weak mixing conditions. We propose an estimator for the quantile spectral density and derive its asympototic sampling properties. We use the quantile spectral density to construct a goodness of fit test for time series and explain how this test can also be used for comparing the sequential dependence structure of two time series. The method is illustrated with simulations and some real data examples.
Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity.
Srinivasan, K; Senthilkumar, D V; Murali, K; Lakshmanan, M; Kurths, J
2011-06-01
Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay τ(1) and coupling delay τ(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay τ(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.
Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo
2016-04-08
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
Distributed robust finite-time nonlinear consensus protocols for multi-agent systems
Zuo, Zongyu; Tie, Lin
2016-04-01
This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.
Directory of Open Access Journals (Sweden)
Luís F. P. Silva
2014-01-01
Full Text Available A convex condition in terms of linear matrix inequalities (LMIs is developed for the synthesis of stabilizing fuzzy state feedback controllers for nonlinear discrete-time systems with time-varying delays. A Takagi-Sugeno (T-S fuzzy model is used to represent exactly the nonlinear system in a restricted domain of the state space, called region of validity. The proposed stabilization condition is based on a Lyapunov-Krasovskii (L-K function and it takes into account the region of validity to determine a set of initial conditions for which the actual closed-loop system trajectories are asymptotically stable and do not evolve outside the region of validity. This set of allowable initial conditions is determined from the level set associated to a fuzzy L-K function as a Cartesian product of two subsets: one characterizing the set of states at the initial instant and another for the delayed state sequence necessary to characterize the initial conditions. Finally, we propose a convex programming problem to design a fuzzy controller that maximizes the set of initial conditions taking into account the shape of the region of validity of the T-S fuzzy model. Numerical simulations are given to illustrate this proposal.
Directory of Open Access Journals (Sweden)
Fengxia Xu
2014-01-01
Full Text Available U-model can approximate a large class of smooth nonlinear time-varying delay system to any accuracy by using time-varying delay parameters polynomial. This paper proposes a new approach, namely, U-model approach, to solving the problems of analysis and synthesis for nonlinear systems. Based on the idea of discrete-time U-model with time-varying delay, the identification algorithm of adaptive neural network is given for the nonlinear model. Then, the controller is designed by using the Newton-Raphson formula and the stability analysis is given for the closed-loop nonlinear systems. Finally, illustrative examples are given to show the validity and applicability of the obtained results.
Jung J. Kim; Kwang-Soo Youm; Reda Taha, Mahmoud M.
2014-01-01
A numerical method to identify thermal conductivity from time history of one-dimensional temperature variations in thermal unsteady-state is proposed. The numerical method considers the change of specific heat and thermal conductivity with respect to temperature. Fire test of reinforced concrete (RC) columns was conducted using a standard fire to obtain time history of temperature variations in the column section. A thermal equilibrium model in unsteady-state condition was developed. The ther...
Pan, Shuokai; Elliott, Stephen J; Teal, Paul D; Lineton, Ben
2015-06-01
Nonlinear models of the cochlea are best implemented in the time domain, but their computational demands usually limit the duration of the simulations that can reasonably be performed. This letter presents a modified state space method and its application to an example nonlinear one-dimensional transmission-line cochlear model. The sparsity pattern of the individual matrices for this alternative formulation allows the use of significantly faster numerical algorithms. Combined with a more efficient implementation of the saturating nonlinearity, the computational speed of this modified state space method is more than 40 times faster than that of the original formulation.
Hou, Huazhou; Zhang, Qingling
2016-11-01
In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method.
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.
Indirect adaptive fuzzy control for a class of nonlinear discrete-time systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.
An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate
Directory of Open Access Journals (Sweden)
Mingming Li
2014-01-01
Full Text Available An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions F(S,I and G(I, respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number R0.
Robust fault diagnosis for a class of nonlinear systems with time delay
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Robust fault diagnosis problems based on adaptive observer technique are studied for a class of time delayed nonlinear system with external disturbance. Adaptive fault updating laws were designed to estimate the fault and to guarantee the stability of the diagnosis system. The effects of adjusting parameters in adaptive fault updating laws on the fault estimation accuracy were analyzed. For a designed fault diagnosis system, the super bounds of the state estimation error and fault estimation error of the adaptive observer were discussed, which further showed how the parameters in the adaptive fault updating laws influenced the fault estimation accuracy.Simulation example demonstrates the effectiveness of the proposed methods and the analysis results.
PD-type iterative learning control for nonlinear time-delay system with external disturbance
Institute of Scientific and Technical Information of China (English)
Zhang Baolin; Tang Gongyou; Zheng Shi
2006-01-01
The PD-type iterative learning control design of a class of affine nonlinear time-delay systems with external disturbances is considered. Sufficient conditions guaranteeing the convergence of the n-norm of the tracking error are derived. It is shown that the system outputs can be guaranteed to converge to desired trajectories in the absence of external disturbances and output measurement noises. And in the presence of state disturbances and measurement noises, the tracking error will be bounded uniformly. A numerical simulation example is presented to validate the effectiveness of the proposed scheme.
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.
Exponential stability of solutions to nonlinear time-delay systems of neutral type
Directory of Open Access Journals (Sweden)
Gennadii V. Demidenko
2016-01-01
Full Text Available We consider a nonlinear time-delay system of neutral equations with constant coefficients in the linear terms $$ \\frac{d}{dt}\\big(y(t + D y(t-\\tau\\big = A y(t + B y(t-\\tau + F(t, y(t, y(t-\\tau, $$ where $$ \\|F(t,u,v\\| \\le q_1\\|u\\|^{1+\\omega_1} + q_2\\|v\\|^{1+\\omega_2}, \\quad q_1, q_2, \\omega_1, \\omega_2 > 0. $$ We obtain estimates characterizing the exponential decay of solutions at infinity and estimates for attraction sets of the zero solution.
Impulsive Containment Control in Nonlinear Multiagent Systems with Time-Delay
Directory of Open Access Journals (Sweden)
Wenshan Hu
2015-01-01
Full Text Available The containment control problems of nonlinear multiagent systems with time-delay via impulsive algorithms under both fixed and switching topologies are studied. By using the Lyapunov methods, several conditions are derived to achieve the containment control. It is shown that the states of the followers can converge into the convex hull spanned by the states of the leaders if every leader has directed paths to all the followers and the impulsive period is short enough. Finally, some simulations are conducted to verify the effectiveness of the proposed algorithms.
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.
Institute of Scientific and Technical Information of China (English)
Yan-ping Chen; Yun-qing Huang
2001-01-01
Improved L2-error estimates are computed for mixed finite element methods for second order nonlinear hyperbolic equations. Results are given for the continuous-time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higherorder spaces. A second paper will present the analysis of a fully discrete scheme (Numer.Math. J. Chinese Univ. vol.9, no.2, 2000, 181-192).
Extracting Knowledge From Time Series An Introduction to Nonlinear Empirical Modeling
Bezruchko, Boris P
2010-01-01
This book addresses the fundamental question of how to construct mathematical models for the evolution of dynamical systems from experimentally-obtained time series. It places emphasis on chaotic signals and nonlinear modeling and discusses different approaches to the forecast of future system evolution. In particular, it teaches readers how to construct difference and differential model equations depending on the amount of a priori information that is available on the system in addition to the experimental data sets. This book will benefit graduate students and researchers from all natural sciences who seek a self-contained and thorough introduction to this subject.
Sensor Fault Diagnosis for a Class of Time Delay Uncertain Nonlinear Systems Using Neural Network
Institute of Scientific and Technical Information of China (English)
Mou Chen; Chang-Sheng Jiang; Qing-Xian Wu
2008-01-01
In this paper, a sliding mode observer scheme of sensor fault diagnosis is proposed for a class of time delay nonlinear systems with input uncertainty based on neural network. The sensor fault and the system input uncertainty are assumed to be unknown but bounded. The radial basis function (RBF) neural network is used to approximate the sensor fault. Based on the output of the RBF neural network, the sliding mode observer is presented. Using the Lyapunov method, a criterion for stability is given in terms of matrix inequality. Finally, an example is given for illustrating the availability of the fault diagnosis based on the proposed sliding mode observer.
Fluctuation theorem, nonlinear response, and the regularity of time reversal symmetry
Porta, Marcello
2010-06-01
The Gallavotti-Cohen fluctuation theorem (FT) implies an infinite set of identities between correlation functions that can be seen as a generalization of Green-Kubo formula to the nonlinear regime. As an application, we discuss a perturbative check of the FT relation through these identities for a simple Anosov reversible system; we find that the lack of differentiability of the time reversal operator implies a violation of the Gallavotti-Cohen fluctuation relation. Finally, a brief comparison to Lebowitz-Spohn FT is reported.
Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition
Directory of Open Access Journals (Sweden)
Nengwei Zhang
2014-01-01
Full Text Available Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
Directory of Open Access Journals (Sweden)
Pedro A. Galvani
2016-08-01
Full Text Available The work presented in this paper has two major aspects: (i investigation of a simple, yet efficient model of the NREL (National Renewable Energy Laboratory 5-MW reference wind turbine; (ii nonlinear control system development through a real-time nonlinear receding horizon control methodology with application to wind turbine control dynamics. In this paper, the results of our simple wind turbine model and a real-time nonlinear control system implementation are shown in comparison with conventional control methods. For this purpose, the wind turbine control problem is converted into an optimization problem and is directly solved by the nonlinear backwards sweep Riccati method to generate the control protocol, which results in a non-iterative algorithm. One main contribution of this paper is that we provide evidence through simulations, that such an advanced control strategy can be used for real-time control of wind turbine dynamics. Examples are provided to validate and demonstrate the effectiveness of the presented scheme.
Generate tri-directional spectra-compatible time histories using HHT method
Energy Technology Data Exchange (ETDEWEB)
Li, Bo; Xie, Wei-Chau, E-mail: xie@uwaterloo.ca; Pandey, Mahesh D.
2016-11-15
Highlights: • Hilbert–Huang Transform are applied to modify real earthquake records. • Generate tri-directional time histories compatible with target spectra. • Both GRS and FRS are considered as target spectra. • Target spectra with multiple damping ratios are considered. - Abstract: This paper proposes two algorithms to generate spectrum-compatible time histories based on two approaches recommended by USNRC Standard Review Plan 3.7.1. Hilbert–Huang Transform technique is used to analyze frequency contents and amplitudes of seed motions. Through adjusting the frequency contents and amplitudes of seed motions, spectrum-compatible time histories are obtained. The first algorithm is to generate tri-directional time histories compatible with multi-damping target design spectra (ground response spectra or floor response spectra). The second algorithm is to generate tri-directional time histories compatible with single-damping target design spectra. Examples are presented to demonstrate versatility of these two proposed algorithms to generate spectra-compatible time histories.
Krishnanathan, Kirubhakaran; Anderson, Sean R.; Billings, Stephen A.; Kadirkamanathan, Visakan
2016-11-01
In this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation.
Huang, Norden E.
2000-04-01
A new method for analyzing nonlinear and nonstationary data has been developed. The key pat of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is define das any function having the same numbers of zero- crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of het data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the IMF yield instantaneous frequencies as functions of time that give sharp identifications of embedded structures. The final presentation of the result is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.
Consensus Control of Nonlinear Multiagent Systems With Time-Varying State Constraints.
Meng, Wenchao; Yang, Qinmin; Si, Jennie; Sun, Youxian
2016-12-01
In this paper, we present a novel adaptive consensus algorithm for a class of nonlinear multiagent systems with time-varying asymmetric state constraints. As such, our contribution is a step forward beyond the usual consensus stabilization result to show that the states of the agents remain within a user defined, time-varying bound. To prove our new results, the original multiagent system is transformed into a new one. Stabilization and consensus of transformed states are sufficient to ensure the consensus of the original networked agents without violating of the predefined asymmetric time-varying state constraints. A single neural network (NN), whose weights are tuned online, is used in our design to approximate the unknown functions in the agent's dynamics. To account for the NN approximation residual, reconstruction error, and external disturbances, a robust term is introduced into the approximating system equation. Additionally in our design, each agent only exchanges the information with its neighbor agents, and thus the proposed consensus algorithm is decentralized. The theoretical results are proved via Lyapunov synthesis. Finally, simulations are performed on a nonlinear multiagent system to illustrate the performance of our consensus design scheme.
Directory of Open Access Journals (Sweden)
A.M. Elnaggar
2016-01-01
Full Text Available An analysis of primary, superharmonic of order five, and subharmonic of order one-three resonances for non-linear s.d.o.f. system with two distinct time-delays under an external excitation is investigated. The method of multiple scales is used to determine two first order ordinary differential equations which describe the modulation of the amplitudes and the phases. Steady-state solutions and their stabilities in each resonance are studied. Numerical results are obtained by using the Software of Mathematica, which presented in a group of figures. The effect of the feedback gains and time-delays on the non-linear response of the system is discussed and it is found that: an appropriate feedback can enhance the control performance. A suitable choice of the feedback gains and time-delays can enlarge the critical force amplitude, and reduce the peak amplitude of the response (or peak amplitude of the free oscillation term for the case of primary resonance (superharmonic resonance. Furthermore, a proper feedback can eliminate saddle-node bifurcation, thereby eliminating jump and hysteresis phenomena taking place in the corresponding uncontrolled system. For subharmonic resonance, an adequate feedback can reduce the regions of subharmonic resonance response.
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.
Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method
Energy Technology Data Exchange (ETDEWEB)
Souza de Paula, Aline [COPPE - Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68503, 21.941-972 Rio de Janeiro, RJ (Brazil)], E-mail: alinesp@ufrj.br; Savi, Marcelo Amorim [COPPE - Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68503, 21.941-972 Rio de Janeiro, RJ (Brazil)], E-mail: savi@mecanica.ufrj.br
2009-12-15
Chaos control is employed for the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The extended time-delayed feedback control uses a continuous feedback loop incorporating information from previous states of the system in order to stabilize unstable orbits. This article deals with the chaos control of a nonlinear pendulum employing the extended time-delayed feedback control method. The control law leads to delay-differential equations (DDEs) that contain derivatives that depend on the solution of previous time instants. A fourth-order Runge-Kutta method with linear interpolation on the delayed variables is employed for numerical simulations of the DDEs and its initial function is estimated by a Taylor series expansion. During the learning stage, the UPOs are identified by the close-return method and control parameters are chosen for each desired UPO by defining situations where the largest Lyapunov exponent becomes negative. Analyses of a nonlinear pendulum are carried out by considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show the capability of the control procedure to stabilize UPOs of the dynamical system, highlighting some difficulties to achieve the stabilization of the desired orbit.
Nonlinear temporal filtering of time-resolved digital particle image velocimetry data
Energy Technology Data Exchange (ETDEWEB)
Fore, L.B.; Tung, A.T.; Buchanan, J.R.; Welch, J.W. [Bechtel Bettis Inc., West Mifflin, PA (United States)
2005-07-01
Nonlinear filtering methods have been developed to identify and replace outlying data points in velocity time series obtained with time-resolved digital particle image velocimetry (PIV) of the flow around a surface-mounted cube at a Reynolds number of 20,000. Nuances associated with the spectral computation of the cross-correlation are highlighted, including the requirement of zero-padding an image interrogation area to eliminate the circular components of the cross-correlation. Three nonlinear filtering methods for the replacement of outliers are applied to the velocity time series sampled at 1,000 Hz: a median filter, a decision-based Hampel filter, and a PIV-specific Hampel filter. The particular benefit of the PIV-specific Hampel filter is that it allows the retention of actual measured data, sometimes derived from alternate peaks in the cross-correlation function, while still providing for the removal of outliers when a consistent, nonoutlying measurement is not available. (orig.)
640 Gbit/s optical time-division add-drop multiplexing in a non-linear optical loop mirror
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Galili, Michael; Oxenløwe, Leif Katsuo
2009-01-01
Error-free 640 Gbit/s all-optical time-division add-drop multiplexing is demonstrated using a non-linear optical loop mirror. Both the add- and drop operations are achieved simultaneously by switching.......Error-free 640 Gbit/s all-optical time-division add-drop multiplexing is demonstrated using a non-linear optical loop mirror. Both the add- and drop operations are achieved simultaneously by switching....
Zhang, Honglu; Cheng, Jun; Wang, Hailing; Chen, Yiping; Xiang, Huili
2016-07-01
This paper investigates the problem of finite-time event-triggered H∞ boundedness for network-based Markovian jump nonlinear system. An improved model is introduced in terms of network-induced delay. By synthesizing the newly event-triggering conditions, the finite-time H∞ boundedness for networked Markovian jump nonlinear systems are guaranteed. At last, a numerical example is given to illustrate the effectiveness of proposed theoretical results.
Directory of Open Access Journals (Sweden)
Laila Khalilzadeh Ganjali-khani
2013-01-01
Full Text Available One of the most effective strategies for steam generator efficiency enhancement is to improve the control system. For such an improvement, it is essential to have an accurate model for the steam generator of power plant. In this paper, an industrial steam generator is considered as a nonlinear multivariable system for identification. An important step in nonlinear system identification is the development of a nonlinear model. In recent years, artificial neural networks have been successfully used for identification of nonlinear systems in many researches. Wavelet neural networks (WNNs also are used as a powerful tool for nonlinear system identification. In this paper we present a time delay neural network model and a WNN model in order to identify an industrial steam generator. Simulation results show the effectiveness of the proposed models in the system identification and demonstrate that the WNN model is more precise to estimate the plant outputs.
García-Calderón, G; Yamada, N; Garcia-Calderon, Gaston; Villavicencio, Jorge; Yamada, Norifumi
2003-01-01
We show the equivalence of the functions $G_{\\rm p}(t)$ and $|\\Psi(d,t)|^2$ for the ``passage time'' in tunneling. The former, obtained within the framework of the real time Feynman histories approach to the tunneling time problem, using the Gell-Mann and Hartle's decoherence functional, and the latter involving an exact analytical solution to the time-dependent Schr\\"{o}dinger equation for cutoff initial waves.
DEFF Research Database (Denmark)
Pretolani, Daniele; Nielsen, Lars Relund; Andersen, Kim Allan;
We compare two different models for multicriterion routing in stochastic time-dependent networks: the classic "time-adaptive'' route choice and the more flexible "history-adaptive'' route choice. We point out some interesting properties of the sets of efficient solutions ("strategies'') found...... under the two models. We also suggest possible directions for improving computational techniques....
Nonlinear Behaviors of Tail Dependence and Cross-Correlation of Financial Time Series Model
Directory of Open Access Journals (Sweden)
Wei Deng
2014-01-01
Full Text Available Nonlinear behaviors of tail dependence and cross-correlation of financial time series are reproduced and investigated by stochastic voter dynamic system. The voter process is a continuous-time Markov process and is one of the interacting dynamic systems. The tail dependence of return time series for pairs of Chinese stock markets and the proposed financial models is studied by copula analysis, in an attempt to detect and illustrate the existence of relevant correlation relationships. Further, the multifractality of cross-correlations for return series is studied by multifractal detrended cross-correlation analysis, which indicates the analogous cross-correlations and some fractal characters for both actual data and simulative data and provides an intuitive evidence for market inefficiency.
Diffusive approximation of a time-fractional Burgers equation in nonlinear acoustics
Lombard, Bruno
2016-01-01
A fractional time derivative is introduced into the Burgers equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling. A diffusive representation of the fractional derivative is adopted here, replacing this nonlocal operator by a continuum of memory variables that satisfy local-in-time ordinary differential equations. Then a quadrature formula yields a system of local partial differential equations, well-suited to numerical integration. The determination of the quadrature coefficients is crucial to ensure both the well-posedness of the system and the computational efficiency of the diffusive approximation. For this purpose, optimization with constraint is shown to be a very efficient strategy. Strang splitting is used to solve successively the hyperbolic part by a shock-capturing scheme, and the diffusive part exactly. Numerical experiments are proposed to assess the efficiency of the numerical modeling, and to illustrate the e...
A Mechanism for Stabilization of Dynamics in Nonlinear Systems with Different Time Scales
Lopez, Raquel M; Camacho, Erika T
2009-01-01
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used to describe the generation of offspring. These characteristics cause the population levels to be reset periodically. A similar phenomenon can be observed in a sociological college drinking model in which the population is reset by the incoming class each year, as described in the 2006 work of Camacho et al. With the latter as our motivation we analytically and numerically investigate the mechanism by which solutions in certain systems with this resetting conditions stabilize. We further utilize the sociological college drinking model as an analogue to analyze certain one-dimensional and two-dimensional nonlinear systems, as we attempt to generalize our results to higher dimensions.
Adaptive output feedback control for nonlinear time-delay systems using neural network
Institute of Scientific and Technical Information of China (English)
Weisheng CHEN; Junmin LI
2006-01-01
This paper extends the adaptive neural network (NN) control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay. Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on LyapunovKrasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved.The feasibility is investigated by two illustrative simulation examples.
Generalized projective synchronization in time-delayed systems: nonlinear observer approach.
Ghosh, Dibakar
2009-03-01
In this paper, we consider the projective-anticipating, projective, and projective-lag synchronization in a unified coupled time-delay system via nonlinear observer design. A new sufficient condition for generalized projective synchronization is derived analytically with the help of Krasovskii-Lyapunov theory for constant and variable time-delay systems. The analytical treatment can give stable synchronization (anticipatory and lag) for a large class of time-delayed systems in which the response system's trajectory is forced to have an amplitude proportional to the drive system. The constant of proportionality is determined by the control law, not by the initial conditions. The proposed technique has been applied to synchronize Ikeda and prototype models by numerical simulation.
Forecasting the future: is it possible for adiabatically time-varying nonlinear dynamical systems?
Yang, Rui; Lai, Ying-Cheng; Grebogi, Celso
2012-09-01
Nonlinear dynamical systems in reality are often under environmental influences that are time-dependent. To assess whether such a system can perform as desired or as designed and is sustainable requires forecasting its future states and attractors based solely on time series. We propose a viable solution to this challenging problem by resorting to the compressive-sensing paradigm. In particular, we demonstrate that, for a dynamical system whose equations are unknown, a series expansion in both dynamical and time variables allows the forecasting problem to be formulated and solved in the framework of compressive sensing using only a few measurements. We expect our method to be useful in addressing issues of significant current concern such as the sustainability of various natural and man-made systems.
Adaptive Control for Nonlinear Systems with Time-Varying Control Gain
Directory of Open Access Journals (Sweden)
Alejandro Rincon
2012-01-01
Full Text Available We propose a scheme for nonlinear plants with time-varying control gain and time-varying plant coefficients, on the basis of a plant model consisting of a Brunovsky-type model with polynomials as approximators. We develop an adaptive robust control scheme for this plant, under the following assumptions: (i the plant terms involve time-varying but bounded coefficients, being its upper bound unknown; (ii the control gain is unknown, not necessarily bounded, and only its signum is known. To achieve robustness, we use a combination of robustifying control inputs and dead zone-type update laws. We apply this methodology to the speed control of a permanent magnet synchronous motor (PMSM, and we achieve proper tracking results.
Nonlinear Least-Squares Time-Difference Estimation from Sub-Nyquist-Rate Samples
Harada, Koji; Sakai, Hideaki
In this paper, time-difference estimation of filtered random signals passed through multipath channels is discussed. First, we reformulate the approach based on innovation-rate sampling (IRS) to fit our random signal model, then use the IRS results to drive the nonlinear least-squares (NLS) minimization algorithm. This hybrid approach (referred to as the IRS-NLS method) provides consistent estimates even for cases with sub-Nyquist sampling assuming the use of compactly-supported sampling kernels that satisfies the recently-developed nonaliasing condition in the frequency domain. Numerical simulations show that the proposed NLS-IRS method can improve performance over the straight-forward IRS method, and provides approximately the same performance as the NLS method with reduced sampling rate, even for closely-spaced time delays. This enables, given a fixed observation time, significant reduction in the required number of samples, while maintaining the same level of estimation performance.
Chen, Weisheng; Jiao, Licheng; Li, Jing; Li, Ruihong
2010-06-01
For the first time, this paper addresses the problem of adaptive output-feedback control for a class of uncertain stochastic nonlinear strict-feedback systems with time-varying delays using neural networks (NNs). The circle criterion is applied to designing a nonlinear observer, and no linear growth condition is imposed on nonlinear functions depending on system states. Under the assumption that time-varying delays exist in the system output, only an NN is employed to compensate for all unknown nonlinear terms depending on the delayed output, and thus, the proposed control algorithm is more simple even than the existing NN backstepping control schemes for uncertain systems described by ordinary differential equations. Three examples are given to demonstrate the effectiveness of the control scheme proposed in this paper.
Directory of Open Access Journals (Sweden)
W. Dzwinel
2005-01-01
Full Text Available We present a novel technique based on a multi-resolutional clustering and nonlinear multi-dimensional scaling of earthquake patterns to investigate observed and synthetic seismic catalogs. The observed data represent seismic activities around the Japanese islands during 1997-2003. The synthetic data were generated by numerical simulations for various cases of a heterogeneous fault governed by 3-D elastic dislocation and power-law creep. At the highest resolution, we analyze the local cluster structures in the data space of seismic events for the two types of catalogs by using an agglomerative clustering algorithm. We demonstrate that small magnitude events produce local spatio-temporal patches delineating neighboring large events. Seismic events, quantized in space and time, generate the multi-dimensional feature space characterized by the earthquake parameters. Using a non-hierarchical clustering algorithm and nonlinear multi-dimensional scaling, we explore the multitudinous earthquakes by real-time 3-D visualization and inspection of the multivariate clusters. At the spatial resolutions characteristic of the earthquake parameters, all of the ongoing seismicity both before and after the largest events accumulates to a global structure consisting of a few separate clusters in the feature space. We show that by combining the results of clustering in both low and high resolution spaces, we can recognize precursory events more precisely and unravel vital information that cannot be discerned at a single resolution.