Soliton dynamics in periodic system with different nonlinear media

International Nuclear Information System (INIS)

Zabolotskij, A.A.

2001-01-01

To analyze pulse dynamics in the optical system consisting of periodic sequence of nonlinear media one uses a composition model covering a model of resonance interaction of light ultrashort pulse with energy transition of medium with regard to pumping of the upper level and quasi-integrable model describing propagation of light field in another medium with cubic nonlinearity and dispersion. One additionally takes account of losses and other types of interaction in the from of perturbation members. On the basis of the method of scattering back problem and perturbation theory one developed a simple method to study peculiarities of soliton evolution in such periodic system. Due to its application one managed to describe different modes of soliton evolution in such a system including chaotic dynamics [ru

The coupled nonlinear dynamics of a lift system

Energy Technology Data Exchange (ETDEWEB)

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)

2014-12-10

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.

Geometric Theory of Reduction of Nonlinear Control Systems

Science.gov (United States)

Elkin, V. I.

2018-02-01

The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).

H∞ Balancing for Nonlinear Systems

NARCIS (Netherlands)

Scherpen, Jacquelien M.A.

1996-01-01

In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H∞ control problem for nonlinear systems we define

Describing Growth Pattern of Bali Cows Using Non-linear Regression Models

Directory of Open Access Journals (Sweden)

Mohd. Hafiz A.W

2016-12-01

Full Text Available The objective of this study was to evaluate the best fit non-linear regression model to describe the growth pattern of Bali cows. Estimates of asymptotic mature weight, rate of maturing and constant of integration were derived from Brody, von Bertalanffy, Gompertz and Logistic models which were fitted to cross-sectional data of body weight taken from 74 Bali cows raised in MARDI Research Station Muadzam Shah Pahang. Coefficient of determination (R2 and residual mean squares (MSE were used to determine the best fit model in describing the growth pattern of Bali cows. Von Bertalanffy model was the best model among the four growth functions evaluated to determine the mature weight of Bali cattle as shown by the highest R2 and lowest MSE values (0.973 and 601.9, respectively, followed by Gompertz (0.972 and 621.2, respectively, Logistic (0.971 and 648.4, respectively and Brody (0.932 and 660.5, respectively models. The correlation between rate of maturing and mature weight was found to be negative in the range of -0.170 to -0.929 for all models, indicating that animals of heavier mature weight had lower rate of maturing. The use of non-linear model could summarize the weight-age relationship into several biologically interpreted parameters compared to the entire lifespan weight-age data points that are difficult and time consuming to interpret.

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

International Nuclear Information System (INIS)

Hedrih, K

2008-01-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

Science.gov (United States)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Spectral decomposition of nonlinear systems with memory

Science.gov (United States)

Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.

2016-02-01

We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

Solutions to the equations describing materials with competing quadratic and cubic nonlinearities

International Nuclear Information System (INIS)

Li-Na, Zhao; Ji, Lin; Zi-Shuang, Tong

2009-01-01

The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations share some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation

Seismic testing and analysis of a prototypic nonlinear piping system

International Nuclear Information System (INIS)

Barta, D.A.; Anderson, M.J.; Severud, L.K.

1982-11-01

A series of seismic tests and analyses of a nonlinear Fast Flux Test Facility (FFTF) prototypic piping system are described, and measured responses are compared with analytical predictions. The test loop was representative of a typical LMFBR insulated small bore piping system and it was supported from a rigid test frame by prototypic dead weight supports, mechanical snubbers and pipe clamps. Various piping support configurations were tested and analyzed to evaluate the effects of free play and other nonlinear stiffness characteristics on the piping system response

Balancing for Unstable Nonlinear Systems

NARCIS (Netherlands)

Scherpen, J.M.A.

1993-01-01

A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By

Coupled bending and torsional vibration of a rotor system with nonlinear friction

International Nuclear Information System (INIS)

Hua, Chunli; Cao, Guohua; Zhu, Zhencai; Rao, Zhushi; Ta, Na

2017-01-01

Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating ma- chinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincaré maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose self- excited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.

Coupled bending and torsional vibration of a rotor system with nonlinear friction

Energy Technology Data Exchange (ETDEWEB)

Hua, Chunli; Cao, Guohua; Zhu, Zhencai [China University of Mining and Technology, Xuzhou (China); Rao, Zhushi; Ta, Na [Shanghai Jiao Tong University, Shanghai (China)

2017-06-15

Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating ma- chinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincaré maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose self- excited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.

A nonlinear complementarity approach for the national energy modeling system

International Nuclear Information System (INIS)

Gabriel, S.A.; Kydes, A.S.

1995-01-01

The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP

Frequency response functions for nonlinear convergent systems

NARCIS (Netherlands)

Pavlov, A.V.; Wouw, van de N.; Nijmeijer, H.

2007-01-01

Convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time-invariant systems. In this note, we extend frequency response functions defined for linear systems to nonlinear convergent systems. Such nonlinear frequency

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

Nonlinear system identification NARMAX methods in the time, frequency, and spatio-temporal domains

CERN Document Server

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

Nonlinear transport of dynamic system phase space

International Nuclear Information System (INIS)

Xie Xi; Xia Jiawen

1993-01-01

The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example

Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

Science.gov (United States)

Raju, Thokala Soloman; Pal, Ritu

2018-05-01

We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.

Nonlinearity of colloid systems oxyhydrate systems

CERN Document Server

Sucharev, Yuri I

2008-01-01

The present monograph is the first systematic study of the non-linear characteristic of gel oxy-hydrate systems involving d- and f- elements. These are the oxyhydrates of rare-earth elements and oxides - hydroxides of d- elements (zirconium, niobium, titanium, etc.) The non-linearity of these gel systems introduces fundamental peculiarities into their structure and, consequently, their properties. The polymer-conformational diversity of energetically congenial gel fragments, which continu-ously transform under the effect of, for instance, system dissipation heat, is central to the au-thor's hy

Empirical Differential Balancing for Nonlinear Systems

NARCIS (Netherlands)

Kawano, Yu; Scherpen, Jacquelien M.A.; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri

In this paper, we consider empirical balancing of nonlinear systems by using its prolonged system, which consists of the original nonlinear system and its variational system. For the prolonged system, we define differential reachability and observability Gramians, which are matrix valued functions

Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion

Directory of Open Access Journals (Sweden)

Jun Wang

2013-01-01

Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.

Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction

Directory of Open Access Journals (Sweden)

Geoff Boeing

2016-11-01

Full Text Available Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.

Augmented nonlinear differentiator design and application to nonlinear uncertain systems.

Science.gov (United States)

Shao, Xingling; Liu, Jun; Li, Jie; Cao, Huiliang; Shen, Chong; Zhang, Xiaoming

2017-03-01

In this paper, an augmented nonlinear differentiator (AND) based on sigmoid function is developed to calculate the noise-less time derivative under noisy measurement condition. The essential philosophy of proposed AND in achieving high attenuation of noise effect is established by expanding the signal dynamics with extra state variable representing the integrated noisy measurement, then with the integral of measurement as input, the augmented differentiator is formulated to improve the estimation quality. The prominent advantages of the present differentiation technique are: (i) better noise suppression ability can be achieved without appreciable delay; (ii) the improved methodology can be readily extended to construct augmented high-order differentiator to obtain multiple derivatives. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, the robust control problems of nonlinear uncertain systems, including a numerical example and a mass spring system, are addressed to demonstrate the effectiveness of AND in precisely estimating the disturbance and providing the unavailable differential estimate to implement output feedback based controller. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Controller Design of Complex System Based on Nonlinear Strength

Directory of Open Access Journals (Sweden)

Rongjun Mu

2015-01-01

Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

Discontinuity and complexity in nonlinear physical systems

CERN Document Server

Baleanu, Dumitru; Luo, Albert

2014-01-01

This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....

Symmetries and semi-invariants in the analysis of nonlinear systems with control applications

CERN Document Server

Menini, Laura

2014-01-01

This volume details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations. The theory is developed for general nonlinear systems and specialized for the class of Hamiltonian systems.

Nonlinear system analysis of renal autoregulation in normotensive and hypertensive rats

DEFF Research Database (Denmark)

Chon, K H; Chen, Y M; Holstein-Rathlou, N H

1998-01-01

We compared the dynamic characteristics in renal autoregulation of blood flow of normotensive Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR), using both linear and nonlinear systems analysis. Linear analysis yielded only limited information about the differences in dynamics......, NMSE are significantly higher in SHR than SDR, suggesting a more complex nonlinear system in SHR. The contribution of the third-order kernel in describing the dynamics of renal autoregulation in arterial blood pressure and blood flow was found to be important. Moreover, we have identified the presence...

Oscillations in nonlinear systems

CERN Document Server

Hale, Jack K

2015-01-01

By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

Nonlinear dynamics of a parametrically driven sine-Gordon system

DEFF Research Database (Denmark)

Grønbech-Jensen, Niels; Kivshar, Yuri S.; Samuelsen, Mogens Rugholm

1993-01-01

We consider a sine-Gordon system, driven by an ac parametric force in the presence of loss. It is demonstrated that a breather can be maintained in a steady state at half of the external frequency. In the small-amplitude limit the effect is described by an effective nonlinear Schrodinger equation...

Nonlinear and stochastic dynamics of coherent structures

DEFF Research Database (Denmark)

Rasmussen, Kim

1997-01-01

This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree of nonli......This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree...... introduces the nonlinear Schrödinger model in one and two dimensions, discussing the soliton solutions in one dimension and the collapse phenomenon in two dimensions. Also various analytical methods are described. Then a derivation of the nonlinear Schrödinger equation is given, based on a Davydov like...... system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

Science.gov (United States)

Rabinowitz, Matthew (Inventor)

2002-01-01

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

On Stabilization of Nonautonomous Nonlinear Systems

International Nuclear Information System (INIS)

Bogdanov, A. Yu.

2008-01-01

The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.

Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

DEFF Research Database (Denmark)

Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole

2001-01-01

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...... the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site....

Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method

Science.gov (United States)

Kenderi, Gábor; Fidlin, Alexander

2014-12-01

The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master-slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.

Accelerating Inexact Newton Schemes for Large Systems of Nonlinear Equations

NARCIS (Netherlands)

Fokkema, D.R.; Sleijpen, G.L.G.; Vorst, H.A. van der

Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general

Advances and applications in nonlinear control systems

CERN Document Server

Volos, Christos

2016-01-01

The book reports on the latest advances and applications of nonlinear control systems. It consists of 30 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of nonlinear control systems such as robotics, nonlinear circuits, power systems, memristors, underwater vehicles, chemical processes, observer design, output regulation, backstepping control, sliding mode control, time-delayed control, variables structure control, robust adaptive control, fuzzy logic control, chaos, hyperchaos, jerk systems, hyperjerk systems, chaos control, chaos synchronization, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in nonlinear control systems. This book will serve as a reference book for graduate students and researchers with a basic knowledge of electrical and control systems engineering. The resulting design proce...

A method for exponential propagation of large systems of stiff nonlinear differential equations

Science.gov (United States)

Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.

1989-01-01

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics

NARCIS (Netherlands)

Yu, Wenwu; Chen, Guanrong; Cao, Ming; Kurths, Juergen; Kurths, Jürgen

This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a

Spatial nonlinearities: Cascading effects in the earth system

Science.gov (United States)

Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

2006-01-01

Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

Parametric Identification of Nonlinear Dynamical Systems

Science.gov (United States)

Feeny, Brian

2002-01-01

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

Vibration suppression in ultrasonic machining described by non-linear differential equations

International Nuclear Information System (INIS)

Kamel, M. M.; El-Ganaini, W. A. A.; Hamed, Y. S.

2009-01-01

Vibrations are usually undesired phenomena as they may cause damage or destruction of the system. However, sometimes they are desirable, as in ultrasonic machining (USM). In such case, the problem is a complicated one, as it is required to reduce the vibration of the machine head and have reasonable amplitude for the tool. In the present work, the coupling of two non-linear oscillators of the tool holder and tool representing ultrasonic cutting process is investigated. This leads to a two-degree-of-freedom system subjected to multi-external excitation force. The aim of this work is to control the tool holder behavior at simultaneous primary and internal resonance condition and have high amplitude for the tool. Multiple scale perturbation method is applied to obtain a solution up to the second order approximations. Other different resonance cases are reported and studied numerically. The stability of the system is investigated applying both phase-plane and frequency response techniques. The effects of the different parameters of the tool on the system behavior are studied numerically. Comparison with the available published work is reported

Dynamics of Nonlinear Time-Delay Systems

CERN Document Server

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...

Transient and chaotic low-energy transfers in a system with bistable nonlinearity

Energy Technology Data Exchange (ETDEWEB)

Romeo, F., E-mail: francesco.romeo@uniroma1.it [Department of Structural and Geotechnical Engineering, SAPIENZA University of Rome, Rome (Italy); Manevitch, L. I. [Institute of Chemical Physics, RAS, Moscow (Russian Federation); Bergman, L. A.; Vakakis, A. [College of Engineering, University of Illinois at Urbana–Champaign, Champaign, Illinois 61820 (United States)

2015-05-15

The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensional projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.

Joint nonlinearity effects in the design of a flexible truss structure control system

Science.gov (United States)

Mercadal, Mathieu

1986-01-01

Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.

The second order extended Kalman filter and Markov nonlinear filter for data processing in interferometric systems

International Nuclear Information System (INIS)

Ermolaev, P; Volynsky, M

2014-01-01

Recurrent stochastic data processing algorithms using representation of interferometric signal as output of a dynamic system, which state is described by vector of parameters, in some cases are more effective, compared with conventional algorithms. Interferometric signals depend on phase nonlinearly. Consequently it is expedient to apply algorithms of nonlinear stochastic filtering, such as Kalman type filters. An application of the second order extended Kalman filter and Markov nonlinear filter that allows to minimize estimation error is described. Experimental results of signals processing are illustrated. Comparison of the algorithms is presented and discussed.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

Science.gov (United States)

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Order-disorder transitions in time-discrete mean field systems with memory: a novel approach via nonlinear autoregressive models

International Nuclear Information System (INIS)

Frank, T D; Mongkolsakulvong, S

2015-01-01

In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)

Balancing for nonlinear systems

NARCIS (Netherlands)

Scherpen, J.M.A.

1993-01-01

We present a method of balancing for nonlinear systems which is an extension of balancing for linear systems in the sense that it is based on the input and output energy of a system. It is a local result, but gives 'broader' results than we obtain by just linearizing the system. Furthermore, the

Universal formats for nonlinear ordinary differential systems

International Nuclear Information System (INIS)

Kerner, E.H.

1981-01-01

It is shown that very general nonlinear ordinary differential systems (embracing all that arise in practice) may, first, be brought down to polynomial systems (where the nonlinearities occur only as polynomials in the dependent variables) by introducing suitable new variables into the original system; second, that polynomial systems are reducible to ''Riccati systems,'' where the nonlinearities are quadratic at most; third, that Riccati systems may be brought to elemental universal formats containing purely quadratic terms with simple arrays of coefficients that are all zero or unity. The elemental systems have representations as novel types of matrix Riccati equations. Different starting systems and their associated Riccati systems differ from one another, at the final elemental level, in order and in initial data, but not in format

Robust stabilization of nonlinear systems: The LMI approach

Directory of Open Access Journals (Sweden)

Šiljak D. D.

2000-01-01

Full Text Available This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI. The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable. We shall broaden the new setting to include design of decentralized control laws for robust stabilization of interconnected systems. Again, the LMI methods will be used to maximize the class of uncertain interconnections which leave the overall system connectively stable. It is useful to learn that the proposed LMI formulation “recognizes” the matching conditions by returning a feedback gain matrix for any prescribed bound on the interconnection terms. More importantly, the new formulation provides a suitable setting for robust stabilization of nonlinear systems where the nonlinear perturbations satisfy the generalized matching conditions.

Complex motions and chaos in nonlinear systems

CERN Document Server

Machado, José; Zhang, Jiazhong

2016-01-01

This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.

Nonlinear Hamiltonian systems

DEFF Research Database (Denmark)

Jørgensen, Michael Finn

1995-01-01

It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...

PWL approximation of nonlinear dynamical systems, part I: structural stability

International Nuclear Information System (INIS)

Storace, M; De Feo, O

2005-01-01

This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topological normal forms). The structural stability of the PWL approximations of such systems is investigated through a bifurcation analysis (via continuation methods)

Expert system for accelerator single-freedom nonlinear components

International Nuclear Information System (INIS)

Wang Sheng; Xie Xi; Liu Chunliang

1995-01-01

An expert system by Arity Prolog is developed for accelerator single-freedom nonlinear components. It automatically yields any order approximate analytical solutions for various accelerator single-freedom nonlinear components. As an example, the eighth order approximate analytical solution is derived by this expert system for a general accelerator single-freedom nonlinear component, showing that the design of the expert system is successful

Nonlinear Approaches in Engineering Applications

CERN Document Server

Jazar, Reza

2012-01-01

Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...

The Influence of Slowly Varying Mass on Severity of Dynamics Nonlinearity of Bearing-Rotor Systems with Pedestal Looseness

Directory of Open Access Journals (Sweden)

Mian Jiang

2018-01-01

Full Text Available Nonlinearity measure is proposed to investigate the influence of slowly varying mass on severity of dynamics nonlinearity of bearing-rotor systems with pedestal looseness. A nonlinear mathematical model including the effect of slowly varying disk mass is developed for a bearing-rotor system with pedestal looseness. The varying of equivalent disk mass is described by a cosine function, and the amplitude coefficient is used as a control parameter. Then, nonlinearity measure is employed to quantify the severity of dynamics nonlinearity of bearing-rotor systems. With the increasing of looseness clearances, the curves that denote the trend of nonlinearity degree are plotted for each amplitude coefficient of mass varying. It can be concluded that larger amplitude coefficients of the disk mass varying will have more influence on the severity of dynamics nonlinearity and generation of chaotic behaviors in rotor systems with pedestal looseness.

Non self-similar collapses described by the non-linear Schroedinger equation

International Nuclear Information System (INIS)

Berge, L.; Pesme, D.

1992-01-01

We develop a rapid method in order to find the contraction rates of the radially symmetric collapsing solutions of the nonlinear Schroedinger equation defined for space dimensions exceeding a threshold value. We explicitly determine the asymptotic behaviour of these latter solutions by solving the non stationary linear problem relative to the nonlinear Schroedinger equation. We show that the self-similar states associated with the collapsing solutions are characterized by a spatial extent which is bounded from the top by a cut-off radius

Poromechanical approach describing the moisture influence on the non-linear quasi-static and dynamic behaviour of porous building materials

NARCIS (Netherlands)

Carmeliet, J.; Abeele, van den K.E.A.

2004-01-01

The non-linear quasi-static and dynamic elastic behaviour of Berea sandstone has been experimentally analysed showing hysteresis and a strong influence of moisture especially in the lower saturation range. It is shown that non-linear hysteretic response originates within the "bond system" of the

PWL approximation of nonlinear dynamical systems, part II: identification issues

International Nuclear Information System (INIS)

De Feo, O; Storace, M

2005-01-01

This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes a black-box identification method based on state space reconstruction and PWL approximation, and applies it to some particularly significant dynamical systems (two topological normal forms and the Colpitts oscillator)

Nonlinear Control Synthesis for Electrical Power Systems Using Controllable Series Capacitors

CERN Document Server

Manjarekar, N S

2012-01-01

In this work we derive asymptotically stabilizing control laws for electrical power systems using two nonlinear control synthesis techniques. For this transient stabilization problem the actuator considered is a power electronic device, a controllable series capacitor (CSC). The power system is described using two different nonlinear models - the second order swing equation and the third order flux-decay model. To start with, the CSC is modeled by the injection model which is based on the assumption that the CSC dynamics is very fast as compared to the dynamics of the power system and hence can be approximated by an algebraic equation. Here, by neglecting the CSC dynamics, the input vector $g(x)$ in the open loop system takes a complex form - the injection model. Using this model, interconnection and damping assignment passivity-based control (IDA-PBC) methodology is demonstrated on two power systems: a single machine infinite bus (SMIB) system and a two machine system. Further, IDA-PBC is used to derive stab...

A study of discrete nonlinear systems

International Nuclear Information System (INIS)

Dhillon, H.S.

2001-04-01

An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

Analysis of nonlinear systems using ARMA [autoregressive moving average] models

International Nuclear Information System (INIS)

Hunter, N.F. Jr.

1990-01-01

While many vibration systems exhibit primarily linear behavior, a significant percentage of the systems encountered in vibration and model testing are mildly to severely nonlinear. Analysis methods for such nonlinear systems are not yet well developed and the response of such systems is not accurately predicted by linear models. Nonlinear ARMA (autoregressive moving average) models are one method for the analysis and response prediction of nonlinear vibratory systems. In this paper we review the background of linear and nonlinear ARMA models, and illustrate the application of these models to nonlinear vibration systems. We conclude by summarizing the advantages and disadvantages of ARMA models and emphasizing prospects for future development. 14 refs., 11 figs

Explicit Nonlinear Model Predictive Control Theory and Applications

CERN Document Server

Grancharova, Alexandra

2012-01-01

Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings.

Science.gov (United States)

Tang, Yang; Gao, Huijun; Zou, Wei; Kurths, Jürgen

2013-02-01

In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

Optimal beamforming in MIMO systems with HPA nonlinearity

KAUST Repository

Qi, Jian

2010-09-01

In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

Optimal beamforming in MIMO systems with HPA nonlinearity

KAUST Repository

Qi, Jian; Aissa, Sonia

2010-01-01

In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

Data based identification and prediction of nonlinear and complex dynamical systems

Science.gov (United States)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-07-01

systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods

Data based identification and prediction of nonlinear and complex dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Wang, Wen-Xu [School of Systems Science, Beijing Normal University, Beijing, 100875 (China); Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Lai, Ying-Cheng, E-mail: Ying-Cheng.Lai@asu.edu [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States); Department of Physics, Arizona State University, Tempe, AZ 85287 (United States); Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom); Grebogi, Celso [Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom)

2016-07-12

dynamical systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods

Data based identification and prediction of nonlinear and complex dynamical systems

International Nuclear Information System (INIS)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01

dynamical systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods

Fault detection and fault-tolerant control for nonlinear systems

CERN Document Server

Li, Linlin

2016-01-01

Linlin Li addresses the analysis and design issues of observer-based FD and FTC for nonlinear systems. The author analyses the existence conditions for the nonlinear observer-based FD systems to gain a deeper insight into the construction of FD systems. Aided by the T-S fuzzy technique, she recommends different design schemes, among them the L_inf/L_2 type of FD systems. The derived FD and FTC approaches are verified by two benchmark processes. Contents Overview of FD and FTC Technology Configuration of Nonlinear Observer-Based FD Systems Design of L2 nonlinear Observer-Based FD Systems Design of Weighted Fuzzy Observer-Based FD Systems FTC Configurations for Nonlinear Systems< Application to Benchmark Processes Target Groups Researchers and students in the field of engineering with a focus on fault diagnosis and fault-tolerant control fields The Author Dr. Linlin Li completed her dissertation under the supervision of Prof. Steven X. Ding at the Faculty of Engineering, University of Duisburg-Essen, Germany...

Modelling and properties of a nonlinear autonomous switching system in fed-batch culture of glycerol

Science.gov (United States)

Wang, Juan; Sun, Qingying; Feng, Enmin

2012-11-01

A nonlinear autonomous switching system is proposed to describe the coupled fed-batch fermentation with the pH as the feedback parameter. We prove the non-Zeno behaviors of the switching system and some basic properties of its solution, including the existence, uniqueness, boundedness and regularity. Numerical simulation is also carried out, which reveals that the proposed system can describe the factual fermentation process properly.

H∞ Excitation Control Design for Stochastic Power Systems with Input Delay Based on Nonlinear Hamiltonian System Theory

Directory of Open Access Journals (Sweden)

Weiwei Sun

2015-01-01

Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.

Adaptive PI Controller for a Nonlinear System

Directory of Open Access Journals (Sweden)

D. Rathikarani

2009-10-01

Full Text Available Most of the industrial processes are inherently nonlinear in their behaviour. Designs of controllers for these nonlinear processes are difficult, as they do not follow superposition theorem. Adaptive controller can change its behaviour in response to changes in the dynamics of the process and disturbances. Hence adaptive controller can be used to control nonlinear processes. Direct Model Reference Adaptive Control is a technique, in which a reference model involving the desired performances is specified. In the present work, a DMRAC is designed and implemented to achieve satisfactory control of a nonlinear system in all its local linear operating regions. The closed loop system is made BIBO stable by proper control techniques. The controller is designed through simulation in Matlab platform and is validated in real time by conducting experiments on the laboratory Air Flow Control System using the dSPACE interface.

Propagation of dispersion-nonlinearity-managed solitons in an inhomogeneous erbium-doped fiber system

International Nuclear Information System (INIS)

Mahalingam, A; Porsezian, K; Mani Rajan, M S; Uthayakumar, A

2009-01-01

In this paper, a generalized nonlinear Schroedinger-Maxwell-Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Baecklund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed

Model reduction of nonlinear systems subject to input disturbances

KAUST Repository

Ndoye, Ibrahima

2017-07-10

The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.

Asymptotic stabilization of nonlinear systems using state feedback

International Nuclear Information System (INIS)

D'Attellis, Carlos

1990-01-01

This paper studies the design of state-feedback controllers for the stabilization of single-input single-output nonlinear systems x = f(x) + g(x)u, y = h(x). Two approaches for the stabilization problem are given; the asymptotic stability is achieved by means of: a) nonlinear state feedback: two nonlinear feedbacks are used; the first separates the system in a controllable linear part and in the zeros-dynamic part. The second feedback generates an asymptotically stable equilibrium on the manifold where this dynamics evolves; b) nonlinear dynamic feedback: conditions are established under which the system can follow the output of a completely controllable bilinear system which uses bounded controls. This fact enables the system to reach, using bounded controls too, a desired output value in finite time. As this value corresponds to a state that lays in the attraction basin of a stable equilibrium with the same output, the system evolves to that point. The two methods are illustrated by examples. (Author) [es

Discrete-time inverse optimal control for nonlinear systems

CERN Document Server

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

Nonlinear time heteronymous damping in nonlinear parametric planetary systems

Czech Academy of Sciences Publication Activity Database

Hortel, Milan; Škuderová, Alena

2014-01-01

Roč. 225, č. 7 (2014), s. 2059-2073 ISSN 0001-5970 Institutional support: RVO:61388998 Keywords : nonlinear dynamics * planetary systems * heteronymous damping Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 1.465, year: 2014

On modulated complex non-linear dynamical systems

International Nuclear Information System (INIS)

Mahmoud, G.M.; Mohamed, A.A.; Rauh, A.

1999-01-01

This paper is concerned with the development of an approximate analytical method to investigate periodic solutions and their stability in the case of modulated non-linear dynamical systems whose equation of motion is describe. Such differential equations appear, for example, in problems of colliding particle beams in high-energy accelerators or one-mass systems with two or more degrees of freedom, e.g. rotors. The significance of periodic solutions lies on the fact that all non-periodic responses, if convergent, would approach to periodic solutions at the steady-state conditions. The example shows a good agreement between numerical and analytical results for small values of ε. The effect of the periodic modulation on the stability of the 2π-periodic solutions is discussed

Useful tools for non-linear systems: Several non-linear integral inequalities

Czech Academy of Sciences Publication Activity Database

Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.

2013-01-01

Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf

Estimation of Nonlinear Functions of State Vector for Linear Systems with Time-Delays and Uncertainties

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.

Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

Energy Technology Data Exchange (ETDEWEB)

Barus, R. P. P., E-mail: rismawan.ppb@gmail.com [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung and Centre for Material and Technical Product, Jalan Sangkuriang No. 14 Bandung (Indonesia); Tjokronegoro, H. A.; Leksono, E. [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia); Ismunandar [Chemistry Study, Faculty of Mathematics and Science, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia)

2014-09-25

Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.

Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

International Nuclear Information System (INIS)

Barus, R. P. P.; Tjokronegoro, H. A.; Leksono, E.; Ismunandar

2014-01-01

Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range

Wave transmission in nonlinear lattices

International Nuclear Information System (INIS)

Hennig, D.; Tsironis, G.P.

1999-01-01

The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Parameter and Structure Inference for Nonlinear Dynamical Systems

Science.gov (United States)

Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

2006-01-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

Fluctuations in Nonlinear Systems: A Short Review

International Nuclear Information System (INIS)

Rubia, F.J. de la; Buceta, J.; Cabrera, J.L.; Olarrea, J.; Parrondo, J.M.R.

2003-01-01

We review some results that illustrate the constructive role of noise in nonlinear systems. Several phenomena are briefly discussed: optimal localization of orbits in a system with limit cycle behavior and perturbed by colored noise; stochastic branch selection at secondary bifurcations; noise- induced order/disorder transitions and pattern formation in spatially extended systems. In all cases the presence of noise is crucial, and the results reinforce the modern view of the importance of noise in the evolution of nonlinear systems. (author)

Periodicity of a class of nonlinear fuzzy systems with delays

International Nuclear Information System (INIS)

Yu Jiali; Yi Zhang; Zhang Lei

2009-01-01

The well known Takagi-Sugeno (T-S) model gives an effective method to combine some simple local systems with their linguistic description to represent complex nonlinear dynamic systems. By using the T-S method, a class of local nonlinear systems having nice dynamic properties can be employed to represent some global complex nonlinear systems. This paper proposes to study the periodicity of a class of global nonlinear fuzzy systems with delays by using T-S method. Conditions for guaranteeing periodicity are derived. Examples are employed to illustrate the theory.

Applications of Nonlinear Dynamics Model and Design of Complex Systems

CERN Document Server

In, Visarath; Palacios, Antonio

2009-01-01

This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

Jump phenomena. [large amplitude responses of nonlinear systems

Science.gov (United States)

Reiss, E. L.

1980-01-01

The paper considers jump phenomena composed of large amplitude responses of nonlinear systems caused by small amplitude disturbances. Physical problems where large jumps in the solution amplitude are important features of the response are described, including snap buckling of elastic shells, chemical reactions leading to combustion and explosion, and long-term climatic changes of the earth's atmosphere. A new method of rational functions was then developed which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter; this method can solve jump problems explicitly.

Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

CERN Document Server

Aliyu, MDS

2011-01-01

A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter

Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation

CERN Document Server

Petráš, Ivo

2011-01-01

"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...

A general U-block model-based design procedure for nonlinear polynomial control systems

Science.gov (United States)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Nonlinear PI control of chaotic systems using singular perturbation theory

International Nuclear Information System (INIS)

Wang Jiang; Wang Jing; Li Huiyan

2005-01-01

In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

Science.gov (United States)

Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

2018-02-01

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

Terahertz semiconductor nonlinear optics

DEFF Research Database (Denmark)

Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias

2013-01-01

In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped semiconductors, using n-GaAs as a model system. The THz...... nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...... to a decrease of plasma frequency in semiconductor and produces a substantial modification of THz-range material dielectric function, described by the Drude model. As a result, the nonlinearity of both absorption coefficient and refractive index of the semiconductor is observed. In particular we demonstrate...

Structural optimization for nonlinear dynamic response

DEFF Research Database (Denmark)

Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.

2015-01-01

by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance......Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...

Indirect learning control for nonlinear dynamical systems

Science.gov (United States)

Ryu, Yeong Soon; Longman, Richard W.

1993-01-01

In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

Nonlinear PDEs a dynamical systems approach

CERN Document Server

Schneider, Guido

2017-01-01

This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced...

Non-linear phenomena in electronic systems consisting of coupled single-electron oscillators

International Nuclear Information System (INIS)

Kikombo, Andrew Kilinga; Hirose, Tetsuya; Asai, Tetsuya; Amemiya, Yoshihito

2008-01-01

This paper describes non-linear dynamics of electronic systems consisting of single-electron oscillators. A single-electron oscillator is a circuit made up of a tunneling junction and a resistor, and produces simple relaxation oscillation. Coupled with another, single electron oscillators exhibit complex behavior described by a combination of continuous differential equations and discrete difference equations. Computer simulation shows that a double-oscillator system consisting of two coupled oscillators produces multi-periodic oscillation with a single attractor, and that a quadruple-oscillator system consisting of four oscillators also produces multi-periodic oscillation but has a number of possible attractors and takes one of them determined by initial conditions

Distributed Fault Detection for a Class of Nonlinear Stochastic Systems

Directory of Open Access Journals (Sweden)

Bingyong Yan

2014-01-01

Full Text Available A novel distributed fault detection strategy for a class of nonlinear stochastic systems is presented. Different from the existing design procedures for fault detection, a novel fault detection observer, which consists of a nonlinear fault detection filter and a consensus filter, is proposed to detect the nonlinear stochastic systems faults. Firstly, the outputs of the nonlinear stochastic systems act as inputs of a consensus filter. Secondly, a nonlinear fault detection filter is constructed to provide estimation of unmeasurable system states and residual signals using outputs of the consensus filter. Stability analysis of the consensus filter is rigorously investigated. Meanwhile, the design procedures of the nonlinear fault detection filter are given in terms of linear matrix inequalities (LMIs. Taking the influence of the system stochastic noises into consideration, an outstanding feature of the proposed scheme is that false alarms can be reduced dramatically. Finally, simulation results are provided to show the feasibility and effectiveness of the proposed fault detection approach.

Bifurcation methods of dynamical systems for handling nonlinear ...

Indian Academy of Sciences (India)

physics pp. 863–868. Bifurcation methods of dynamical systems for handling nonlinear wave equations. DAHE FENG and JIBIN LI. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology .... (b) It can be shown from (15) and (18) that the balance between the weak nonlinear.

Capability of LEP-type surfaces to describe noncollinear reactions 2 - Polyatomic systems

CERN Document Server

Espinosa-Garcia, Joaquin

2001-01-01

In this second article of the series, the popular LEP-type surface for collinear reaction paths and a "bent" surface, which involves a saddle point geometry with a nonlinear central angle, were used to examine the capacity of LEP-type surfaces to describe the kinetics and dynamics of noncollinear reaction paths in polyatomic systems. Analyzing the geometries, vibrational frequencies, curvature along the reaction path (to estimate the tunneling effect and the reaction coordinate-bound modes coupling), and the variational transition- state theory thermal rate constants for the NH//3 + O(**3P) reaction, we found that the "collinear" LEP-type and the "bent" surfaces for this polyatomic system show similar behavior, thus allowing a considerable saving in time and computational effort. This agreement is especially encouraging for this polyatomic system because in the Cs symmetry the reaction proceeds via two electronic states of symmetries **3A prime and **3A double prime , which had to be independently calibrated....

Nonclassical state generation for linear quantum systems via nonlinear feedback control

International Nuclear Information System (INIS)

Ohki, Kentaro; Tsumura, Koji; Takeuchi, Reiji

2017-01-01

In this paper, we propose a measurement nonlinear feedback control scheme to generate Wigner-function negativity in an optical cavity having dynamics described as a linear quantum system. In general, linear optical quantum systems can be easily constructed with reliable devices; therefore, the idea of constructing the entire system with such an optical system and nonlinear feedback is reasonable for generating Wigner-function negativity. However, existing studies have insufficiently examined the realizability or actual implementation of feedback control, which essentially requires fast responses from the sensors and actuators. In order to solve this problem, we consider the realizable feedback control of the optical phase of a pumping beam supplied to a cavity by using electro-optical modulation, which can be utilized as a fast control actuator. Then, we introduce mathematical models of the feedback-controlled system and evaluate its effect on the generation of the Wigner-function negativity by using numerical simulation. Through various numerical simulations, we show that the proposed feedback control can effectively generate the negativity of the Wigner function. (paper)

Fuzzy model-based servo and model following control for nonlinear systems.

Science.gov (United States)

Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O

2009-12-01

This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.

Nonlinear systems techniques for dynamical analysis and control

CERN Document Server

Lefeber, Erjen; Arteaga, Ines

2017-01-01

This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participan...

Observer-based Fault Detection and Isolation for Nonlinear Systems

DEFF Research Database (Denmark)

Lootsma, T.F.

With the rise in automation the increase in fault detectionand isolation & reconfiguration is inevitable. Interest in fault detection and isolation (FDI) for nonlinear systems has grown significantly in recent years. The design of FDI is motivated by the need for knowledge about occurring faults...... in fault-tolerant control systems (FTC systems). The idea of FTC systems is to detect, isolate, and handle faults in such a way that the systems can still perform in a required manner. One prefers reduced performance after occurrence of a fault to the shut down of (sub-) systems. Hence, the idea of fault......-output decoupling is described. It is a new idea based on the solution of the input-output decoupling problem. The idea is to include FDI considerations already during the control design....

From Hamiltonian chaos to complex systems a nonlinear physics approach

CERN Document Server

Leonetti, Marc

2013-01-01

From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of  research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...

MINPACK-1, Subroutine Library for Nonlinear Equation System

International Nuclear Information System (INIS)

Garbow, Burton S.

1984-01-01

1 - Description of problem or function: MINPACK1 is a package of FORTRAN subprograms for the numerical solution of systems of non- linear equations and nonlinear least-squares problems. The individual programs are: Identification/Description: - CHKDER: Check gradients for consistency with functions, - DOGLEG: Determine combination of Gauss-Newton and gradient directions, - DPMPAR: Provide double precision machine parameters, - ENORM: Calculate Euclidean norm of vector, - FDJAC1: Calculate difference approximation to Jacobian (nonlinear equations), - FDJAC2: Calculate difference approximation to Jacobian (least squares), - HYBRD: Solve system of nonlinear equations (approximate Jacobian), - HYBRD1: Easy-to-use driver for HYBRD, - HYBRJ: Solve system of nonlinear equations (analytic Jacobian), - HYBRJ1: Easy-to-use driver for HYBRJ, - LMDER: Solve nonlinear least squares problem (analytic Jacobian), - LMDER1: Easy-to-use driver for LMDER, - LMDIF: Solve nonlinear least squares problem (approximate Jacobian), - LMDIF1: Easy-to-use driver for LMDIF, - LMPAR: Determine Levenberg-Marquardt parameter - LMSTR: Solve nonlinear least squares problem (analytic Jacobian, storage conserving), - LMSTR1: Easy-to-use driver for LMSTR, - QFORM: Accumulate orthogonal matrix from QR factorization QRFAC Compute QR factorization of rectangular matrix, - QRSOLV: Complete solution of least squares problem, - RWUPDT: Update QR factorization after row addition, - R1MPYQ: Apply orthogonal transformations from QR factorization, - R1UPDT: Update QR factorization after rank-1 addition, - SPMPAR: Provide single precision machine parameters. 4. Method of solution - MINPACK1 uses the modified Powell hybrid method and the Levenberg-Marquardt algorithm

Euclidean null controllability of nonlinear infinite delay systems with ...

African Journals Online (AJOL)

Sufficient conditions for the Euclidean null controllability of non-linear delay systems with time varying multiple delays in the control and implicit derivative are derived. If the uncontrolled system is uniformly asymptotically stable and if the control system is controllable, then the non-linear infinite delay system is Euclidean null ...

Nonlinear control synthesis for electrical power systems using controllable series capacitors

Energy Technology Data Exchange (ETDEWEB)

Manjarekar, N.S.; Banavar, Ravi N. [Indian Institute of Technology Bombay, Mumbai (India). Systems and Control Engineering

2012-07-01

In this work we derive asymptotically stabilizing control laws for electrical power systems using two nonlinear control synthesis techniques. For this transient stabilization problem the actuator considered is a power electronic device, a controllable series capacitor (CSC). The power system is described using two different nonlinear models - the second order swing equation and the third order flux-decay model. To start with, the CSC is modeled by the injection model which is based on the assumption that the CSC dynamics is very fast as compared to the dynamics of the power system and hence can be approximated by an algebraic equation. Here, by neglecting the CSC dynamics, the input vector g(x) in the open loop system takes a complex form - the injection model. Using this model, interconnection and damping assignment passivity-based control (IDA-PBC) methodology is demonstrated on two power systems: a single machine infinite bus (SMIB) system and a two machine system. Further, IDA-PBC is used to derive stabilizing controllers for power systems, where the CSC dynamics are included as a first order system. Next, we consider a different control methodology, immersion and invariance (I and I), to synthesize an asymptotically stabilizing control law for the SMIB system with a CSC. The CSC is described by a first order system. As a generalization of I and I, we incorporate the power balance algebraic constraints in the load bus to the SMIB swing equation, and extend the design philosophy to a class of differential algebraic systems. The proposed result is then demonstrated on another example: a two-machine system with two load buses and a CSC. The controller performances are validated through simulations for all cases.

Hadron–Quark Combustion as a Nonlinear, Dynamical System

Science.gov (United States)

Ouyed, Amir; Ouyed, Rachid; Jaikumar, Prashanth

2018-03-01

The hadron-quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron-quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

Science.gov (United States)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

A non-linear regression analysis program for describing electrophysiological data with multiple functions using Microsoft Excel.

Science.gov (United States)

Brown, Angus M

2006-04-01

The objective of this present study was to demonstrate a method for fitting complex electrophysiological data with multiple functions using the SOLVER add-in of the ubiquitous spreadsheet Microsoft Excel. SOLVER minimizes the difference between the sum of the squares of the data to be fit and the function(s) describing the data using an iterative generalized reduced gradient method. While it is a straightforward procedure to fit data with linear functions, and we have previously demonstrated a method of non-linear regression analysis of experimental data based upon a single function, it is more complex to fit data with multiple functions, usually requiring specialized expensive computer software. In this paper we describe an easily understood program for fitting experimentally acquired data, in this case the stimulus-evoked compound action potential from the mouse optic nerve, with multiple Gaussian functions. The program is flexible and can be applied to describe data with a wide variety of user-input functions.

Positive real balancing for nonlinear systems

NARCIS (Netherlands)

Ionescu, Tudor C.; Scherpen, Jacquelien M.A.; Ciuprina, G; Ioan, D

2007-01-01

We extend the positive real balancing procedure for passive linear systems to the nonlinear systems case. We show that, just like in the linear case, model reduction based on this technique preserves passivity.

Investigation of the Nonlinear Model of the Cellular Population System Development

Directory of Open Access Journals (Sweden)

M. S. Vinogradova

2014-01-01

Full Text Available An isolated population system is considered which consists of two types of human stem cells: normal cells and cells with chromosomal anomalies (abnormal. In the paper the nonlinear dynamic model which describes dynamics of cell populations developing in vitro is elaborated. The model allows to investigate the processes of the formation of the abnormal cells population from the abnormal cells population of normal cells as well as joint development of these populations. The model takes into account the limited resources.An important feature of the developed model is the use of biological characteristics of processes in the cell population system, such as the proportion of cells, divided over a specified time, the proportion of cells whish are not divided, and which are "lost" and which are passed in the population of abnormal cells from the normal population. This approach allows a more detailed analysis of the impact of various "primary" parameters on the evolution of the population system.Under cultivation of cell populations in vitro a struggle for resources primarily affects the processes of the cell reproduction. This is reflected in the existence of the dividing cells frequency dependence of the total population of normal and abnormal cells. For the account of such dependencies different non-linear functions are typically used. However, the use of such non-linear relationships leads to the difficulties in finding confidence intervals for the estimates of the model parameters at subsequent stages of research. At the same time, the problem of the system parameters estimating and finding of the corresponding confidence intervals for estimates can be solved easy in case when the nonlinear system is linear with respect to the unknown parameters. In the paper it is achieved due to the piecewise linear approximation of nonlinear dependencies.An important feature of the model is a different view of the right part of the differential equations system

Nonlinear wave-beam kinetic equilibrium in decelerating systems

International Nuclear Information System (INIS)

Grishin, V.K.; Shaposhnikova, E.N.

1981-01-01

The equilibrium state of the wave-beam system arising during the interaction of a particle beam and excited electromagnetic wave has been investigated on the basis of the analysis of the exact polution of a non-linear self-consistent linear equation using the complete system of conservation laws. A waveguide with a dielectric filler, into which a monoenergetic particle beam magnetized in a transverse plane is continuously injected, is used as a model of an decelerating system. A dispersion equation describing the system state and expression for the evaluation of efficiency of the beam energy conversion to the field energy have been obtained. It is concluded that larae fields and high efficiency of energy conversion are achieved during the marked beam reconstruction. States with different values of current and beam velocity but similar amplitudes of a longitudinal field are possible in the system considered [ru

Energy flow theory of nonlinear dynamical systems with applications

CERN Document Server

Xing, Jing Tang

2015-01-01

This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...

Resonant driving of a nonlinear Hamiltonian system

International Nuclear Information System (INIS)

Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro

2013-01-01

As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.

Inverse operator method for solutions of nonlinear dynamical system and application to Lorentz equation

International Nuclear Information System (INIS)

Fang Jinqing; Yao Weiguang

1993-01-01

The inverse operator method (IOM) for solutions of nonlinear dynamical systems (NDS) is briefly described and realized by the Mathematics-Mechanization (MM) in computers. For the first time IOM and MM are successfully applied to study the chaotic behaviors of Lorentz equation

Structure Learning in Stochastic Non-linear Dynamical Systems

Science.gov (United States)

Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.

2005-12-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.

Hadron–Quark Combustion as a Nonlinear, Dynamical System

Directory of Open Access Journals (Sweden)

Amir Ouyed

2018-03-01

Full Text Available The hadron–quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron–quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.

Weakly nonlinear dynamics in noncanonical Hamiltonian systems with applications to fluids and plasmas

Energy Technology Data Exchange (ETDEWEB)

Morrison, P.J., E-mail: morrison@physics.utexas.edu [Department of Physics and Institute for Fusion Studies, University of Texas, Austin (United States); Vanneste, J. [School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh (United Kingdom)

2016-05-15

A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria of systems possessing Hamiltonian form in terms of noncanonical Poisson brackets. The procedure applies to systems like fluids and plasmas in terms of Eulerian variables that have such noncanonical Poisson brackets, i.e., brackets with nonstandard and possibly degenerate form. A collection of examples of both finite and infinite dimensions is presented.

Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.

Science.gov (United States)

Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua

2016-11-14

In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

Nonlinear dynamical system identification using unscented Kalman filter

Science.gov (United States)

Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan

2016-11-01

Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.

Two-dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions. II. Gaussian-Markovian case

NARCIS (Netherlands)

Tanimura, Y; Steffen, T

2000-01-01

The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator.

Science.gov (United States)

Botari, Tiago; Leonel, Edson D

2013-01-01

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization.

Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay

Directory of Open Access Journals (Sweden)

S. J. Sadati

2010-01-01

Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.

Nonlinear dynamics in biological systems

CERN Document Server

Carballido-Landeira, Jorge

2016-01-01

This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...

Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

Directory of Open Access Journals (Sweden)

S. L. Han

2012-01-01

Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.

Nonlinear quenches of power-law confining traps in quantum critical systems

International Nuclear Information System (INIS)

Collura, Mario; Karevski, Dragi

2011-01-01

We describe the coherent quantum evolution of a quantum many-body system with a time-dependent power-law confining potential. The amplitude of the inhomogeneous potential is driven in time along a nonlinear ramp which crosses a critical point. Using Kibble-Zurek-like scaling arguments we derive general scaling laws for the density of excitations and energy excess generated during the nonlinear sweep of the confining potential. It is shown that, with respect to the sweeping rate, the densities follow algebraic laws with exponents that depend on the space-time properties of the potential and on the scaling dimensions of the densities. We support our scaling predictions with both analytical and numerical results on the Ising quantum chain with an inhomogeneous transverse field varying in time.

Nonlinear and Complex Dynamics in Real Systems

OpenAIRE

William Barnett; Apostolos Serletis; Demitre Serletis

2005-01-01

This paper was produced for the El-Naschie Symposium on Nonlinear Dynamics in Shanghai in December 2005. In this paper we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems with nonlinear chaotic dynamics and discuss some techniques used in distinguishing between stochastic and deterministic behavior. Moreover, we look at the issue of where and when the ideas of chaos could p...

Model reduction of nonlinear systems subject to input disturbances

KAUST Repository

Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem

2017-01-01

The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order

Neural network modeling of nonlinear systems based on Volterra series extension of a linear model

Science.gov (United States)

Soloway, Donald I.; Bialasiewicz, Jan T.

1992-01-01

A Volterra series approach was applied to the identification of nonlinear systems which are described by a neural network model. A procedure is outlined by which a mathematical model can be developed from experimental data obtained from the network structure. Applications of the results to the control of robotic systems are discussed.

Mathematical Systems Theory : from Behaviors to Nonlinear Control

CERN Document Server

Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien

2015-01-01

This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...

Features and states of microscopic particles in nonlinear quantum-mechanics systems

Institute of Scientific and Technical Information of China (English)

2008-01-01

In this paper,we present the elementary principles of nonlinear quantum mechanics(NLQM),which is based on some problems in quantum mechanics.We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles.Concretely speaking,we study in this paper the wave-particle duality of the solution of the nonlinear Schr6dinger equation,the stability of microscopic particles described by NLQM,invariances and conservation laws of motion of particles,the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations,the classical rule of microscopic particle motion,the mechanism and rules of particle collision,the features of reflection and the transmission of particles at interfaces,and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles,and so on.We obtained the invariance and conservation laws of mass,energy and momentum and angular momenturn for the microscopic particles,which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions.We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics(LQM).They have a lot of new properties;for example,the particles possess the real wave-corpuscle duality,obey the classical rule of motion and conservation laws of energy,momentum and mass,satisfy minimum uncertainty relation,can be localized due to the nonlinear interaction,and its position and momentum can also be determined,etc.From these studies,we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM.Therefore,the NLQM is a new physical theory,and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems,which can

New developments in state estimation for Nonlinear Systems

DEFF Research Database (Denmark)

Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole

2000-01-01

Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a mult......-known estimators, such as the extended Kalman filter (EKF) and its higher-order relatives, in most practical applications....

Increase of nonlinear signal distortions due to linear mode coupling in space division multiplexed systems

DEFF Research Database (Denmark)

Kutluyarov, Ruslan V.; Bagmanov, Valeriy Kh; Antonov, Vyacheslav V.

2017-01-01

This paper is focused on the analysis of linear and nonlinear mode coupling in space division multiplexed (SDM) optical communications over step-index fiber in few-mode regime. Linear mode coupling is caused by the fiber imperfections, while the nonlinear coupling is caused by the Kerr......-nonlinearities. Therefore, we use the system of generalized coupled nonlinear Schrödinger equations (GCNLSE) to describe the signal propagation. We analytically show that the presence of linear mode coupling may cause increasing of the nonlinear signal distortions. For the detailed study we solve GCNLSE numerically...... for the standard step index fiber at the wavelength of 850 nm in the basis of spatial modes with helical phase front (vortex modes) and for a special kind of few-mode fiber with enlarged core, providing propagation of five spatial modes at 1550 nm. Simulation results confirm that the linear mode coupling may lead...

Nonlinear analysis of a reaction-diffusion system: Amplitude equations

Energy Technology Data Exchange (ETDEWEB)

Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

2012-10-15

A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

Science.gov (United States)

Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

2014-11-21

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

An unusual nonlinear system in the magnetosphere: A possible driver for auroral pulsations

International Nuclear Information System (INIS)

Davidson, G.T.; Chiu, Y.T.

1991-01-01

Many aspects of the relation between spatial and temporal structures in morningside aurorae can be explained with the aid of a nonlinear model that describes the interactions between energetic electrons and VLF waves. The simplest form of the model consists of three differential equations, with time derivatives generated in reference frames moving with either the energetic electrons, the cold plasma; or the VLF waves that interact with the energetic electrons. Although unstable solutions that could explain the origin of spatial structures are not found, the existence of spatial structures having sufficiently fine scales can provide a repetitive perturbation that maintains the temporal variations. An analysis of the behavior of solutions of the nonlinear system reveals that a strange attractor does not occur in the autonomous system; but when the repetitive perturbations are regarded as external periodic forcing terms, unusual forms of nonlinear behavior are revealed. If the frequencies of the forcing terms are not commensurate with the natural periods of the system, the solutions present some of the characteristics of deterministic chaos. The nearest analogy is a driven nonlinear oscillator with asymmetric damping. However, because of the stiffness of the system, even those solutions that are not truly chaotic (in the commonly accepted usage) will be indistinguishable from chaos over tens to hundreds of pulsation cycles. In certain cases, when damping terms are reduced to zero, the system displays a form of behavior with many of the important characteristics of chaos, but the phase trajectories do not appear to be bounded

Nonlinear control for a class of hydraulic servo system.

Science.gov (United States)

Yu, Hong; Feng, Zheng-jin; Wang, Xu-yong

2004-11-01

The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.

Noninteracting control of nonlinear systems based on relaxed control

NARCIS (Netherlands)

Jayawardhana, B.

2010-01-01

In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to

Decreasing the LHC impedance with a nonlinear collimation system

CERN Document Server

Resta-López, J; Zimmermann, F

2007-01-01

A two-stage nonlinear collimation system based on a pair of skew sextupoles is presented for the LHC.We show the details of the optics design and study the halo cleaning efficiency of such a system. This nonlinear collimation system would allow opening up collimator gaps, and thereby reduce the collimator impedance, which presently limits the LHC beam intensity. Assuming the nominal LHC beam at 7 TeV, the transverse coherent tune shifts of rigid-dipole coupled-bunch modes are computed for both the baseline linear collimation system and the proposed nonlinear one. In either case, the tune shifts of the most unstable modes are compared with the stability diagrams for Landau damping.

A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

Directory of Open Access Journals (Sweden)

S.H. Chen

1996-01-01

Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

Nonlinear wave chaos: statistics of second harmonic fields.

Science.gov (United States)

Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M

2017-10-01

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

Dynamical Chaos Rise in the System of Large Number of Nonlinear Coupled Oscillators

International Nuclear Information System (INIS)

Buts, V.A.; Koval'chuk, I.K.; Tarasov, D.V.

2007-01-01

The problem of dynamical chaos arising in distributed systems is considered. It was shown that in many cases it is possible to allocate relatively isolated subsystem which may be simpler for investigation. We suppose that chaos in this subsystem leads to chaotic behaviour of all system. Besides, the allocated subsystem may be used for describing complex dynamics of nonlinear three-wave interaction, in particular, in plasma systems. The analytical criterion of arising dynamics chaos in distributed system was obtained. This criterion was confirmed by numerical simulation

Controllability of nonlinear delay oscillating systems

Directory of Open Access Journals (Sweden)

Chengbin Liang

2017-05-01

Full Text Available In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix.

Stability analysis of nonlinear systems with slope restricted nonlinearities.

Science.gov (United States)

Liu, Xian; Du, Jiajia; Gao, Qing

2014-01-01

The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities

Directory of Open Access Journals (Sweden)

Xian Liu

2014-01-01

Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

A deep belief network with PLSR for nonlinear system modeling.

Science.gov (United States)

Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

2017-10-31

Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Nonlinear dynamics of a coherent polariton-biexciton system

International Nuclear Information System (INIS)

Nguyen Trung Dan; Vo Tinh

1994-08-01

The nonlinear dynamics of a coherent interacting polariton-biexciton system in optically excited semiconductors is investigated. We consider the case when two macroscopically coherent modes - a lower branch polariton and a biexciton existing simultaneously in a direct-gap semiconductor. The conditions for exhibiting optical bistability in stationary regime are obtained. Numerical simulation for the nonlinear dynamics equations of the system is also carried out. (author). 16 refs, 4 figs

Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications

OpenAIRE

Hou, Chuanjing; Hu, Lisheng; Zhang, Yingwei

2015-01-01

An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.

Nonlinear dynamic analysis of piping systems using the pseudo force method

International Nuclear Information System (INIS)

Prachuktam, S.; Bezler, P.; Hartzman, M.

1979-01-01

Simple piping systems are composed of linear elastic elements and can be analyzed using conventional linear methods. The introduction of constraint springs separated from the pipe with clearance gaps to such systems to cope with the pipe whip or other extreme excitation conditions introduces nonlinearities to the system, the nonlinearities being associated with the gaps. Since these spring-damper constraints are usually limited in number, descretely located, and produce only weak nonlinearities, the analysis of linear systems including these nonlinearities can be carried out by using modified linear methods. In particular, the application of pseudo force methods wherein the nonlinearities are treated as displacement dependent forcing functions acting on the linear system were investigated. The nonlinearities induced by the constraints are taken into account as generalized pseudo forces on the right-hand side of the governing dynamic equilibrium equations. Then an existing linear elastic finite element piping code, EPIPE, was modified to permit application of the procedure. This option was inserted such that the analyses could be performed using either the direct integration method or via a modal superposition method, the Newmark-Beta integration procedure being employed in both methods. The modified code was proof tested against several problems taken from the literature or developed with the nonlinear dynamics code OSCIL. The problems included a simple pipe loop, cantilever beam, and lumped mass system subjected to pulsed and periodic forcing functions. The problems were selected to gage the overall accuracy of the method and to insure that it properly predicted the jump phenomena associated with nonlinear systems. (orig.)

Optimisation-based worst-case analysis and anti-windup synthesis for uncertain nonlinear systems

Science.gov (United States)

Menon, Prathyush Purushothama

This thesis describes the development and application of optimisation-based methods for worst-case analysis and anti-windup synthesis for uncertain nonlinear systems. The worst-case analysis methods developed in the thesis are applied to the problem of nonlinear flight control law clearance for highly augmented aircraft. Local, global and hybrid optimisation algorithms are employed to evaluate worst-case violations of a nonlinear response clearance criterion, for a highly realistic aircraft simulation model and flight control law. The reliability and computational overheads associated with different opti misation algorithms are compared, and the capability of optimisation-based approaches to clear flight control laws over continuous regions of the flight envelope is demonstrated. An optimisation-based method for computing worst-case pilot inputs is also developed, and compared with current industrial approaches for this problem. The importance of explicitly considering uncertainty in aircraft parameters when computing worst-case pilot demands is clearly demonstrated. Preliminary results on extending the proposed framework to the problems of limit-cycle analysis and robustness analysis in the pres ence of time-varying uncertainties are also included. A new method for the design of anti-windup compensators for nonlinear constrained systems controlled using nonlinear dynamics inversion control schemes is presented and successfully applied to some simple examples. An algorithm based on the use of global optimisation is proposed to design the anti-windup compensator. Some conclusions are drawn from the results of the research presented in the thesis, and directions for future work are identified.

Feedback-Equivalence of Nonlinear Systems with Applications to Power System Equations.

Science.gov (United States)

Marino, Riccardo

The key concept of the dissertation is feedback equivalence among systems affine in control. Feedback equivalence to linear systems in Brunovsky canonical form and the construction of the corresponding feedback transformation are used to: (i) design a nonlinear regulator for a detailed nonlinear model of a synchronous generator connected to an infinite bus; (ii) establish which power system network structures enjoy the feedback linearizability property and design a stabilizing control law for these networks with a constraint on the control space which comes from the use of d.c. lines. It is also shown that the feedback linearizability property allows the use of state feedback to contruct a linear controllable system with a positive definite linear Hamiltonian structure for the uncontrolled part if the state space is even; a stabilizing control law is derived for such systems. Feedback linearizability property is characterized by the involutivity of certain nested distributions for strongly accessible analytic systems; if the system is defined on a manifold M diffeomorphic to the Euclidean space, it is established that the set where the property holds is a submanifold open and dense in M. If an analytic output map is defined, a set of nested involutive distributions can be always defined and that allows the introduction of an observability property which is the dual concept, in some sense, to feedback linearizability: the goal is to investigate when a nonlinear system affine in control with an analytic output map is feedback equivalent to a linear controllable and observable system. Finally a nested involutive structure of distributions is shown to guarantee the existence of a state feedback that takes a nonlinear system affine in control to a single input one, both feedback equivalent to linear controllable systems, preserving one controlled vector field.

Point source identification in nonlinear advection–diffusion–reaction systems

International Nuclear Information System (INIS)

Mamonov, A V; Tsai, Y-H R

2013-01-01

We consider a problem of identification of point sources in time-dependent advection–diffusion systems with a nonlinear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of nonlinear algebraic equations via the use of adjoint equations. We extend this approach by constructing an algorithm that solves the problem iteratively to account for the nonlinearity of the reaction term. We study the question of improving the quality of source identification by adding more measurements adaptively using the solution obtained previously with a smaller number of measurements. (paper)

Quantum-Classical correspondence in nonlinear multidimensional systems: enhanced di usion through soliton wave-particles

KAUST Repository

Brambila, Danilo

2012-05-01

Quantum chaos has emerged in the half of the last century with the notorious problem of scattering of heavy nuclei. Since then, theoreticians have developed powerful techniques to approach disordered quantum systems. In the late 70\\'s, Casati and Chirikov initiated a new field of research by studying the quantum counterpart of classical problems that are known to exhibit chaos. Among the several quantum-classical chaotic systems studied, the kicked rotor stimulated a lot of enthusiasm in the scientific community due to its equivalence to the Anderson tight binding model. This equivalence allows one to map the random Anderson model into a set of fully deterministic equations, making the theoretical analysis of Anderson localization considerably simpler. In the one-dimensional linear regime, it is known that Anderson localization always prevents the diffusion of the momentum. On the other hand, for higher dimensions it was demonstrated that for certain conditions of the disorder parameter, Anderson localized modes can be inhibited, allowing then a phase transition from localized (insulating) to delocalized (metallic) states. In this thesis we will numerically and theoretically investigate the properties of a multidimensional quantum kicked rotor in a nonlinear medium. The presence of nonlinearity is particularly interesting as it raises the possibility of having soliton waves as eigenfunctions of the systems. We keep the generality of our approach by using an adjustable diffusive nonlinearity, which can describe several physical phenomena. By means of Variational Calculus we develop a chaotic map which fully describes the soliton dynamics. The analysis of such a map shows a rich physical scenario that evidences the wave-particle behavior of a soliton. Through the nonlinearity, we trace a correspondence between quantum and classical mechanics, which has no equivalent in linearized systems. Matter waves experiments provide an ideal environment for studying Anderson

Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems

DEFF Research Database (Denmark)

Bayat, M.; Shahidi, M.; Barari, Amin

2011-01-01

approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...

Measurement Model Nonlinearity in Estimation of Dynamical Systems

Science.gov (United States)

Majji, Manoranjan; Junkins, J. L.; Turner, J. D.

2012-06-01

The role of nonlinearity of the measurement model and its interactions with the uncertainty of measurements and geometry of the problem is studied in this paper. An examination of the transformations of the probability density function in various coordinate systems is presented for several astrodynamics applications. Smooth and analytic nonlinear functions are considered for the studies on the exact transformation of uncertainty. Special emphasis is given to understanding the role of change of variables in the calculus of random variables. The transformation of probability density functions through mappings is shown to provide insight in to understanding the evolution of uncertainty in nonlinear systems. Examples are presented to highlight salient aspects of the discussion. A sequential orbit determination problem is analyzed, where the transformation formula provides useful insights for making the choice of coordinates for estimation of dynamic systems.

Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications

Directory of Open Access Journals (Sweden)

Chuanjing Hou

2015-01-01

Full Text Available An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.

Nonlinear control and filtering using differential flatness approaches applications to electromechanical systems

CERN Document Server

Rigatos, Gerasimos G

2015-01-01

This monograph presents recent advances in differential flatness theory and analyzes its use for nonlinear control and estimation. It shows how differential flatness theory can provide solutions to complicated control problems, such as those appearing in highly nonlinear multivariable systems and distributed-parameter systems. Furthermore, it shows that differential flatness theory makes it possible to perform filtering and state estimation for a wide class of nonlinear dynamical systems and provides several descriptive test cases. The book focuses on the design of nonlinear adaptive controllers and nonlinear filters, using exact linearization based on differential flatness theory. The adaptive controllers obtained can be applied to a wide class of nonlinear systems with unknown dynamics, and assure reliable functioning of the control loop under uncertainty and varying operating conditions. The filters obtained outperform other nonlinear filters in terms of accuracy of estimation and computation speed. The bo...

A universal approach to the study of nonlinear systems

Science.gov (United States)

Hwa, Rudolph C.

2004-07-01

A large variety of nonlinear systems have been treated by a common approach that emphasizes the fluctuation of spatial patterns. By using the same method of analysis it is possible to discuss the chaotic behaviors of quark jets and logistic map in the same language. Critical behaviors of quark-hadron phase transition in heavy-ion collisions and of photon production at the threshold of lasing can also be described by a common scaling behavior. The universal approach also makes possible an insight into the recently discovered phenomenon of wind reversal in cryogenic turbulence as a manifestation of self-organized criticality.

A nonlinear beam model to describe the postbuckling of wide neo-Hookean beams

Science.gov (United States)

Lubbers, Luuk A.; van Hecke, Martin; Coulais, Corentin

2017-09-01

Wide beams can exhibit subcritical buckling, i.e. the slope of the force-displacement curve can become negative in the postbuckling regime. In this paper, we capture this intriguing behaviour by constructing a 1D nonlinear beam model, where the central ingredient is the nonlinearity in the stress-strain relation of the beams constitutive material. First, we present experimental and numerical evidence of a transition to subcritical buckling for wide neo-Hookean hyperelastic beams, when their width-to-length ratio exceeds a critical value of 12%. Second, we construct an effective 1D energy density by combining the Mindlin-Reissner kinematics with a nonlinearity in the stress-strain relation. Finally, we establish and solve the governing beam equations to analytically determine the slope of the force-displacement curve in the postbuckling regime. We find, without any adjustable parameters, excellent agreement between the 1D theory, experiments and simulations. Our work extends the understanding of the postbuckling of structures made of wide elastic beams and opens up avenues for the reverse-engineering of instabilities in soft and metamaterials.

Robust receding horizon control for networked and distributed nonlinear systems

CERN Document Server

Li, Huiping

2017-01-01

This book offers a comprehensive, easy-to-understand overview of receding-horizon control for nonlinear networks. It presents novel general strategies that can simultaneously handle general nonlinear dynamics, system constraints, and disturbances arising in networked and large-scale systems and which can be widely applied. These receding-horizon-control-based strategies can achieve sub-optimal control performance while ensuring closed-loop stability: a feature attractive to engineers. The authors address the problems of networked and distributed control step-by-step, gradually increasing the level of challenge presented. The book first introduces the state-feedback control problems of nonlinear networked systems and then studies output feedback control problems. For large-scale nonlinear systems, disturbance is considered first, then communication delay separately, and lastly the simultaneous combination of delays and disturbances. Each chapter of this easy-to-follow book not only proposes and analyzes novel ...

Nonlinear dynamics of fractional order Duffing system

International Nuclear Information System (INIS)

Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

2015-01-01

In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

Applications of equivalent linearization approaches to nonlinear piping systems

International Nuclear Information System (INIS)

Park, Y.; Hofmayer, C.; Chokshi, N.

1997-01-01

The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA's are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations

Analysis and design of robust decentralized controllers for nonlinear systems

Energy Technology Data Exchange (ETDEWEB)

Schoenwald, D.A.

1993-07-01

Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.

Improved Minimum Entropy Filtering for Continuous Nonlinear Non-Gaussian Systems Using a Generalized Density Evolution Equation

Directory of Open Access Journals (Sweden)

Jinliang Xu

2013-06-01

Full Text Available This paper investigates the filtering problem for multivariate continuous nonlinear non-Gaussian systems based on an improved minimum error entropy (MEE criterion. The system is described by a set of nonlinear continuous equations with non-Gaussian system noises and measurement noises. The recently developed generalized density evolution equation is utilized to formulate the joint probability density function (PDF of the estimation errors. Combining the entropy of the estimation error with the mean squared error, a novel performance index is constructed to ensure the estimation error not only has small uncertainty but also approaches to zero. According to the conjugate gradient method, the optimal filter gain matrix is then obtained by minimizing the improved minimum error entropy criterion. In addition, the condition is proposed to guarantee that the estimation error dynamics is exponentially bounded in the mean square sense. Finally, the comparative simulation results are presented to show that the proposed MEE filter is superior to nonlinear unscented Kalman filter (UKF.

Nonlinear dynamical system approaches towards neural prosthesis

International Nuclear Information System (INIS)

Torikai, Hiroyuki; Hashimoto, Sho

2011-01-01

An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.

Passivity Based Stabilization of Non-minimum Phase Nonlinear Systems

Czech Academy of Sciences Publication Activity Database

Travieso-Torres, J.C.; Duarte-Mermoud, M.A.; Zagalak, Petr

2009-01-01

Roč. 45, č. 3 (2009), s. 417-426 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : nonlinear systems * stabilisation * passivity * state feedback Subject RIV: BC - Control Systems Theory Impact factor: 0.445, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-passivity based stabilization of non-minimum phase nonlinear systems.pdf

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

Science.gov (United States)

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Non-linear dynamics of wind turbine wings

DEFF Research Database (Denmark)

Larsen, Jesper Winther; Nielsen, Søren R.K.

2006-01-01

The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced...

Nonlinear Predictive Sliding Mode Control for Active Suspension System

Directory of Open Access Journals (Sweden)

Dazhuang Wang

2018-01-01

Full Text Available An active suspension system is important in meeting the requirements of the ride comfort and handling stability for vehicles. In this work, a nonlinear model of active suspension system and a corresponding nonlinear robust predictive sliding mode control are established for the control problem of active suspension. Firstly, a seven-degree-of-freedom active suspension model is established considering the nonlinear effects of springs and dampers; and secondly, the dynamic model is expanded in the time domain, and the corresponding predictive sliding mode control is established. The uncertainties in the controller are approximated by the fuzzy logic system, and the adaptive controller reduces the approximation error to increase the robustness of the control system. Finally, the simulation results show that the ride comfort and handling stability performance of the active suspension system is better than that of the passive suspension system and the Skyhook active suspension. Thus, the system can obviously improve the shock absorption performance of vehicles.

TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods

Energy Technology Data Exchange (ETDEWEB)

Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science

1996-12-31

This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.

Is DNA a nonlinear dynamical system where solitary conformational ...

Indian Academy of Sciences (India)

Unknown

DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The ... nonlinear differential equations and their soliton-like solu- .... structure and dynamics can be added till the most accurate.

Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters

Directory of Open Access Journals (Sweden)

S. Vaidyanathan

2013-09-01

Full Text Available This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (B. In this work, a detailed qualitative analysis of the novel chaotic systems (A and (B has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE for the novel chaotic systems (A and (B has a large value, viz. for the system (A and for the system (B. Thus, both the novel chaotic systems (A and (B display strong chaotic behaviour. This research work also discusses the problem of finding adaptive controllers for the global chaos synchronization of identical chaotic systems (A, identical chaotic systems (B and nonidentical chaotic systems (A and (B with unknown system parameters. The adaptive controllers for achieving global chaos synchronization of the novel chaotic systems (A and (B have been derived using adaptive control theory and Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A and (B, and also the adaptive synchronization results derived for the novel chaotic systems (A and (B.

Robust model predictive control for constrained continuous-time nonlinear systems

Science.gov (United States)

Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong

2018-02-01

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.

NONLINEAR TIDES IN CLOSE BINARY SYSTEMS

International Nuclear Information System (INIS)

Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh

2012-01-01

We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' ∼> 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P ∼ 3 [P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P ∼< a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing

Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

Science.gov (United States)

Yao, Jianyong

2018-06-01

Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.

Nonlinear physical systems spectral analysis, stability and bifurcations

CERN Document Server

Kirillov, Oleg N

2013-01-01

Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

International Nuclear Information System (INIS)

Niu Yu-Jun; Pei Bing-Nan; Wang Xing-Yuan

2012-01-01

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor. (general)

Incremental passivity and output regulation for switched nonlinear systems

Science.gov (United States)

Pang, Hongbo; Zhao, Jun

2017-10-01

This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.

Nonlinear von Neumann equations for quantum dissipative systems

International Nuclear Information System (INIS)

Messer, J.; Baumgartner, B.

1978-01-01

For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)

Nonlinear von Neumann equations for quantum dissipative systems

International Nuclear Information System (INIS)

Messer, J.; Baumgartner, B.

For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)

Methodology for global nonlinear analysis of nuclear systems

International Nuclear Information System (INIS)

Cacuci, D.G.; Cacuci, G.L.

1987-01-01

This paper outlines a general method for globally computing the crucial features of nonlinear problems: bifurcations, limit points, saddle points, extrema (maxima and minima); our method also yields the local sensitivities (i.e., first order derivatives) of the system's state variables (e.g., fluxes, power, temperatures, flows) at any point in the system's phase space. We also present an application of this method to the nonlinear BWR model discussed in Refs. 8 and 11. The most significant novel feature of our method is the recasting of a general mathematical problem comprising three aspects: (1) nonlinear constrained optimization, (2) sensitivity analysis, into a fixed point problem of the form F[u(s), λ(s)] = 0 whose global zeros and singular points are related to the special features (i.e., extrema, bifurcations, etc.) of the original problem

Nonlinear transport properties of non-ideal systems

International Nuclear Information System (INIS)

Pavlov, G A

2009-01-01

The theory of nonlinear transport is elaborated to determine the Burnett transport properties of non-ideal multi-element plasma and neutral systems. The procedure for the comparison of the phenomenological conservation equations of a continuous dense medium and the microscopic equations for dynamical variable operators is used for the definition of these properties. The Mori algorithm is developed to derive the equations of motion of dynamical value operators of a non-ideal system in the form of the generalized nonlinear Langevin equations. In consequence, the microscopic expressions of transport coefficients corresponding to second-order thermal disturbances (temperature, mass velocity, etc) have been found in the long wavelength and low frequency limits

Network science, nonlinear science and infrastructure systems

CERN Document Server

2007-01-01

Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems. .

Control and synchronization of chaos in nonlinear systems and prospects for application. Pt.1

International Nuclear Information System (INIS)

Fang Jinqing

1996-01-01

Main progress in one challenging subject of nonlinear science--control and synchronization of chaos in nonlinear systems are reviewed systematically, including recent advance in controlling and synchronizing hyperchaos. Current methods and principles of schemes of chaos control and synchronization are classified and summarized in detail. Potential prospects for application are commented both in theory and experiment. The whole review is divided into two parts. In the first one, subject on the mechanism and method of chaos control are analyzed and discussed extensively. In the second one, the synchronization of non-chaos, chaos, hyperchaos and their control and application are described. Main trends for development of the subject is mentioned. (101 refs.)

A combined modification of Newton`s method for systems of nonlinear equations

Energy Technology Data Exchange (ETDEWEB)

Monteiro, M.T.; Fernandes, E.M.G.P. [Universidade do Minho, Braga (Portugal)

1996-12-31

To improve the performance of Newton`s method for the solution of systems of nonlinear equations a modification to the Newton iteration is implemented. The modified step is taken as a linear combination of Newton step and steepest descent directions. In the paper we describe how the coefficients of the combination can be generated to make effective use of the two component steps. Numerical results that show the usefulness of the combined modification are presented.

Upport vector machines for nonlinear kernel ARMA system identification.

Science.gov (United States)

Martínez-Ramón, Manel; Rojo-Alvarez, José Luis; Camps-Valls, Gustavo; Muñioz-Marí, Jordi; Navia-Vázquez, Angel; Soria-Olivas, Emilio; Figueiras-Vidal, Aníbal R

2006-11-01

Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA2K) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based system identification nonlinear models is presented, based on the use of composite Mercer's kernels. This general class can improve model flexibility by emphasizing the input-output cross information (SVM-ARMA4K), which leads to straightforward and natural combinations of implicit and explicit ARMA models (SVR-ARMA2K and SVR-ARMA4K). Capabilities of these different SVM-based system identification schemes are illustrated with two benchmark problems.

Effects of error feedback on a nonlinear bistable system with stochastic resonance

International Nuclear Information System (INIS)

Li Jian-Long; Zhou Hui

2012-01-01

In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing

Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint

CERN Document Server

Martínez-Guerra, Rafael

2017-01-01

This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

Calculations on nonlinear optical properties for large systems the elongation method

CERN Document Server

Gu, Feng Long; Springborg, Michael; Kirtman, Bernard

2014-01-01

For design purposes one needs to relate the structure of proposed materials to their NLO (nonlinear optical) and other properties, which is a situation where theoretical approaches can be very helpful in providing suggestions for candidate systems that subsequently can be synthesized and studied experimentally. This brief describes the quantum-mechanical treatment of the response to one or more external oscillating electric fields for molecular and macroscopic, crystalline systems. To calculate NLO properties of large systems, a linear scaling generalized elongation method for the efficient and accurate calculation is introduced. The reader should be aware that this treatment is particularly feasible for complicated three-dimensional and/or delocalized systems that are intractable when applied to conventional or other linear scaling methods.

Comparison of a nonlinear dynamic model of a piping system to test data

International Nuclear Information System (INIS)

Blakely, K.D.; Howard, G.E.; Walton, W.B.; Johnson, B.A.; Chitty, D.E.

1983-01-01

Response of a nonlinear finite element model of the Heissdampfreaktor recirculation piping loop (URL) was compared to measured data, representing the physical benchmarking of a nonlinear model. Analysis-test comparisons of piping response are presented for snapback tests that induced extreme nonlinear behavior of the URL system. Nonlinearities in the system are due to twelve swaybraces (pipe supports) that possessed nonlinear force-deflection characteristics. These nonlinearities distorted system damping estimates made by using the half-power bandwidth method on Fourier transforms of measured accelerations, with the severity of distortion increasing with increasing degree of nonlinearity. Time domain methods, which are not so severely affected by the presence of nonlinearities, were used to compute system damping ratios. Nonlinear dynamic analyses were accurately and efficiently performed using the pseudo-force technique and the finite element program MSC/NASTRAN. Measured damping was incorporated into the model for snapback simulations. Acceleration time histories, acceleration Fourier transforms, and swaybrace force time histories of the nonlinear model, plus several linear models, were compared to test measurements. The nonlinear model predicted three-fourths of the measured peak accelerations to within 50%, half of the accelerations to within 25%, and one-fifth of the accelerations to within 10%. This nonlinear model predicted accelerations (in the time and frequency domains) and swaybrace forces much better than did any of the linear models, demonstrating the increased accuracy resulting from properly simulating nonlinear support behavior. In addition, earthquake response comparisons were made between the experimentally validated nonlinear model and a linear model. Significantly lower element stresses were predicted for the nonlinear model, indicating the potential usefulness of nonlinear simulations in piping design assessments. (orig.)

Stability Analysis of Fractional-Order Nonlinear Systems with Delay

Directory of Open Access Journals (Sweden)

Yu Wang

2014-01-01

Full Text Available Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

Integrability and soliton solutions for an inhomogeneous generalized fourth-order nonlinear Schrödinger equation describing the inhomogeneous alpha helical proteins and Heisenberg ferromagnetic spin chains

International Nuclear Information System (INIS)

Wang, Pan; Tian, Bo; Jiang, Yan; Wang, Yu-Feng

2013-01-01

For describing the dynamics of alpha helical proteins with internal molecular excitations, nonlinear couplings between lattice vibrations and molecular excitations, and spin excitations in one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin with the octupole–dipole interactions, we consider an inhomogeneous generalized fourth-order nonlinear Schrödinger equation. Based on the Ablowitz–Kaup–Newell–Segur system, infinitely many conservation laws for the equation are derived. Through the auxiliary function, bilinear forms and N-soliton solutions for the equation are obtained. Interactions of solitons are discussed by means of the asymptotic analysis. Effects of linear inhomogeneity on the interactions of solitons are also investigated graphically and analytically. Since the inhomogeneous coefficient of the equation h=α x+β, the soliton takes on the parabolic profile during the evolution. Soliton velocity is related to the parameter α, distance scale coefficient and biquadratic exchange coefficient, but has no relation with the parameter β. Soliton amplitude and width are only related to α. Soliton position is related to β

Applications and algorithms for mixed integer nonlinear programming

International Nuclear Information System (INIS)

Leyffer, Sven; Munson, Todd; Linderoth, Jeff; Luedtke, James; Miller, Andrew

2009-01-01

The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scientific applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.

Graphical user interface for input output characterization of single variable and multivariable highly nonlinear systems

Directory of Open Access Journals (Sweden)

Shahrukh Adnan Khan M. D.

2017-01-01

Full Text Available This paper presents a Graphical User Interface (GUI software utility for the input/output characterization of single variable and multivariable nonlinear systems by obtaining the sinusoidal input describing function (SIDF of the plant. The software utility is developed on MATLAB R2011a environment. The developed GUI holds no restriction on the nonlinearity type, arrangement and system order; provided that output(s of the system is obtainable either though simulation or experiments. An insight to the GUI and its features are presented in this paper and example problems from both single variable and multivariable cases are demonstrated. The formulation of input/output behavior of the system is discussed and the nucleus of the MATLAB command underlying the user interface has been outlined. Some of the industries that would benefit from this software utility includes but not limited to aerospace, defense technology, robotics and automotive.

Nonlinear Impairment Compensation Using Expectation Maximization for PDM 16-QAM Systems

DEFF Research Database (Denmark)

Zibar, Darko; Winther, Ole; Franceschi, Niccolo

2012-01-01

We show experimentally that by using non-linear signal processing based algorithm, expectation maximization, nonlinear system tolerance can be increased by 2 dB. Expectation maximization is also effective in combating I/Q modulator nonlinearities and laser linewidth....

Nonlinear Photonic Systems for V- and W-Band Antenna Remoting Applications

Science.gov (United States)

2016-10-22

AFRL-AFOSR-JP-TR-2016-0088 Nonlinear Photonic Systems for V- and W-Band Antenna Remoting Applications Sheng-Kwang Hwang NATIONAL CHENG KUNG...2016 2. REPORT TYPE Final 3. DATES COVERED (From - To) 26 May 2015 to 25 May 2016 4. TITLE AND SUBTITLE Nonlinear Photonic Systems for V- and W-Band...TERMS nonlinear, photonic , antenna, remote, microwave, amplification, bandwith, modulation 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR

On Redundancy in Describing Linguistic Systems

Directory of Open Access Journals (Sweden)

Vladimir Borissov Pericliev

2015-12-01

Full Text Available On Redundancy in Describing Linguistic Systems The notion of system of linguistic elements figures prominently in most post-Saussurian linguistics up to the present. A “system” is the network of the contrastive (or, distinctive features each element in the system bears to the remaining elements. The meaning (valeur of each element in the system is the set of features that are necessary and jointly sufficient to distinguish this element from all others. The paper addresses the problems of “redundancy”, i.e. the occurrence of features that are not strictly necessary in describing an element in a system. Redundancy is shown to smuggle into the description of linguistic systems, this infelicitous practice illustrated with some examples from the literature (e.g. the classical phonemic analysis of Russian by Cherry, Halle, and Jakobson, 1953. The logic and psychology of the occurrence of redundancy are briefly sketched and it is shown that, in addition to some other problems, redundancy leads to a huge and unresolvable ambiguity of descriptions of linguistic systems (the Buridan’s ass problem.

ASYS: a computer algebra package for analysis of nonlinear algebraic equations systems

International Nuclear Information System (INIS)

Gerdt, V.P.; Khutornoj, N.V.

1992-01-01

A program package ASYS for analysis of nonlinear algebraic equations based on the Groebner basis technique is described. The package is written in REDUCE computer algebra language. It has special facilities to treat polynomial ideals of positive dimension, corresponding to algebraic systems with infinitely many solutions. Such systems can be transformed to an equivalent set of subsystems with reduced number of variables in completely automatic way. It often allows to construct the explicit form of a solution set in many problems of practical importance. Some examples and results of comparison with the standard Reduce package GROEBNER and special-purpose systems FELIX and A1PI are given. 21 refs.; 2 tabs

Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system

Science.gov (United States)

Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

2017-05-01

We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.

Nonlinear stability research on the hydraulic system of double-side rolling shear

Science.gov (United States)

Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu

2015-10-01

This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.

The Design of Feedback Control Systems Containing a Saturation Type Nonlinearity

Science.gov (United States)

Schmidt, Stanley F.; Harper, Eleanor V.

1960-01-01

A derivation of the optimum response for a step input for plant transfer functions which have an unstable pole and further data on plants with a single zero in the left half of the s plane. The calculated data are presented tabulated in normalized form. Optimum control systems are considered. The optimum system is defined as one which keeps the error as small as possible regardless of the input, under the constraint that the input to the plant (or controlled system) is limited. Intuitive arguments show that in the case where only the error can be sensed directly, the optimum system is obtained from the optimum relay or on-off solution. References to known solutions are presented. For the case when the system is of the sampled-data type, arguments are presented which indicate the optimum sampled-data system may be extremely difficult if not impossible to realize practically except for very simple plant transfer functions. Two examples of aircraft attitude autopilots are presented, one for a statically stable and the other for a statically unstable airframe. The rate of change of elevator motion is assumed limited for these examples. It is shown that by use of nonlinear design techniques described in NASA TN D-20 one can obtain near optimum response for step inputs and reason- able response to sine wave inputs for either case. Also, the nonlinear design prevents inputs from driving the system unstable for either case.

Conservation laws for certain time fractional nonlinear systems of partial differential equations

Science.gov (United States)

Singla, Komal; Gupta, R. K.

2017-12-01

In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.

A kernel-based approach to MIMO LPV state-space identification and application to a nonlinear process system

NARCIS (Netherlands)

Rizvi, S.Z.; Mohammadpour, J.; Toth, R.; Meskin, N.

2015-01-01

This paper first describes the development of a nonparametric identification method for linear parameter-varying (LPV) state-space models and then applies it to a nonlinear process system. The proposed method uses kernel-based least-squares support vector machines (LS-SVM). While parametric

Controlling chaotic systems via nonlinear feedback control

International Nuclear Information System (INIS)

Park, Ju H.

2005-01-01

In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived

A hierarchy of systems of nonlinear equations

International Nuclear Information System (INIS)

Falkensteiner, P.; Grosse, H.

1985-01-01

Imposing isospectral invariance for the one-dimensional Dirac operator yields an infinite hierarchy of systems of chiral invariant nonlinear partial differential equations. The same system is obtained through a Lax pair construction and finally a formulation in terms of Kac-Moody generators is given. (Author)

Robust approximation-free prescribed performance control for nonlinear systems and its application

Science.gov (United States)

Sun, Ruisheng; Na, Jing; Zhu, Bin

2018-02-01

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.

Model Predictive Control of a Nonlinear System with Known Scheduling Variable

DEFF Research Database (Denmark)

Mirzaei, Mahmood; Poulsen, Niels Kjølstad; Niemann, Hans Henrik

2012-01-01

Model predictive control (MPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Consequently...... the control problem of the nonlinear system is simplied into a quadratic programming. Wind turbine is chosen as the case study and we choose wind speed as the scheduling variable. Wind speed is measurable ahead of the turbine, therefore the scheduling variable is known for the entire prediction horizon....

Nonlinear damping based semi-active building isolation system

Science.gov (United States)

Ho, Carmen; Zhu, Yunpeng; Lang, Zi-Qiang; Billings, Stephen A.; Kohiyama, Masayuki; Wakayama, Shizuka

2018-06-01

Many buildings in Japan currently have a base-isolation system with a low stiffness that is designed to shift the natural frequency of the building below the frequencies of the ground motion due to earthquakes. However, the ground motion observed during the 2011 Tohoku earthquake contained strong long-period waves that lasted for a record length of 3 min. To provide a novel and better solution against the long-period waves while maintaining the performance of the standard isolation range, the exploitation of the characteristics of nonlinear damping is proposed in this paper. This is motivated by previous studies of the authors, which have demonstrated that nonlinear damping can achieve desired performance over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Simulation results have shown strong vibration isolation performance on a building model with identified parameters and have indicated that nonlinear damping can achieve low acceleration transmissibilities round the structural natural frequency as well as the higher ground motion frequencies that have been frequently observed during most earthquakes in Japan. In addition, physical building model based laboratory experiments are also conducted, The results demonstrate the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. In comparison with the tuned-mass damper and other active control methods, the proposed solution offers a more pragmatic, low-cost, robust and effective alternative that can be readily installed into the base-isolation system of most buildings.

Nonlinear stability of spin-flip excitations

International Nuclear Information System (INIS)

Arunasalam, V.

1975-01-01

A rather complete discussion of the nonlinear electrodynamic behavior of a negative-temperature spin system is presented. The method presented here is based on a coupled set of master equations, one describing the time evolution of the photon (i.e., the spin-flip excitation) distribution function and the other describing the time evolution of the particle distribution function. It is found that the initially unstable (i.e., growing) spin-flip excitations grow to such a large amplitude that their nonlinear reaction on the particle distribution function becomes important. It is then shown that the initially totally inverted two-level spin system evolves rapidly (through this nonlinear photon-particle coupling) towards a quasilinear steady state where the populations of the spin-up and the spin-down states are equal to each other. Explicit expressions for the time taken to reach this quasilinear steady state and the energy in the spin-flip excitations at this state are also presented

Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

Science.gov (United States)

Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

2018-05-01

Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

A novel auto-tuning PID control mechanism for nonlinear systems.

Science.gov (United States)

Cetin, Meric; Iplikci, Serdar

2015-09-01

In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Forced vibration of nonlinear system with symmetrical piecewise-linear characteristics

International Nuclear Information System (INIS)

Watanabe, Takeshi

1983-01-01

It is fairly difficult to treat exactly the analysis of a vibrating system including some play because it is accompanied by a strong nonlinear phenomenon of collision. The author attempted the theoretical analysis by the exact solution using series solution and the approximate solution, treating the forced vibration of a system having some play as the forced vibration of a continuous system with nonlinear boundary condition or the colliding vibration of a continuum. In this report, the problem of such system with play is treated as a nonlinear system having the symmetrical, piecewise linear characteristics of one degree of freedom. That is, it is considered that at the time of collision due to play, the collided body causes the deformation accompanied by triangular hystersis elastically and plastically, and the spring characteristics of restitution force change piecewise by the collision. The exact solution using series solution and the approximate solution are performed, and the effectiveness of these theoretical solutions is confirmed by comparing with the solution using an analog computer. The relation between the accuracy of two analysis methods and nonlinear parameters is shown by the examples of numerical calculation. (Kako, I.)

Nonlinear evolution equations and solving algebraic systems: the importance of computer algebra

International Nuclear Information System (INIS)

Gerdt, V.P.; Kostov, N.A.

1989-01-01

In the present paper we study the application of computer algebra to solve the nonlinear polynomial systems which arise in investigation of nonlinear evolution equations. We consider several systems which are obtained in classification of integrable nonlinear evolution equations with uniform rank. Other polynomial systems are related with the finding of algebraic curves for finite-gap elliptic potentials of Lame type and generalizations. All systems under consideration are solved using the method based on construction of the Groebner basis for corresponding polynomial ideals. The computations have been carried out using computer algebra systems. 20 refs

Experimental chaos in nonlinear vibration isolation system

International Nuclear Information System (INIS)

Lou Jingjun; Zhu Shijian; He Lin; He Qiwei

2009-01-01

The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.

Effects produced by oscillations applied to nonlinear dynamic systems: a general approach and examples

DEFF Research Database (Denmark)

Blekhman, I. I.; Sorokin, V. S.

2016-01-01

A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics.......g., the requirement for the involved nonlinearities to be weak. The approach is illustrated by several relevant examples from various fields of science, e.g., mechanics, physics, chemistry and biophysics....... equations). The approach is named as the oscillatory strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that capture the averaged effect of oscillations. The method of direct separation of motions appears to be an efficient...

A new extended H∞ filter for discrete nonlinear systems

Institute of Scientific and Technical Information of China (English)

张永安; 周荻; 段广仁

2004-01-01

Nonlinear estimation problem is investigated in this paper. By extension of a linear H∞ estimation with corrector-predictor form to nonlinear cases, a new extended H∞ filter is proposed for time-varying discretetime nonlinear systems. The new filter has a simple observer structure based on a local linearization model, and can be viewed as a general case of the extended Kalman filter (EKF). An example demonstrates that the new filter with a suitable-chosen prescribed H∞ bound performs better than the EKF.

Lotka-Volterra representation of general nonlinear systems.

Science.gov (United States)

Hernández-Bermejo, B; Fairén, V

1997-02-01

In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class possesses a unique representative under the classical quadratic Lotka-Volterra form. We show how other standard modeling forms of biological interest, such as S-systems or mass-action systems, are naturally embedded into the GLV form, which thus provides a formal framework for their comparison and for the establishment of transformation rules. We also focus on the issue of recasting of general nonlinear systems into the GLV format. We present a procedure for doing so and point at possible sources of ambiguity that could make the resulting Lotka-Volterra system dependent on the path followed. We then provide some general theorems that define the operational and algorithmic framework in which this is not the case.

Nonlinear System Identification Using Neural Networks Trained with Natural Gradient Descent

Directory of Open Access Journals (Sweden)

Ibnkahla Mohamed

2003-01-01

Full Text Available We use natural gradient (NG learning neural networks (NNs for modeling and identifying nonlinear systems with memory. The nonlinear system is comprised of a discrete-time linear filter followed by a zero-memory nonlinearity . The NN model is composed of a linear adaptive filter followed by a two-layer memoryless nonlinear NN. A Kalman filter-based technique and a search-and-converge method have been employed for the NG algorithm. It is shown that the NG descent learning significantly outperforms the ordinary gradient descent and the Levenberg-Marquardt (LM procedure in terms of convergence speed and mean squared error (MSE performance.

Distributed Cooperative Control of Nonlinear and Non-identical Multi-agent Systems

DEFF Research Database (Denmark)

Bidram, Ali; Lewis, Frank; Davoudi, Ali

2013-01-01

This paper exploits input-output feedback linearization technique to implement distributed cooperative control of multi-agent systems with nonlinear and non-identical dynamics. Feedback linearization transforms the synchronization problem for a nonlinear and heterogeneous multi-agent system...... for electric power microgrids. The effectiveness of the proposed control is verified by simulating a microgrid test system....

Numerical Solution of Nonlinear Volterra Integral Equations System Using Simpson’s 3/8 Rule

Directory of Open Access Journals (Sweden)

Adem Kılıçman

2012-01-01

Full Text Available The Simpson’s 3/8 rule is used to solve the nonlinear Volterra integral equations system. Using this rule the system is converted to a nonlinear block system and then by solving this nonlinear system we find approximate solution of nonlinear Volterra integral equations system. One of the advantages of the proposed method is its simplicity in application. Further, we investigate the convergence of the proposed method and it is shown that its convergence is of order O(h4. Numerical examples are given to show abilities of the proposed method for solving linear as well as nonlinear systems. Our results show that the proposed method is simple and effective.

Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

KAUST Repository

Abdelkefi, Abdessattar

2013-06-18

In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.

Application of nonlinear systems in nanomechanics and nanofluids analytical methods and applications

CERN Document Server

Ganji, Davood Domairry

2015-01-01

With Application of Nonlinear Systems in Nanomechanics and Nanofluids the reader gains a deep and practice-oriented understanding of nonlinear systems within areas of nanotechnology application as well as the necessary knowledge enabling the handling of such systems. The book helps readers understand relevant methods and techniques for solving nonlinear problems, and is an invaluable reference for researchers, professionals and PhD students interested in research areas and industries where nanofluidics and dynamic nano-mechanical systems are studied or applied. The book is useful in areas suc

Model reduction of systems with localized nonlinearities.

Energy Technology Data Exchange (ETDEWEB)

Segalman, Daniel Joseph

2006-03-01

An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.

Controlling chaos in dynamical systems described by maps

International Nuclear Information System (INIS)

Crispin, Y.; Marduel, C.

1994-01-01

The problem of suppressing chaotic behavior in dynamical systems is treated using a feedback control method with limited control effort. The proposed method is validated on archetypal systems described by maps, i.e. discrete-time difference equations. The method is also applicable to dynamical systems described by flows, i.e. by systems of ordinary differential equations. Results are presented for the one-dimensional logistic map and for a two-dimensional Lotka-Volterra map describing predator-prey population dynamics. It is shown that chaos can be suppressed and the system stabilized about a period-1 fixed point of the maps

Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems

Science.gov (United States)

Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...

A Comparative Study of Neural Networks and Fuzzy Systems in Modeling of a Nonlinear Dynamic System

Directory of Open Access Journals (Sweden)

Metin Demirtas

2011-07-01

Full Text Available The aim of this paper is to compare the neural networks and fuzzy modeling approaches on a nonlinear system. We have taken Permanent Magnet Brushless Direct Current (PMBDC motor data and have generated models using both approaches. The predictive performance of both methods was compared on the data set for model configurations. The paper describes the results of these tests and discusses the effects of changing model parameters on predictive and practical performance. Modeling sensitivity was used to compare for two methods.

On nonlinear control design for autonomous chaotic systems of integer and fractional orders

International Nuclear Information System (INIS)

Ahmad, Wajdi M.; Harb, Ahmad M.

2003-01-01

In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations

Nonlinear systems

National Research Council Canada - National Science Library

Drazin, P. G

1992-01-01

This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...

Vibrational mechanics nonlinear dynamic effects, general approach, applications

CERN Document Server

Blekhman, Iliya I

2000-01-01

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat

Inferring Instantaneous, Multivariate and Nonlinear Sensitivities for the Analysis of Feedback Processes in a Dynamical System: Lorenz Model Case Study

Science.gov (United States)

Aires, Filipe; Rossow, William B.; Hansen, James E. (Technical Monitor)

2001-01-01

A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.

Stabilization of switched nonlinear systems with unstable modes

CERN Document Server

Yang, Hao; Cocquempot, Vincent

2014-01-01

This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant systems in space- and aircraft; traffic control; and heat propagation control of semiconductor power chips. The practical background is emphasized throughout the book; interesting practical examples frequently illustrate the theoretical results with aircraft and spacecraft given particular prominence. Stabilization of Switched Nonlinear Systems with Unstable Modes treats several different subclasses of SNS according to the characteristics of the individual system (time-varying and distributed parameters, for example), the state composition of individual modes and the degree and distribution of instability in its various modes. Achievement and maintenance of stability across the system as a whole is bolstered by trading off between individual modes which may be either stable or unstable, or by exploiting areas of part...

Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

International Nuclear Information System (INIS)

Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.

2007-01-01

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves

Exactly and completely integrable nonlinear dynamical systems

International Nuclear Information System (INIS)

Leznov, A.N.; Savel'ev, M.V.

1987-01-01

The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

DEFF Research Database (Denmark)

True, Hans

1999-01-01

We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed......., and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice...

Predictable nonlinear dynamics: Advances and limitations

International Nuclear Information System (INIS)

Anosov, L.A.; Butkovskii, O.Y.; Kravtsov, Y.A.; Surovyatkina, E.D.

1996-01-01

Methods for reconstruction chaotic dynamical system structure directly from experimental time series are described. Effectiveness of general methods is illustrated with the results of numerical simulation. It is of common interest that from the single time series it is possible to reconstruct a set of interconnected variables. Predictive power of dynamical models, provided by the nonlinear dynamics inverse problem solution, is limited firstly by the noise level in the system under study and is characterized by the horizon of predictability. New physical results are presented, concerning nonstationary and bifurcation nonlinear systems: (1) algorithms for revealing of nonstationarity in random-like chaotic time-series are suggested based on discriminant analysis with nonlinear discriminant function; (2) an opportunity is established to predict the final state in bifurcation system with quickly varying control parameters; (3) hysteresis is founded out in bifurcation system with quickly varying parameters; (4) delayed correlation left-angle noise-prediction error right-angle in chaotic systems is revealed. copyright 1996 American Institute of Physics

ℋ∞ Adaptive observer for nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima

2016-06-23

In this paper, an adaptive observer is proposed for the joint estimation of states and parameters of a fractional nonlinear system with external perturbations. The convergence of the proposed observer is derived in terms of linear matrix inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü\\'s systems. © 2016 John Wiley & Sons, Ltd.

Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit

International Nuclear Information System (INIS)

Wang Jinzhi; Duan Zhisheng; Huang Lin

2006-01-01

In this Letter a new method of chaos control for Chua's circuit and the modified canonical Chua's electrical circuit is proposed by using the results of dichotomy in nonlinear systems. A linear feedback control based on linear matrix inequality (LMI) is given such that chaos oscillation or hyperchaos phenomenon of circuit systems injected control signal disappear. Numerical simulations are presented to illustrate the efficiency of the proposed method

Fuzzy Control Model and Simulation for Nonlinear Supply Chain System with Lead Times

Directory of Open Access Journals (Sweden)

Songtao Zhang

2017-01-01

Full Text Available A new fuzzy robust control strategy for the nonlinear supply chain system in the presence of lead times is proposed. Based on Takagi-Sugeno fuzzy control system, the fuzzy control model of the nonlinear supply chain system with lead times is constructed. Additionally, we design a fuzzy robust H∞ control strategy taking the definition of maximal overlapped-rules group into consideration to restrain the impacts such as those caused by lead times, switching actions among submodels, and customers’ stochastic demands. This control strategy can not only guarantee that the nonlinear supply chain system is robustly asymptotically stable but also realize soft switching among subsystems of the nonlinear supply chain to make the less fluctuation of the system variables by introducing the membership function of fuzzy system. The comparisons between the proposed fuzzy robust H∞ control strategy and the robust H∞ control strategy are finally illustrated through numerical simulations on a two-stage nonlinear supply chain with lead times.

Nonlinear MHD-equations: symmetries, solutions and conservation laws

International Nuclear Information System (INIS)

Samokhin, A.V.

1985-01-01

To investigate stability and nonlinear effects in a high-temperature plasma the system of two scalar nonlinear equations is considered. The algebra of classical symmetries of this system and a certain natural part of its conservation laws are described. It is shown that first, with symmetries one can derive invariant (self-similar) solutions, second, acting with symmetry on the known solution the latter can be included into parametric family

Nonlinear response of the quantum Hall system to a strong electromagnetic radiation

International Nuclear Information System (INIS)

Avetissian, H.K.; Mkrtchian, G.F.

2016-01-01

We study nonlinear response of a quantum Hall system in semiconductor-hetero-structures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity have a characteristic Hall plateaus feature. These nonlinear effects remain robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and Faraday rotation angle, which are within the experimental feasibility. - Highlights: • Nonlinear optical response of a quantum Hall system has specific plateaus feature. • This effect remains robust against the significant broadening of Landau levels. • It can be observed via the third harmonic signal and the nonlinear Faraday effect.

Exploring Nonlinearities in Financial Systemic Risk

NARCIS (Netherlands)

Wolski, M.

2013-01-01

We propose a new methodology of assessing the effects of individual institution's risk on the others and on the system as a whole. We build upon the Conditional Value-at-Risk approach, however, we introduce the explicit Granger causal linkages and we account for possible nonlinearities in the

Investigation on the Nonlinear Control System of High-Pressure Common Rail (HPCR) System in a Diesel Engine

Science.gov (United States)

Cai, Le; Mao, Xiaobing; Ma, Zhexuan

2018-02-01

This study first constructed the nonlinear mathematical model of the high-pressure common rail (HPCR) system in the diesel engine. Then, the nonlinear state transformation was performed using the flow’s calculation and the standard state space equation was acquired. Based on sliding-mode variable structure control (SMVSC) theory, a sliding-mode controller for nonlinear systems was designed for achieving the control of common rail pressure and the diesel engine’s rotational speed. Finally, on the simulation platform of MATLAB, the designed nonlinear HPCR system was simulated. The simulation results demonstrate that sliding-mode variable structure control algorithm shows favorable control performances and overcome the shortcomings of traditional PID control in overshoot, parameter adjustment, system precision, adjustment time and ascending time.

Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts

International Nuclear Information System (INIS)

Emans, Joseph; Wiercigroch, Marian; Krivtsov, Anton M.

2005-01-01

The nonlinear analysis of a common beam system was performed, and the method for such, outlined and presented. Nonlinear terms for the governing dynamic equations were extracted and the behaviour of the system was investigated. The analysis was carried out with and without physically realistic parameters, to show the characteristics of the system, and the physically realistic responses. Also, the response as part of a more complex system was considered, in order to investigate the cumulative effects of nonlinearities. Chaos, as well as periodic motion was found readily for the physically unrealistic parameters. In addition, nonlinear behaviour such as co-existence of attractors was found even at modest oscillation levels during investigations with realistic parameters. When considered as part of a more complex system with further nonlinearities, comparisons with linear beam theory show the classical approach to be lacking in accuracy of qualitative predictions, even at weak oscillations

Accelerator-feasible N-body nonlinear integrable system

Directory of Open Access Journals (Sweden)

V. Danilov

2014-12-01

Full Text Available Nonlinear N-body integrable Hamiltonian systems, where N is an arbitrary number, have attracted the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.

Robust Nonlinear Control with Compensation Operator for a Peltier System

Directory of Open Access Journals (Sweden)

Sheng-Jun Wen

2014-01-01

Full Text Available Robust nonlinear control with compensation operator is presented for a Peltier actuated system, where the compensation operator is designed by using a predictive model on heat radiation. For the Peltier system, the heat radiation is related to the fourth power of temperature. So, the heat radiation is affected evidently by the temperature when it is high and temperature difference between the system and environment is large. A new nonlinear model with the heat radiation is set up for the system according to some thermal conduction laws. To ensure robust stability of the nonlinear system, operator based robust right coprime factorization design is considered. Also, a compensation operator based on a predictive model is proposed to cancel effect of the heat radiation, where the predictive model is set up by using radial basis kernel function based SVM (support vector machine method. Finally, simulation results are given to show the effectiveness of the proposed scheme.

Noise level estimation in weakly nonlinear slowly time-varying systems

International Nuclear Information System (INIS)

Aerts, J R M; Dirckx, J J J; Lataire, J; Pintelon, R

2008-01-01

Recently, a method using multisine excitation was proposed for estimating the frequency response, the nonlinear distortions and the disturbing noise of weakly nonlinear time-invariant systems. This method has been demonstrated on the measurement of nonlinear distortions in the vibration of acoustically driven systems such as a latex membrane, which is a good example of a time-invariant system [1]. However, not all systems are perfectly time invariant, e.g. biomechanical systems. This time variation can be misinterpreted as an elevated noise floor, and the classical noise estimation method gives a wrong result. Two improved methods to retrieve the correct noise information from the measurements are presented. Both of them make use of multisine excitations. First, it is demonstrated that the improved methods give the same result as the classical noise estimation method when applied to a time-invariant system (high-quality microphone membrane). Next, it is demonstrated that the new methods clearly give an improved estimate of the noise level on time-varying systems. As an application example results for the vibration response of an eardrum are shown

XXIII International Conference on Nonlinear Dynamics of Electronic Systems

CERN Document Server

Stoop, Ruedi; Stramaglia, Sebastiano

2017-01-01

This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.

Symbolic computation of nonlinear wave interactions on MACSYMA

International Nuclear Information System (INIS)

Bers, A.; Kulp, J.L.; Karney, C.F.F.

1976-01-01

In this paper the use of a large symbolic computation system - MACSYMA - in determining approximate analytic expressions for the nonlinear coupling of waves in an anisotropic plasma is described. MACSYMA was used to implement the solutions of a fluid plasma model nonlinear partial differential equations by perturbation expansions and subsequent iterative analytic computations. By interacting with the details of the symbolic computation, the physical processes responsible for particular nonlinear wave interactions could be uncovered and appropriate approximations introduced so as to simplify the final analytic result. Details of the MACSYMA system and its use are discussed and illustrated. (Auth.)

System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time

DEFF Research Database (Denmark)

Sun, Zhen; Yang, Zhenyu

2011-01-01

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....

Optimal perturbations for nonlinear systems using graph-based optimal transport

Science.gov (United States)

Grover, Piyush; Elamvazhuthi, Karthik

2018-06-01

We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems.

Stability properties of nonlinear dynamical systems and evolutionary stable states

Energy Technology Data Exchange (ETDEWEB)

Gleria, Iram, E-mail: iram@fis.ufal.br [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)

2017-03-18

Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.

Fault prediction for nonlinear stochastic system with incipient faults based on particle filter and nonlinear regression.

Science.gov (United States)

Ding, Bo; Fang, Huajing

2017-05-01

This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

Science.gov (United States)

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

Model checking biological systems described using ambient calculus

DEFF Research Database (Denmark)

Mardare, Radu Iulian; Priami, Corrado; Qualia, Paola

2005-01-01

Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005.......Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005....

Stabilization and regulation of nonlinear systems a robust and adaptive approach

CERN Document Server

Chen, Zhiyong

2015-01-01

The core of this textbook is a systematic and self-contained treatment of the nonlinear stabilization and output regulation problems. Its coverage embraces both fundamental concepts and advanced research outcomes and includes many numerical and practical examples. Several classes of important uncertain nonlinear systems are discussed. The state-of-the art solution presented uses robust and adaptive control design ideas in an integrated approach which demonstrates connections between global stabilization and global output regulation allowing both to be treated as stabilization problems. Stabilization and Regulation of Nonlinear Systems takes advantage of rich new results to give students up-to-date instruction in the central design problems of nonlinear control, problems which are a driving force behind the furtherance of modern control theory and its application. The diversity of systems in which stabilization and output regulation become significant concerns in the mathematical formulation of practical contr...

Nonlinear Waves in Complex Systems

DEFF Research Database (Denmark)

2007-01-01

The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...

Linear time heteronymous damping in nonlinear parametric systems

Czech Academy of Sciences Publication Activity Database

Hortel, Milan; Škuderová, Alena; Houfek, Martin

2016-01-01

Roč. 40, 23-24 (2016), s. 10038-10051 ISSN 0307-904X Institutional support: RVO:61388998 Keywords : nonlinear dynamics of systems * parametric systems * time heteronymous damping * gears Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 2.350, year: 2016

Hofstadter butterflies in nonlinear Harper lattices, and their optical realizations

International Nuclear Information System (INIS)

Manela, Ofer; Segev, Mordechai; Christodoulides, Demetrios N; Kip, Detlef

2010-01-01

The ubiquitous Hofstadter butterfly describes a variety of systems characterized by incommensurable periodicities, ranging from Bloch electrons in magnetic fields and the quantum Hall effect to cold atoms in optical lattices and more. Here, we introduce nonlinearity into the underlying (Harper) model and study the nonlinear spectra and the corresponding extended eigenmodes of nonlinear quasiperiodic systems. We show that the spectra of the nonlinear eigenmodes form deformed versions of the Hofstadter butterfly and demonstrate that the modes can be classified into two families: nonlinear modes that are a 'continuation' of the linear modes of the system and new nonlinear modes that have no counterparts in the linear spectrum. Finally, we propose an optical realization of the linear and nonlinear Harper models in transversely modulated waveguide arrays, where these Hofstadter butterflies can be observed. This work is relevant to a variety of other branches of physics beyond optics, such as disorder-induced localization in ultracold bosonic gases, localization transition processes in disordered lattices, and more.

Hofstadter butterflies in nonlinear Harper lattices, and their optical realizations

Energy Technology Data Exchange (ETDEWEB)

Manela, Ofer; Segev, Mordechai [Department of Physics and Solid State Institute, Technion, Haifa 32000 (Israel); Christodoulides, Demetrios N [College of Optics/CREOL, University of Central Florida, FL 32816-2700 (United States); Kip, Detlef, E-mail: msegev@tx.technion.ac.i [Department of Electrical Engineering, Helmut Schmidt University, 22043 Hamburg (Germany)

2010-05-15

The ubiquitous Hofstadter butterfly describes a variety of systems characterized by incommensurable periodicities, ranging from Bloch electrons in magnetic fields and the quantum Hall effect to cold atoms in optical lattices and more. Here, we introduce nonlinearity into the underlying (Harper) model and study the nonlinear spectra and the corresponding extended eigenmodes of nonlinear quasiperiodic systems. We show that the spectra of the nonlinear eigenmodes form deformed versions of the Hofstadter butterfly and demonstrate that the modes can be classified into two families: nonlinear modes that are a 'continuation' of the linear modes of the system and new nonlinear modes that have no counterparts in the linear spectrum. Finally, we propose an optical realization of the linear and nonlinear Harper models in transversely modulated waveguide arrays, where these Hofstadter butterflies can be observed. This work is relevant to a variety of other branches of physics beyond optics, such as disorder-induced localization in ultracold bosonic gases, localization transition processes in disordered lattices, and more.

Application of nonlinear transformations to automatic flight control

Science.gov (United States)

Meyer, G.; Su, R.; Hunt, L. R.

1984-01-01

The theory of transformations of nonlinear systems to linear ones is applied to the design of an automatic flight controller for the UH-1H helicopter. The helicopter mathematical model is described and it is shown to satisfy the necessary and sufficient conditions for transformability. The mapping is constructed, taking the nonlinear model to canonical form. The performance of the automatic control system in a detailed simulation on the flight computer is summarized.

Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

Science.gov (United States)

Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying

2018-03-01

Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

Exact solutions for a system of nonlinear plasma fluid equations

International Nuclear Information System (INIS)

Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

1991-04-01

A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

Integrability of a system of two nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Zhukhunashvili, V.Z.

1989-01-01

In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants

Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information

Science.gov (United States)

Li, Songting; Xiao, Yanyang; Zhou, Douglas; Cai, David

2018-05-01

The Granger causality (GC) analysis has been extensively applied to infer causal interactions in dynamical systems arising from economy and finance, physics, bioinformatics, neuroscience, social science, and many other fields. In the presence of potential nonlinearity in these systems, the validity of the GC analysis in general is questionable. To illustrate this, here we first construct minimal nonlinear systems and show that the GC analysis fails to infer causal relations in these systems—it gives rise to all types of incorrect causal directions. In contrast, we show that the time-delayed mutual information (TDMI) analysis is able to successfully identify the direction of interactions underlying these nonlinear systems. We then apply both methods to neuroscience data collected from experiments and demonstrate that the TDMI analysis but not the GC analysis can identify the direction of interactions among neuronal signals. Our work exemplifies inference hazards in the GC analysis in nonlinear systems and suggests that the TDMI analysis can be an appropriate tool in such a case.

On Similarity Invariance of Balancing for Nonlinear Systems

NARCIS (Netherlands)

Scherpen, Jacquelien M.A.

1995-01-01

A previously obtained balancing method for nonlinear systems is investigated on similarity in variance by generalization of the observations on the similarity invariance of the linear balanced realization theory. For linear systems it is well known that the Hankel singular values are similarity

Model Updating Nonlinear System Identification Toolbox, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — ZONA Technology (ZONA) proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology that utilizes flight data with...

Symmetry and exact solutions of nonlinear spinor equations

International Nuclear Information System (INIS)

Fushchich, W.I.; Zhdanov, R.Z.

1989-01-01

This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)

Neural networks for feedback feedforward nonlinear control systems.

Science.gov (United States)

Parisini, T; Zoppoli, R

1994-01-01

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

Using non-linear analogue of Nyquist diagrams for analysis of the equation describing the hemodynamics in blood vessels near pathologies

Science.gov (United States)

Cherevko, A. A.; Bord, E. E.; Khe, A. K.; Panarin, V. A.; Orlov, K. J.; Chupakhin, A. P.

2016-06-01

This article considers method of describing the behaviour of hemodynamic parameters near vascular pathologies. We study the influence of arterial aneurysms and arteriovenous malformations on the vascular system. The proposed method involves using generalized model of Van der Pol-Duffing to find out the characteristic behaviour of blood flow parameters. These parameters are blood velocity and pressure in the vessel. The velocity and pressure are obtained during the neurosurgery measurements. It is noted that substituting velocity on the right side of the equation gives good pressure approximation. Thus, the model reproduces clinical data well enough. In regard to the right side of the equation, it means external impact on the system. The harmonic functions with various frequencies and amplitudes are substituted on the right side of the equation to investigate its properties. Besides, variation of the right side parameters provides additional information about pressure. Non-linear analogue of Nyquist diagrams is used to find out how the properties of solution depend on the parameter values. We have analysed 60 cases with aneurysms and 14 cases with arteriovenous malformations. It is shown that the diagrams are divided into classes. Also, the classes are replaced by another one in the definite order with increasing of the right side amplitude.

Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

Directory of Open Access Journals (Sweden)

Ahmed HamdyM

2010-01-01

Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

Modeling of memristor-based chaotic systems using nonlinear Wiener adaptive filters based on backslash operator

International Nuclear Information System (INIS)

Zhao, Yibo; Jiang, Yi; Feng, Jiuchao; Wu, Lifu

2016-01-01

Highlights: • A novel nonlinear Wiener adaptive filters based on the backslash operator are proposed. • The identification approach to the memristor-based chaotic systems using the proposed adaptive filters. • The weight update algorithm and convergence characteristics for the proposed adaptive filters are derived. - Abstract: Memristor-based chaotic systems have complex dynamical behaviors, which are characterized as nonlinear and hysteresis characteristics. Modeling and identification of their nonlinear model is an important premise for analyzing the dynamical behavior of the memristor-based chaotic systems. This paper presents a novel nonlinear Wiener adaptive filtering identification approach to the memristor-based chaotic systems. The linear part of Wiener model consists of the linear transversal adaptive filters, the nonlinear part consists of nonlinear adaptive filters based on the backslash operator for the hysteresis characteristics of the memristor. The weight update algorithms for the linear and nonlinear adaptive filters are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics. Comparing with the adaptive nonlinear polynomial filters, the proposed nonlinear adaptive filters have less identification error.

Synchronization of two different chaotic systems via nonlinear ...

African Journals Online (AJOL)

ADOWIE PERE

ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.

On the power amplifier nonlinearity in MIMO transmit beamforming systems

KAUST Repository

Qi, Jian

2012-03-01

In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT. © 2012 IEEE.

On the power amplifier nonlinearity in MIMO transmit beamforming systems

KAUST Repository

Qi, Jian; Aissa, Sonia

2012-01-01

In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT. © 2012 IEEE.

Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities

Energy Technology Data Exchange (ETDEWEB)

Teixeira, Rafael M.P.; Cardoso, Wesley B., E-mail: wesleybcardoso@gmail.com

2016-08-12

In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schrödinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enables us the possibility of controlling the scattering of solitons as well as the lifetime of bound states. - Highlights: • We study the interaction of Gaussian solitons in a system with log-law nonlinearity. • The model is described by the coupled logarithmic nonlinear Schrödinger equations. • We observe a fractal-scattering phenomenon of the solitons.

Stability properties of a general class of nonlinear dynamical systems

Science.gov (United States)

Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

2001-05-01

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

Stability properties of a general class of nonlinear dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Gleria, I.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: iram@ucb.br; Figueiredo, A. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: annibal@helium.fis.unb.br; Rocha, T.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: marciano@helium.fis.unb.br

2001-05-04

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format. (author)

Nonlinear analysis on power reactor dynamics

International Nuclear Information System (INIS)

Konno, H.; Hayashi, K.

1997-01-01

We have shown that the origin of intermittent oscillation observed in a BWR can be ascribed to the couplings among the spatial modes starting from a non-linear center manifold equation with a delay-time and a spatial diffusion. We can reduce the problem to the stochastic coupled van der Pol oscillators with non-linear coupling term. This non-linear coupling term plays an important role to break the symmetry of the system and the non-linear damping of the system. The phenomenological generalization of van der Pol oscillator coupled by the linear diffusion term is not appropriate for describing the nuclear power reactors. However, one must start from the coupled partial differential equations by taking into account the two energy group neutrons, the thermo-hydraulic equations including two-phase flow. In this case, the diffusion constant must be a complex number as is demonstrated in a previous paper. The results will be reported in the near future. (J.P.N.)

Linearly and nonlinearly bidirectionally coupled synchronization of hyperchaotic systems

International Nuclear Information System (INIS)

Zhou Jin; Lu Junan; Wu Xiaoqun

2007-01-01

To date, there have been many results about unidirectionally coupled synchronization of chaotic systems. However, much less work is reported on bidirectionally-coupled synchronization. In this paper, we investigate the synchronization of two bidirectionally coupled Chen hyperchaotic systems, which are coupled linearly and nonlinearly respectively. Firstly, linearly coupled synchronization of two hyperchaotic Chen systems is investigated, and a theorem on how to choose the coupling coefficients are developed to guarantee the global asymptotical synchronization of two coupled hyperchaotic systems. Analysis shows that the choice of the coupling coefficients relies on the bound of the chaotic system. Secondly, the nonlinearly coupled synchronization is studied; a sufficient condition for the locally asymptotical synchronization is derived, which is independent of the bound of the hyperchaotic system. Finally, numerical simulations are included to verify the effectiveness and feasibility of the developed theorems

Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty

NARCIS (Netherlands)

van der Schaft, Arjan

1995-01-01

The approach to robust stabilization of linear systems using normalized left coprime factorizations with H∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust

Describing function theory as applied to thermal and neutronic problems

International Nuclear Information System (INIS)

Nassersharif, B.

1983-01-01

Describing functions have traditionally been used to obtain the solutions of systems of ordinary differential equations. In this work the describing function concept has been extended to include nonlinear, distributed parameter partial differential equations. A three-stage solution algorithm is presented which can be applied to any nonlinear partial differential equation. Two generalized integral transforms were developed as the T-transform for the time domain and the B-transform for the spatial domain. The thermal diffusion describing function (TDDF) is developed for conduction of heat in solids and a general iterative solution along with convergence criteria is presented. The proposed solution method is used to solve the problem of heat transfer in nuclear fuel rods with annular fuel pellets. As a special instance the solid cylindrical fuel pellet is examined. A computer program is written which uses the describing function concept for computing fuel pin temperatures in the radial direction during reactor transients. The second problem investigated was the neutron diffusion equation which is intrinsically different from the first case. Although, for most situations, it can be treated as a linear differential equation, the describing function method is still applicable. A describing function solution is derived for two possible cases: constant diffusion coefficient and variable diffusion coefficient. Two classes of describing functions are defined for each case which portray the leakage and absorption phenomena. For the specific case of a slab reactor criticality problem the comparison between analytical and describing function solutions revealed an excellent agreement

Nonlinear signal processing using neural networks: Prediction and system modelling

Energy Technology Data Exchange (ETDEWEB)

Lapedes, A.; Farber, R.

1987-06-01

The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.

Computational Models for Nonlinear Aeroelastic Systems, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate new and efficient computational methods of modeling nonlinear aeroelastic systems. The...

The nonlinear response of the complex structural system in nuclear reactors using dynamic substructure method

International Nuclear Information System (INIS)

Zheng, Z.C.; Xie, G.; Du, Q.H.

1987-01-01

Because of the existence of nonlinear characteristics in practical engineering structures, such as large steam turbine-foundation system and offshore platform, it is necessary to predict nonlinear dynamic responses for these very large and complex structural systems subjected extreme load. Due to the limited storage and high executing cost of computers, there are still some difficulties in the analysis for such systems although the traditional finite element methods provide basic available methods to the problems. The dynamic substructure methods, which were developed as a branch of general structural dynamics in the past more than 20 years and have been widely used from aircraft, space vehicles to other mechanical and civil engineering structures, present a powerful method to the analysis of very large structural systems. The key to success is due to the considerable reduction in the number of degrees of freedom while not changing the physical essence of the problems investigated. The dynamic substructure method has been extended to nonlinear system and applicated to the analysis of nonlinear dynamic response of an offshore platform by Z.C. Zheng, et al. (1983, 1985a, b, c). In this paper, the method is presented to analyze dynamic responses of the systems contained intrinsic nonlinearities and with nonlinear attachments and nonlinear supports of nuclear structural systems. The efficiency of the method becomes more clear for nonlinear dynamic problems due to the adoption of iterating processes. For simplicity, the analysis procedure is demonstrated briefly. The generalized substructure method of nonlinear systems is similar to linear systems, only the nonlinear terms are treated as pseudo-forces. Interface coordinates are classified into two categories, the connecting interface coordinates which connect with each other directly in the global system and the linking interface coordinates which link to each other through attachments. (orig./GL)

Generation of Caustics and Rogue Waves from Nonlinear Instability.

Science.gov (United States)

Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W

2017-11-17

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

Complex dynamics and morphogenesis an introduction to nonlinear science

CERN Document Server

Misbah, Chaouqi

2017-01-01

This book offers an introduction to the physics of nonlinear phenomena through two complementary approaches: bifurcation theory and catastrophe theory. Readers will be gradually introduced to the language and formalisms of nonlinear sciences, which constitute the framework to describe complex systems. The difficulty with complex systems is that their evolution cannot be fully predicted because of the interdependence and interactions between their different components. Starting with simple examples and working toward an increasing level of universalization, the work explores diverse scenarios of bifurcations and elementary catastrophes which characterize the qualitative behavior of nonlinear systems. The study of temporal evolution is undertaken using the equations that characterize stationary or oscillatory solutions, while spatial analysis introduces the fascinating problem of morphogenesis. Accessible to undergraduate university students in any discipline concerned with nonlinear phenomena (physics, mathema...

Develop advanced nonlinear signal analysis topographical mapping system

Science.gov (United States)

1994-01-01

The Space Shuttle Main Engine (SSME) has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature, pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system; (2) develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amount of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. High compression ratio can be achieved to allow minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities; and (3) integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of

Introduction to nonlinear acoustics

Science.gov (United States)

Bjørnø, Leif

2010-01-01

A brief review of the basic principles of fluid mechanics needed for development of linear and nonlinear ultrasonic concepts will be given. The fundamental equations of nonlinear ultrasonics will be derived and their physical properties explained. It will be shown how an originally monochromatic finite-amplitude ultrasonic wave, due to nonlinear effects, will distort during its propagation in time and space to form higher harmonics to its fundamental frequency. The concepts of shock formation will be presented. The material nonlinearity, described by the nonlinearity parameter B/A of the material, and the convective nonlinearity, described by the ultrasonic Mach Number, will be explained. Two procedures for determination of B/A will briefly be described and some B/A-values characterizing biological materials will be presented. Shock formation, described by use of the Goldberg Number,and Ultrasonic Saturation will be discussed.. An introduction to focused ultrasonic fields will be given and it will be shown how the ultrasonic intensity will vary axially and laterally in and near the focal region and how the field parameters of interest to biomedical applications may be described by use of the KZK-Model. Finally, an introduction will be given to the parametric acoustic array formed by mixing and interaction of two monochromatic, finite-amplitude ultrasonic waves in a liquid and the potentials of this mixing process in biomedical ultrasound will briefly be mentioned.

Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.

Science.gov (United States)

Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang

2017-06-12

Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite

An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2016-06-01

Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.

Nonlinear Dynamics of Controlled Synchronizations of Manipulator System

Directory of Open Access Journals (Sweden)

Qingkai Han

2014-01-01

Full Text Available The nonlinear dynamics of the manipulator system which is controlled to achieve the synchronization motions is investigated in the paper. Firstly, the control strategies and modeling approaches of the manipulator system are given, in which the synchronization goal is defined by both synchronization errors and its derivatives. The synchronization controllers applied on the manipulator system include neuron synchronization controller, improved OPCL synchronization controller, and MRAC-PD synchronization controller. Then, an improved adaptive synchronized control strategy is proposed in order to estimate online the unknown structure parameters and state variables of the manipulator system and to realize the needed synchronous compensation. Furthermore, a robust adaptive synchronization controller is also researched to guarantee the dynamic stability of the system. Finally, the stability of motion synchronizations of the manipulator system possessing nonlinear component is discussed, together with the effect of control parameters and joint friction and others. Some typical motions such as motion bifurcations and the loss of synchronization of it are obtained and illustrated as periodic, multiperiodic, and/or chaotic motion patterns.

Frequency domain performance analysis of nonlinearly controlled motion systems

NARCIS (Netherlands)

Pavlov, A.V.; Wouw, van de N.; Pogromski, A.Y.; Heertjes, M.F.; Nijmeijer, H.

2007-01-01

At the heart of the performance analysis of linear motion control systems lie essential frequency domain characteristics such as sensitivity and complementary sensitivity functions. For a class of nonlinear motion control systems called convergent systems, generalized versions of these sensitivity

Linearization and Control of Series-Series Compensated Inductive Power Transfer System Based on Extended Describing Function Concept

Directory of Open Access Journals (Sweden)

Kunwar Aditya

2016-11-01

Full Text Available The extended describing function (EDF is a well-known method for modelling resonant converters due to its high accuracy. However, it requires complex mathematical formulation effort. This paper presents a simplified non-linear mathematical model of series-series (SS compensated inductive power transfer (IPT system, considering zero-voltage switching in the inverter. This simplified mathematical model permits the user to derive the small-signal model using the EDF method, with less computational effort, while maintaining the accuracy of an actual physical model. The derived model has been verified using a frequency sweep method in PLECS. The small-signal model has been used to design the voltage loop controller for a SS compensated IPT system. The designed controller was implemented on a 3.6 kW experimental setup, to test its robustness.

Computational Models for Nonlinear Aeroelastic Systems, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate a new and efficient computational method of modeling nonlinear aeroelastic systems. The...

Symmetries in Hall-like systems: microwave and nonlinear transport effects

International Nuclear Information System (INIS)

Torres, Manuel; Kunold, Alejandro

2008-01-01

In this work, we present a model to describe the nonlinear response to a dc electrical current of a two-dimensional electron system subjected to magnetic and microwave fields. Considering the separation of the electron coordinates into the non-commuting relative and guiding center coordinates, we obtain a unitary transformation that exactly solves the time-dependent Schroedinger equation in the presence of arbitrarily strong electric, magnetic and microwave fields. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. We discuss results related to the recently discovered zero-resistance states and to the microwave-induced resistivity oscillations and the Hall-induced resistivity oscillations

Control of self-organizing nonlinear systems

CERN Document Server

Klapp, Sabine; Hövel, Philipp

2016-01-01

The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.

Digital nonlinearity compensation in high-capacity optical communication systems considering signal spectral broadening effect.

Science.gov (United States)

Xu, Tianhua; Karanov, Boris; Shevchenko, Nikita A; Lavery, Domaniç; Liga, Gabriele; Killey, Robert I; Bayvel, Polina

2017-10-11

Nyquist-spaced transmission and digital signal processing have proved effective in maximising the spectral efficiency and reach of optical communication systems. In these systems, Kerr nonlinearity determines the performance limits, and leads to spectral broadening of the signals propagating in the fibre. Although digital nonlinearity compensation was validated to be promising for mitigating Kerr nonlinearities, the impact of spectral broadening on nonlinearity compensation has never been quantified. In this paper, the performance of multi-channel digital back-propagation (MC-DBP) for compensating fibre nonlinearities in Nyquist-spaced optical communication systems is investigated, when the effect of signal spectral broadening is considered. It is found that accounting for the spectral broadening effect is crucial for achieving the best performance of DBP in both single-channel and multi-channel communication systems, independent of modulation formats used. For multi-channel systems, the degradation of DBP performance due to neglecting the spectral broadening effect in the compensation is more significant for outer channels. Our work also quantified the minimum bandwidths of optical receivers and signal processing devices to ensure the optimal compensation of deterministic nonlinear distortions.

Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

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.

Periodic Solutions for Highly Nonlinear Oscillation Systems

DEFF Research Database (Denmark)

Ghadimi, M; Barari, Amin; Kaliji, H.D

2012-01-01

In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...

Study on Nonlinear Vibration Analysis of Gear System with Random Parameters

Science.gov (United States)

Tong, Cao; Liu, Xiaoyuan; Fan, Li

2018-03-01

In order to study the dynamic characteristics of gear nonlinear vibration system and the influence of random parameters, firstly, a nonlinear stochastic vibration analysis model of gear 3-DOF is established based on Newton’s Law. And the random response of gear vibration is simulated by stepwise integration method. Secondly, the influence of stochastic parameters such as meshing damping, tooth side gap and excitation frequency on the dynamic response of gear nonlinear system is analyzed by using the stability analysis method such as bifurcation diagram and Lyapunov exponent method. The analysis shows that the stochastic process can not be neglected, which can cause the random bifurcation and chaos of the system response. This study will provide important reference value for vibration engineering designers.

PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

Science.gov (United States)

Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai

2017-09-01

In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

Recent results on nonlinear delay control systems in honor of Miroslav Krstic

CERN Document Server

Pepe, Pierdomenico; Mazenc, Frederic; Karafyllis, Iasson

2016-01-01

This volume collects recent advances in nonlinear delay systems, with an emphasis on constructive generalized Lyapunov and predictive approaches that certify stability properties. The book is written by experts in the field and includes two chapters by Miroslav Krstic, to whom this volume is dedicated. This volume is suitable for all researchers in mathematics and engineering who deal with nonlinear delay control problems and students who would like to understand the current state of the art in the control of nonlinear delay systems.

Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

International Nuclear Information System (INIS)

Liu Chunliang; Xie Xi; Chen Yinbao

1991-01-01

The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

RCLED Optimization and Nonlinearity Compensation in a Polymer Optical Fiber DMT System

Directory of Open Access Journals (Sweden)

Pu Miao

2016-09-01

Full Text Available In polymer optical fiber (POF systems, the nonlinear transfer function of the resonant cavity light emitting diode (RCLED drastically degrades the communication performance. After investigating the characteristics of the RCLED nonlinear behavior, an improved digital look-up-table (LUT pre-distorter, based on an adaptive iterative algorithm, is proposed. Additionally, the system parameters, including the bias current, the average electrical power, the LUT size and the step factor are also jointly optimized to achieve a trade-off between the system linearity, reliability and the computational complexity. With the proposed methodology, both the operating point and efficiency of RCLED are enhanced. Moreover, in the practical 50 m POF communication system with the discrete multi-tone (DMT modulation, the bit error rate performance is improved by over 12 dB when RCLED is operating in the nonlinear region. Therefore, the proposed pre-distorter can both resist the nonlinearity and improve the operating point of RCLED.

A Unique Method to Describe the Bonding Strength in a Bonded Solid–Solid Interface by Contact Acoustic Nonlinearity

International Nuclear Information System (INIS)

Jian-Jun, Chen; De, Zhang; Yi-Wei, Mao; Jian-Chun, Cheng

2009-01-01

We present a unique method to describe the bonding strength at a bonded solid–solid interface in a multilayered composite material by contact acoustic nonlinearity (CAN) parameter. A CAN model on the bonded solid–solid interface is depicted. It can be seen from the model that CAN parameter is very sensitive to the bonding strength at the interface. When an incident focusing acoustic longitudinal wave scans the interface in two dimensions, the transmitted wave can be used to extract CAN parameter. The contour of the bonding strength for a sample is obtained by CAN parameter. The results show that the region with weak bonding strength can be easily distinguished from the contour

Model Updating Nonlinear System Identification Toolbox, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — ZONA Technology proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology by adopting the flight data with state-of-the-art...

Nonlinear dynamical systems for theory and research in ergonomics.

Science.gov (United States)

Guastello, Stephen J

2017-02-01

Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.

Chaos synchronization of a new chaotic system via nonlinear control

International Nuclear Information System (INIS)

Zhang Qunjiao; Lu Junan

2008-01-01

This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method

Non-linear model predictive supervisory controller for building, air handling unit with recuperator and refrigeration system with heat waste recovery

DEFF Research Database (Denmark)

Minko, Tomasz; Wisniewski, Rafal; Bendtsen, Jan Dimon

2016-01-01

. The retrieved heat excess can be stored in the water tank. For this purpose the charging and the discharging water loops has been designed. We present the non-linear model of the above described system and a non-linear model predictive supervisory controller that according to the received price signal......, occupancy information and ambient temperature minimizes the operation cost of the whole system and distributes set points to local controllers of supermarkets subsystems. We find that when reliable information about the high price period is available, it is profitable to use the refrigeration system...... to generate heat during the low price period, store it and use it to substitute the conventional heater during the high price period....

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

Science.gov (United States)

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Field guide to nonlinear optics

CERN Document Server

Powers, Peter E

2013-01-01

Optomechanics is a field of mechanics that addresses the specific design challenges associated with optical systems. This [i]Field Guide [/i]describes how to mount optical components, as well as how to analyze a given design. It is intended for practicing optical and mechanical engineers whose work requires knowledge in both optics and mechanics. This Field Guide is designed for those looking for a condensed and concise source of key concepts, equations, and techniques for nonlinear optics. Topics covered include technologically important effects, recent developments in nonlinear optics

Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations

International Nuclear Information System (INIS)

Qu Changzheng; Kang Jing

2008-01-01

In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Those systems have physical applications in soil science, mathematical biology, and invariant curve flows in R 3 . Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.

Nonlinear dynamics non-integrable systems and chaotic dynamics

CERN Document Server

Borisov, Alexander

2017-01-01

This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.

Implementation of neural network based non-linear predictive

DEFF Research Database (Denmark)

Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole

1998-01-01

The paper describes a control method for non-linear systems based on generalized predictive control. Generalized predictive control (GPC) was developed to control linear systems including open loop unstable and non-minimum phase systems, but has also been proposed extended for the control of non......-linear systems. GPC is model-based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis on an efficient Quasi......-Newton optimization algorithm. The performance is demonstrated on a pneumatic servo system....

ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

KAUST Repository

Ndoye, Ibrahima; Voos, Holger; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed

2014-01-01

In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown

Online prediction and control in nonlinear stochastic systems

DEFF Research Database (Denmark)

Nielsen, Torben Skov

2002-01-01

speed and the relationship between (primarily) wind speed and wind power (the power curve). In paper G the model parameters are estimated using a RLS algorithm and any systematic time-variation of the model parameters is disregarded. Two di erent parameterizations of the power curve is considered...... are estimated using the algorithm proposed in paper C. The power curve and the diurnal variation of wind speed is estimated separately using the local polynomial regression procedure described in paper A . In paper J the parameters of the prediction model is assumed to be smooth functions of wind direction (and......The present thesis consists of a summary report and ten research papers. The subject of the thesis is on-line prediction and control of non-linear and non-stationary systems based on stochastic modelling. The thesis consists of three parts where the rst part deals with on-line estimation in linear...

Renormgroup symmetries in problems of nonlinear geometrical optics

International Nuclear Information System (INIS)

Kovalev, V.F.

1996-01-01

Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)

Workshop on Nonlinear Phenomena in Complex Systems

CERN Document Server

1989-01-01

This book contains a thorough treatment of neural networks, cellular-automata and synergetics, in an attempt to provide three different approaches to nonlinear phenomena in complex systems. These topics are of major interest to physicists active in the fields of statistical mechanics and dynamical systems. They have been developed with a high degree of sophistication and include the refinements necessary to work with the complexity of real systems as well as the more recent research developments in these areas.

Self-sustained solitons in systems with nonlinear damping

International Nuclear Information System (INIS)

Gonzalez, J.A.

1993-05-01

The existence and stability of kinks in systems with nonlinear damping are investigated. We discuss the mechanism of a bifurcation after which the kink becomes a non-stationary state. (author). 9 refs

Nonlinear system identification of smart structures under high impact loads

International Nuclear Information System (INIS)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-01-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure–MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure–MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes. (paper)

Nonlinear system identification of smart structures under high impact loads

Science.gov (United States)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-05-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.

Integrable systems with quadratic nonlinearity in Fourier space

International Nuclear Information System (INIS)

Marikhin, V.G.

2003-01-01

The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed

Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

Science.gov (United States)

Killingsworth, W. R., Jr.

1972-01-01

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Controllable behaviours of rogue wave triplets in the nonautonomous nonlinear and dispersive system

International Nuclear Information System (INIS)

Dai Chaoqing; Tian Qing; Zhu Shiqun

2012-01-01

A similarity transformation connecting the variable coefficient nonlinear Schrödinger equation with the standard nonlinear Schrödinger equation is constructed. The self-similar rogue wave triplet solutions (rational solutions) are analytically obtained for the nonautonomous nonlinear and dispersive system. The controllable behaviours of rogue wave triplets in two typical soliton management systems are discussed. In the exponential dispersion decreasing fibre, three kinds of rogue wave triplets with controllable behaviours are analysed. In the periodic distributed system, the rogue wave triplets recur periodically in the form of a cluster. (paper)

A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

Directory of Open Access Journals (Sweden)

Mountassir Hamdi Cherif

2017-11-01

Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions

International Nuclear Information System (INIS)

Maccari, A.

1997-01-01

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio endash temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a open-quotes universalclose quotes character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. copyright 1997 American Institute of Physics

Development of nonlinear dynamic analysis program for nuclear piping systems

International Nuclear Information System (INIS)

Kamichika, Ryoichi; Izawa, Masahiro; Yamadera, Masao

1980-01-01

In the design for nuclear power piping, pipe-whip protection shall be considered in order to keep the function of safety related system even when postulated piping rupture occurs. This guideline was shown in U.S. Regulatory Guide 1.46 for the first time and has been applied in Japanese nuclear power plants. In order to analyze the dynamic behavior followed by pipe rupture, nonlinear analysis is required for the piping system including restraints which play the role of an energy absorber. REAPPS (Rupture Effective Analysis of Piping Systems) has been developed for this purpose. This program can be applied to general piping systems having branches etc. Pre- and post- processors are prepared in this program in order to easily input the data for the piping engineer and show the results optically by use of a graphic display respectively. The piping designer can easily solve many problems in his daily work by use of this program. This paper describes about the theoretical background and functions of this program and shows some examples. (author)

Turbulent Evolution of a Plasma Described Through Classical Mechanics Only

International Nuclear Information System (INIS)

Escande, D.F.; Elskens, Y.

2003-01-01

For the first time an old dream of the XIXth century comes true: the non trivial evolution of a macroscopic many-body system is described through classical mechanics only. This is done for the relaxation of a warm electron beam in a plasma, which results in the generation of Langmuir turbulence and in the formation of a plateau in the velocity distribution function of the electrons. Our derivation starts from the hamiltonian describing the one-dimensional N-body system corresponding to the beam and plasma bulk electrons in electrostatic interaction. For such a system, the dynamics can be reduced to the resonant interaction of M Langmuir waves with N'( > 1 Langmuir waves with N' >> 1 beam particles. This yields the proof of the classical quasilinear equations describing the coupled evolution of the wave spectrum and of the beam velocity distribution function in the strongly nonlinear regime where their validity is the matter of a longstanding controversy

Information theory and stochastics for multiscale nonlinear systems

CERN Document Server

Majda, Andrew J; Grote, Marcus J

2005-01-01

This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...

Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

Science.gov (United States)

Silva, Walter A.

1993-01-01

A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

Adaptive estimation for control of uncertain nonlinear systems with applications to target tracking

Science.gov (United States)

Madyastha, Venkatesh Kattigari

2005-08-01

Design of nonlinear observers has received considerable attention since the early development of methods for linear state estimation. The most popular approach is the extended Kalman filter (EKF), that goes through significant degradation in the presence of nonlinearities, particularly if unmodeled dynamics are coupled to the process and the measurement. For uncertain nonlinear systems, adaptive observers have been introduced to estimate the unknown state variables where no priori information about the unknown parameters is available. While establishing global results, these approaches are applicable only to systems transformable to output feedback form. Over the recent years, neural network (NN) based identification and estimation schemes have been proposed that relax the assumptions on the system at the price of sacrificing on the global nature of the results. However, most of the NN based adaptive observer approaches in the literature require knowledge of the full dimension of the system, therefore may not be suitable for systems with unmodeled dynamics. We first propose a novel approach to nonlinear state estimation from the perspective of augmenting a linear time invariant observer with an adaptive element. The class of nonlinear systems treated here are finite but of otherwise unknown dimension. The objective is to improve the performance of the linear observer when applied to a nonlinear system. The approach relies on the ability of the NNs to approximate the unknown dynamics from finite time histories of available measurements. Next we investigate nonlinear state estimation from the perspective of adaptively augmenting an existing time varying observer, such as an EKF. EKFs find their applications mostly in target tracking problems. The proposed approaches are robust to unmodeled dynamics, including unmodeled disturbances. Lastly, we consider the problem of adaptive estimation in the presence of feedback control for a class of uncertain nonlinear systems

Study on Nonlinear Vibration and Crack Fault of Rotor-bearing-seal Coupling System

Directory of Open Access Journals (Sweden)

Yuegang LUO

2014-02-01

Full Text Available The nonlinear dynamic model of rotor-bearing-seal system with crack in shaft is set up based on the coupling model of nonlinear oil-film force and Muszyska’s nonlinear seal fluid force. The dynamic vibration characteristics of the rotor-bearing-seal system and the effects of physical and structural parameters of labyrinth seal and crack fault on movement character of the rotor were analyzed. The increases of seal length, seal pressure differential, seal radius and axial velocity are in favor of the stability of the system, and it of seal gap and crack depth are not in favor of the stability of the system.

Reduced Complexity Volterra Models for Nonlinear System Identification

Directory of Open Access Journals (Sweden)

Hacıoğlu Rıfat

2001-01-01

Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.

Computer Simulation of Hydraulic Systems with Typical Nonlinear Characteristics

Directory of Open Access Journals (Sweden)

D. N. Popov

2017-01-01

Full Text Available The task was to synthesise an adjustable hydraulic system structure, the mathematical model of which takes into account its inherent nonlinearity. Its solution suggests using a successive computer simulations starting with a structure of the linearized stable hydraulic system, which is then complicated by including the essentially non-linear elements. The hydraulic system thus obtained may be unable to meet the Lyapunov stability criterion and be unstable. This can be eliminated through correcting elements. Control of correction results is provided according to the form of transition processes due to stepwise variation of the control signal.Computer simulation of a throttle-controlled electrohydraulic servo drive with the rotary output element illustrates the proposed method application. A constant pressure power source provides fluid feed for the drive under pressure.For drive simulation the following models were involved: the linear model, the model taking into consideration a non-linearity of the flow-dynamic characteristics of a spool-type valve, and the non-linear models that take into account the dry friction in the spool-type valve, the backlash in the steering angle sensor of the motor shaft.The paper shows possibility of damping oscillation caused by variable hydrodynamic forces through introducing a correction device.The list of references attached contains 16 sources, which were used to justify and explain certain factors of the automatic control theory and the fluid mechanics of unsteady flows.The article presents 6 block-diagrams of the electrohydraulic servo drive and their appropriate transition processes, which have been studied.

Convergence criteria for systems of nonlinear elliptic partial differential equations

International Nuclear Information System (INIS)

Sharma, R.K.

1986-01-01

This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

On nonequilibrium many-body systems III: nonlinear transport theory

International Nuclear Information System (INIS)

Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.

1986-01-01

A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt

Explicit analytical solution of the nonlinear Vlasov Poisson system

International Nuclear Information System (INIS)

Skarka, V.; Mahajan, S.M.; Fijalkow, E.

1993-10-01

In order to describe the time evolution of an inhomogeneous collisionless plasma the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series, one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a better insight into the problem and it has the advantage to be simpler, and also accessible in some range of parameters where it is difficult to find numerical solutions. (author). 27 refs, 12 figs

Cross-talk dynamics of optical solitons in a broadband Kerr nonlinear system with weak cubic loss

International Nuclear Information System (INIS)

Peleg, Avner; Nguyen, Quan M.; Chung, Yeojin

2010-01-01

We study the dynamics of fast soliton collisions in a Kerr nonlinear optical waveguide with weak cubic loss. We obtain analytic expressions for the amplitude and frequency shifts in a single two-soliton collision and show that the impact of a fast three-soliton collision is given by the sum of the two-soliton interactions. Our analytic predictions are confirmed by numerical simulations with the perturbed nonlinear Schroedinger (NLS) equation. Furthermore, we show that the deterministic collision-induced dynamics of soliton amplitudes in a broadband waveguide system with N frequency channels is described by a Lotka-Volterra model for N competing species. For a two-channel system we find that stable transmission with equal prescribed amplitudes can be achieved by a proper choice of linear amplifier gain. The predictions of the Lotka-Volterra model are confirmed by numerical solution of a perturbed coupled-NLS model.

Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system

Science.gov (United States)

Avitabile, D.; Desroches, M.; Knobloch, E.; Krupa, M.

2017-11-01

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of solutions describing the possible location of stationary fronts are identified, whose origin is traced to the onset of convective and absolute instability when the system is unbounded. The former are present only for non-zero upstream boundary conditions and provide a quantitative understanding of noise-sustained structures in systems of this type. The latter correspond to the onset of a global mode and are present even with zero upstream boundary conditions. The role of canard trajectories in the nonlinear transition between these states is clarified and the stability properties of the resulting spatial structures are determined. Front location in the convective regime is highly sensitive to the upstream boundary condition, and its dependence on this boundary condition is studied using a combination of numerical continuation and Monte Carlo simulations of the partial differential equation. Statistical properties of the system subjected to random or stochastic boundary conditions at the inlet are interpreted using the deterministic slow-fast spatial dynamical system.

On-line Multiple-model Based Adaptive Control Reconfiguration for a Class of Non-linear Control Systems

DEFF Research Database (Denmark)

Yang, Z.; Izadi-Zamanabadi, R.; Blanke, Mogens

2000-01-01

of LTI models are employed to approximate the faulty, reconfigured and nominal nonlinear systems respectively with respect to the on-line information of the operating system, and a set of compensating modules are proposed and designed so as to make the local LTI model approximating to the reconfigured...... nonlinear system match the corresponding LTI model approximating to the nominal nonlinear system in some optimal sense. The compensating modules are designed by the Pseudo-Inverse Method based on the local LTI models for the nominal and faulty nonlinear systems. Moreover, these modules should update...... corresponding to the updating of local LTI models, which validations are determined by the model approximation errors and the optimal index of local design. The test on a nonlinear ship propulsion system shows the promising potential of this method for system reconfiguration...

Nonlinear stochastic systems with network-induced phenomena recursive filtering and sliding-mode design

CERN Document Server

Hu, Jun; Gao, Huijun

2014-01-01

This monograph introduces methods for handling filtering and control problems in nonlinear stochastic systems arising from network-induced phenomena consequent on limited communication capacity. Such phenomena include communication delay, packet dropout, signal quantization or saturation, randomly occurring nonlinearities and randomly occurring uncertainties.The text is self-contained, beginning with an introduction to nonlinear stochastic systems, network-induced phenomena and filtering and control, moving through a collection of the latest research results which focuses on the three aspects

Forward-backward equations for nonlinear propagation in axially invariant optical systems

International Nuclear Information System (INIS)

Ferrando, Albert; Zacares, Mario; Fernandez de Cordoba, Pedro; Binosi, Daniele; Montero, Alvaro

2005-01-01

We present a general framework to deal with forward and backward components of the electromagnetic field in axially invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components, explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dirac-like form, out of which conserved quantities can be calculated in an elegant manner. Finally, these equations inherently incorporate spatiotemporal couplings, so that they can be easily particularized to deal with purely temporal or purely spatial effects. Nonlinear forward pulse propagation and nonparaxial evolution of spatial structures are analyzed as examples

Rigorous Verification for the Solution of Nonlinear Interval System ...

African Journals Online (AJOL)

We survey a general method for solving nonlinear interval systems of equations. In particular, we paid special attention to the computational aspects of linear interval systems since the bulk of computations are done during the stage of computing outer estimation of the including linear interval systems. The height of our ...

Perspectives of nonlinear dynamics

International Nuclear Information System (INIS)

Jackson, E.A.

1985-03-01

Four lectures were given weekly in October and November, 1984, and some of the ideas presented here will be of use in the future. First, a brief survey of the historical development of nonlinear dynamics since about 1890 was given, and then, a few topics were discussed in detail. The objective was to introduce some of many concepts and methods which are presently used for describing nonlinear dynamics. The symbiotic relationship between sciences of all types and mathematics, two main categories of the models describing nature, the method for describing the dynamics of a system, the idea of control parameters and topological dimension, the asymptotic properties of dynamics, abstract dynamics, the concept of embedding, singular perturbation theory, strange attractor, Fermi-Pasta-Ulam phenomena, an example of computer heuristics, the idea of elementary catastrophe theory and so on were explained. The logistic map is the simplest introduction to complex dynamics. The complicated dynamics is referred to as strange attractors. Two-dimensional maps are the highest dimensional maps commonly studied. These were discussed in detail. (Kako, I.)

Sliding mode control for uncertain unified chaotic systems with input nonlinearity

International Nuclear Information System (INIS)

Chiang, T.-Y.; Hung, M.-L.; Yan, J.-J.; Yang, Y.-S.; Chang, J.-F.

2007-01-01

This paper investigates the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Using the sliding mode control technique, a robust control law is established which stabilizes the uncertain unified chaotic systems even when the nonlinearity in the actuators is present. A novel adaptive switching surface is introduced to simplify the task of assigning the stability of the closed-loop system in the sliding mode motion. An illustrative example is given to demonstrate the effectiveness of the proposed sliding mode control design

Dynamic behaviors for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a non-Kerr medium

Science.gov (United States)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Liu, De-Yin

2017-04-01

Effects of quantic nonlinearity on the propagation of the ultrashort optical pulses in a non-Kerr medium, like an optical fiber, can be described by a perturbed nonlinear Schrödinger equation with the power law nonlinearity, which is studied in this paper from a planar-dynamic-system view point. We obtain the equivalent two-dimensional planar dynamic system of such an equation, for which, according to the bifurcation theory and qualitative theory, phase portraits are given. Through the analysis of those phase portraits, we present the relations among the Hamiltonian, orbits of the dynamic system and types of the analytic solutions. Analytic expressions of the periodic-wave solutions, kink- and bell-shaped solitary-wave solutions are derived, and we find that the periodic-wave solutions can be reduced to the kink- and bell-shaped solitary-wave solutions.

Nonlinear observer based phase synchronization of chaotic systems

International Nuclear Information System (INIS)

Meng Juan; Wang Xingyuan

2007-01-01

This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme

Recent advance in nonlinear aeroelastic analysis and control of the aircraft

Directory of Open Access Journals (Sweden)

Xiang Jinwu

2014-02-01

Full Text Available A review on the recent advance in nonlinear aeroelasticity of the aircraft is presented in this paper. The nonlinear aeroelastic problems are divided into three types based on different research objects, namely the two dimensional airfoil, the wing, and the full aircraft. Different nonlinearities encountered in aeroelastic systems are discussed firstly, where the emphases is placed on new nonlinear model to describe tested nonlinear relationship. Research techniques, especially new theoretical methods and aeroelastic flutter control methods are investigated in detail. The route to chaos and the cause of chaotic motion of two-dimensional aeroelastic system are summarized. Various structural modeling methods for the high-aspect-ratio wing with geometric nonlinearity are discussed. Accordingly, aerodynamic modeling approaches have been developed for the aeroelastic modeling of nonlinear high-aspect-ratio wings. Nonlinear aeroelasticity about high-altitude long-endurance (HALE and fight aircrafts are studied separately. Finally, conclusions and the challenges of the development in nonlinear aeroelasticity are concluded. Nonlinear aeroelastic problems of morphing wing, energy harvesting, and flapping aircrafts are proposed as new directions in the future.

Spontaneous symmetry breaking in ΡΤ symmetric systems with nonlinear damping

International Nuclear Information System (INIS)

Karthiga, S.; Chandrasekar, V.K.; Senthilvelan, M.; Lakshmanan, M.

2016-01-01

In this talk, we discuss the remarkable role of position dependent damping in determining the parametric regions of symmetry breaking in nonlinear ΡΤ -symmetric systems. We illustrate the nature of ΡΤ-symmetry preservation and breaking with reference to a remarkable integrable scalar nonlinear system. In the two dimensional cases of such position dependent damped systems, we unveil the existence of a class of novel bi-ΡΤ -symmetric systems which have two fold ΡΤ symmetries. We discuss the dynamics of these systems and show how symmetry breaking occurs, that is whether the symmetry breaking of the two ΡΤ symmetries occurs in pair or occurs one by one. The addition of linear damping in these nonlinearly damped systems induces competition between the two types of damping. This competition results in a ΡΤ phase transition in which the ΡΤ symmetry is broken for lower loss/gain strength and is restored by increasing the loss/gain strength. We also show that by properly designing the form of the position dependent damping, we can tailor the ΡΤ-symmetric regions of the system. (author)

The Nonlinear Distortions in the Oscillatory System of Generator on CFOA

Directory of Open Access Journals (Sweden)

Yuriy Konstantinovich Rybin

2012-01-01

Full Text Available In recent years, many articles came out where one could find the analysis of oscillatory systems of electric sinusoid signals generators with amplifiers called CFOA—current feedback operational amplifiers. As a rule, the analysis of such systems is made by applying mathematical modeling methods on the basis of the amplifier linear model, which does not allow estimating advantages and disadvantages of the systems realized with those amplifiers in comparison with classical systems. A nonlinear model of a current feedback operational amplifier (CFOA is introduced in the paper; nonlinearity of “current mirror” is reflected in the form of current double limiting. The analysis of two known oscillatory systems has been carried out with the use of this non-linear model. Dependence between current limiting level, output voltage amplitude, and maximum oscillation frequency has been obtained. The paper shows that output current limiting under current output connection of capacitive load reduces frequency range and output voltage amplitude considerably and increases harmonic distortions in comparison with classical oscillatory systems. The research done has found that the application of new amplifiers does not give considerable advantages to the oscillatory systems with CFOA.

Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems.

Science.gov (United States)

Mei, Jie; Ren, Wei; Li, Bing; Ma, Guangfu

2015-09-01

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach

Science.gov (United States)

Aminzare, Zahra; Dey, Biswadip; Davison, Elizabeth N.; Leonard, Naomi Ehrich

2018-04-01

Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

Science.gov (United States)

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Nonlinear modeling and stability analysis of hydro-turbine governing system with sloping ceiling tailrace tunnel under load disturbance

International Nuclear Information System (INIS)

Guo, Wencheng; Yang, Jiandong; Wang, Mingjiang; Lai, Xu

2015-01-01

Highlights: • Novel nonlinear mathematical model of hydro-turbine governing system is proposed. • Hopf bifurcation analysis on the governing system is conducted. • Stability of the system under load disturbance is studied. • Influence of four factors on stability is analyzed. • Optimization methods of improving system stability are put forward. - Abstract: In order to overcome the problem of nonlinear dynamics of hydro-turbine governing system with sloping ceiling tailrace tunnel, which is caused by the interface movement of the free surface-pressurized flow in the tailrace tunnel, and the difficulty of analyzing the stability of system, this paper uses the Hopf bifurcation theory to study the stability of hydro-turbine governing system of hydropower station with sloping ceiling tailrace tunnel. Firstly, a novel and rational nonlinear mathematical model of the hydro-turbine governing system is proposed. This model contains the dynamic equation of pipeline system which can accurately describe the motion characteristics of the interface of free surface-pressurized flow in sloping ceiling tailrace tunnel. According to the nonlinear mathematical model, the existence and direction of Hopf bifurcation of the nonlinear dynamic system are analyzed. Furthermore, the algebraic criterion of the occurrence of Hopf bifurcation is derived. Then the stability domain and bifurcation diagram of hydro-turbine governing system are drawn by the algebraic criterion, and the characteristics of stability under different state parameters are investigated. Finally, the influence of step load value, ceiling slope angle and section form of tailrace tunnel and water depth at the interface in tailrace tunnel on stability are analyzed based on stable domain. The results indicate that: The Hopf bifurcation of hydro-turbine governing system with sloping ceiling tailrace tunnel is supercritical. The phase space trajectories of characteristic variables stabilize at the equilibrium points

Nonlinear phenomena at cyclotron resonance

International Nuclear Information System (INIS)

Subbarao, D.; Uma, R.

1986-01-01

Finite amplitude electromagnetic waves in a magnetoplasma which typically occur in situations as in present day wave heating, current drives and other schemes in magnetically confined fusion systems, can show qualitatively different absorption and emission characteristics around resonant frequencies of the plasma because of anharmonicity. Linear wave plasma coupling as well as weak nonlinear effects such as parametric instabilities generally overlook this important effect even though the thresholds for the two phenomena as shown here are comparable. Though the effects described here are relevant to a host of nonlinear resonance effects in fusion plasmas, the authors mainly limit themselves to ECRH

Sky-Hook Control and Kalman Filtering in Nonlinear Model of Tracked Vehicle Suspension System

Directory of Open Access Journals (Sweden)

Jurkiewicz Andrzej

2017-09-01

Full Text Available The essence of the undertaken topic is application of the continuous sky-hook control strategy and the Extended Kalman Filter as the state observer in the 2S1 tracked vehicle suspension system. The half-car model of this suspension system consists of seven logarithmic spiral springs and two magnetorheological dampers which has been described by the Bingham model. The applied continuous sky-hook control strategy considers nonlinear stiffness characteristic of the logarithmic spiral springs. The control is determined on estimates generated by the Extended Kalman Filter. Improve of ride comfort is verified by comparing simulation results, under the same driving conditions, of controlled and passive vehicle suspension systems.

The nonlinear dynamics of a coupled fission system

International Nuclear Information System (INIS)

Bilanovic, Z.; Harms, A.A.

1993-01-01

The dynamic properties of a nonlinear and in situ vibrationally perturbed nuclear-to-thermal coupled neutron multiplying medium are examined. Some unique self-organizational temporal patterns appear in such fission systems and suggest a complex underlying dynamic. (Author)

Determination of nonlinear nanomechanical resonator-qubit coupling coefficient in a hybrid quantum system.

Science.gov (United States)

Geng, Qi; Zhu, Ka-Di

2016-07-10

We have theoretically investigated a hybrid system that is composed of a traditional optomechanical component and an additional charge qubit (Cooper pair box) that induces a new nonlinear interaction. It is shown that the peak in optomechanically induced transparency has been split by the new nonlinear interaction, and the width of the splitting is proportional to the coupling coefficient of this nonlinear interaction. This may give a way to measure the nanomechanical oscillator-qubit coupling coefficient in hybrid quantum systems.

On Active Surge Control of Compression Systems via Characteristic Linearization and Model Nonlinearity Cancellation

Directory of Open Access Journals (Sweden)

Yohannes S.M. Simamora

2014-09-01

Full Text Available A simple approach of active surge control of compression systems is presented. Specifically, nonlinear components of the pressure ratio and rotating speed states of the Moore-Greitzer model are transferred into the input vectors. Subsequently, the compressor characteristic is linearized into two modes, which describe the stable region and the unstable region respectively. As a result, the system’s state and input matrices both appear linear, to which linear realization and analysis are applicable. A linear quadratic regulator plus integrator is then chosen as closed-loop controller. By simulation it was shown that the modified model and characteristics can describe surge behavior, while the closed-loop controller can stabilize the system in the unstable operating region. The last-mentioned was achieved when massflow was 5.38 per cent less than the surge point.

An analytical study of non-linear behaviour of coupled 2+2x0.5 DOF electro-magneto-mechanical system by a method of multiple scales

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2013-01-01

An electro-magneto-mechanical system combines three physical domains - a mechanical structure, a magnetic field and an electric circuit. The interaction between these domains is analysed for a structure with two degrees of freedom (translational and rotational) and two electrical circuits. Each...... electrical circuit is described by a differential equation of the 1st order, which is considered to contribute to the coupled system by 0.5 DOF. The electrical and mechanical systems are coupled via a magnetic circuit, which is inherently non-linear, due to a non-linear nature of the electro-magnetic force...

Six-component semi-discrete integrable nonlinear Schrödinger system

Science.gov (United States)

Vakhnenko, Oleksiy O.

2018-01-01

We suggest the six-component integrable nonlinear system on a quasi-one-dimensional lattice. Due to its symmetrical form, the general system permits a number of reductions; one of which treated as the semi-discrete integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell is considered in considerable details. Besides six truly independent basic field variables, the system is characterized by four concomitant fields whose background values produce three additional types of inter-site resonant interactions between the basic fields. As a result, the system dynamics becomes associated with the highly nonstandard form of Poisson structure. The elementary Poisson brackets between all field variables are calculated and presented explicitly. The richness of system dynamics is demonstrated on the multi-component soliton solution written in terms of properly parameterized soliton characteristics.

On the orthogonalised reverse path method for nonlinear system identification

Science.gov (United States)

Muhamad, P.; Sims, N. D.; Worden, K.

2012-09-01

The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.

Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

Science.gov (United States)

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.

Nonlinear beam expander for ESNIT

International Nuclear Information System (INIS)

Rusthoi, D.P.; Blind, B.; Garnett, R.W.; Hanna, D.S.; Jason, A.J.; Kraus, R.H. Jr.; Neri, F.

1994-01-01

We describe the design of a beam-redistribution and expansion system for the Japanese Atomic Energy Research Institute (JAERI) Energy Selective Neutron Irradiation Test Facility (ESNIT). The system tailors the beam exiting a deuteron accelerator at energies from 20 to 35 MeV for deposition on a lithium neutron-production target. A uniform beam-intensity distribution in a well-defined irradiation area is inquired at the target and is achieved by the use of nonlinear elements. The design of the high-energy beam transport (HEBT) for ESNIT includes a 90 degree achromatic bend, a matching section with an energy-compacting cavity, a nonlinear beam expander, a target imager, a shielding dipole, and an rf-cavity system to add energy spread to the beam before it impinges on the target. The system meets performance requirements at multiple energies and currents, and for different spot sizes on target

Nonlinear oscillations

CERN Document Server

Nayfeh, Ali Hasan

1995-01-01

Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim

MECHANISM OF OPTICAL NONLINEARITY IN “LYOTROPIC LIQUID CRYSTAL — VIOLOGEN” SYSTEM

Directory of Open Access Journals (Sweden)

Hanna Bordyuh

2014-06-01

Full Text Available In the present work we analyze the characteristics of holographic grating recording and consider a mechanism of optical nonlinearity in the lyotropic liquid crystal (LLC — viologen samples. Taking into account structural and electrooptical properties of the admixture molecules it is possible to suggest that the recording is realized due to the change of polarizability of π-electron system of coloured viologen derivatives under the action of laser radiation. The main nonlinear optical parameters such as nonlinear refraction coefficient n2, cubic nonlinear susceptibility χ(3, and hyperpolarizability γ were calculated.

An improved fuzzy Kalman filter for state estimation of nonlinear systems

International Nuclear Information System (INIS)

Zhou, Z-J; Hu, C-H; Chen, L; Zhang, B-C

2008-01-01

The extended fuzzy Kalman filter (EFKF) is developed recently and used for state estimation of the nonlinear systems with uncertainty. Based on extension of the orthogonality principle and the extended fuzzy Kalman filter, an improved fuzzy Kalman filters (IFKF) is proposed in this paper, which is more applicable and can deal with the state estimation of the nonlinear systems better than the EFKF. A simulation study is provided to verify the efficiency of the proposed method

Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity

International Nuclear Information System (INIS)

Sun, Y.-J.

2009-01-01

In this Letter, the concept of practical synchronization is introduced and the chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity is investigated. Based on the time-domain approach, a tracking control is proposed to realize chaos synchronization for the uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity. Moreover, the guaranteed exponential convergence rate and convergence radius can be pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

Science.gov (United States)