Experimental Switchings in Bistability Domains Induced by Resonant Perturbations

1998 ◽  
Vol 08 (09) ◽  
pp. 1777-1782 ◽  
Author(s):  
V. N. Chizhevsky ◽  
R. Vilaseca ◽  
R. Corbalan
Keyword(s):  
Nonlinear Systems ◽  
Feedback System ◽  
Chaotic State ◽  
Coexisting Attractors ◽  
Numerical Examples ◽  
Fast Switching ◽  
Pulse Perturbation ◽  
Initial States

We show that a combination of a resonant perturbation which induces bistability in the system with the targeting technique based on the action of a short-lived pulse perturbation makes the nonfeedback control of nonlinear systems (not only in a chaotic state) more flexible and even competitive with OGY's method in the sense of fast switching between controlled orbits belonging to coexisting attractors. For different initial states we present several experimental and numerical examples of such a type of control, which does not require feedback system.

Compensation of Time-Varying Input and State Delays for Nonlinear Systems

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Time Varying ◽  
Feedback Systems ◽  
Feedback Controllers ◽  
Stabilizing Controller ◽  
Numerical Examples ◽  
Infinite Dimensional ◽  
State Delays ◽  
Main Challenge

We consider general nonlinear systems with time-varying input and state delays for which we design predictor-based feedback controllers. Based on a time-varying infinite-dimensional backstepping transformation that we introduce, our controller achieves global asymptotic stability in the presence of a time-varying input delay, which is proved with the aid of a strict Lyapunov function that we construct. Then, we “backstep” one time-varying integrator and we design a globally stabilizing controller for nonlinear strict-feedback systems with time-varying delays on the virtual inputs. The main challenge in this case is the construction of the backstepping transformations since the predictors for different states use different prediction windows. Our designs are illustrated by three numerical examples, including unicycle stabilization.

ON IMPULSIVE CONTROL AND ITS APPLICATION TO CHEN'S CHAOTIC SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1191-1197 ◽  
Author(s):  
ZHI-HONG GUAN ◽  
RUI-QUAN LIAO ◽  
FENG ZHOU ◽  
HUA O. WANG
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Chaotic System ◽  
Control Method ◽  
Impulsive Control ◽  
Asymptotical Stability ◽  
Impulsive Systems ◽  
Chaotic State ◽  
Chaos Suppression ◽  
Zero Equilibrium

In this paper, impulsive control of nonlinear systems and its application to Chen's chaotic system are considered. A new impulsive control method for chaos suppression, using Chen's system as an example, is developed. Some new general criteria for exponential stability and asymptotical stability of nonlinear impulsive systems are established and, particularly, some simple conditions sufficient for driving the chaotic state of Chen's system to its zero equilibrium are presented.

Stability and Accuracy for Nonlinear Systems

2005 ◽  
Author(s):  
Shuenn-Yih Chang
Keyword(s):  
Nonlinear Systems ◽  
Stability Limit ◽  
Stable Method ◽  
Numerical Accuracy ◽  
Unconditionally Stable ◽  
Numerical Examples ◽  
Linear Elastic ◽  
Elastic Systems ◽  
Degree Of Convergence ◽  
Stability And Accuracy

Stability and accuracy of the Newmark method for solving nonlinear systems are analytically evaluated. It is proved that an unconditionally stable method for linear elastic systems is also unconditionally stable for nonlinear systems and a conditionally stable method for linear elastic systems remains conditionally stable for nonlinear systems except that the upper stability limit might vary with the step degree of nonlinearity and step degree of convergence. It is also found that numerical accuracy in the solution of nonlinear systems is highly related to the step degree of nonlinearity and the step degree of convergence although its general properties are similar to those of linear elastic systems. Analytical results are confirmed with numerical examples.

scholarly journals Transformation of CLF to ISS-CLF for Nonlinear Systems with Disturbance and Construction of Nonlinear Robust Controller withL2Gain Performance

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Keizo Okano ◽  
Kojiro Hagino ◽  
Hidetoshi Oya
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Linearization ◽  
Feedback System ◽  
Stability Control ◽  
Control Law ◽  
Robust Controller ◽  
Control Lyapunov Function ◽  
Nonlinear Control Law ◽  
Nonlinear Robust

A new nonlinear control law for a class of nonlinear systems with disturbance is proposed. A control law is designed by transforming control Lyapunov function (CLF) to input-to-state stability control Lyapunov function (ISS-CLF). The transformed CLF satisfies a Hamilton-Jacobi-Isaacs (HJI) equation. The feedback system by the proposed control law has characteristics ofL2gain. Finally, it is shown by a numerical example that the proposed control law makes a controller by feedback linearization robust against disturbance.

A Stochastic Averaging Approach for Feedback Control Design of Nonlinear Systems Under Random Excitations

2002 ◽  
Vol 124 (4) ◽  
pp. 561-565 ◽  
Author(s):  
O. Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Control Design ◽  
Stochastic Averaging ◽  
Moment Equation ◽  
Design Criteria ◽  
Numerical Examples ◽  
Rayleigh Approximation ◽  
Stochastic Controls ◽  
The Moment

This paper presents a method for designing and quantifying the performance of feedback stochastic controls for nonlinear systems. The design makes use of the method of stochastic averaging to reduce the dimension of the state space and to derive the Ito^ stochastic differential equation for the response amplitude process. The moment equation of the amplitude process closed by the Rayleigh approximation is used as a means to characterize the transient performance of the feedback control. The steady state and transient response of the amplitude process are used as the design criteria for choosing the feedback control gains. Numerical examples are studied to demonstrate the performance of the control.

Granular Synthesis of Rule-Based Models and Function Approximation Using Rough Sets

2010 ◽  
pp. 408-425 ◽  
Author(s):  
Carlos Pinheiro ◽  
Fernando Gomide ◽  
Otávio Carpinteiro ◽  
Isaías Lima
Keyword(s):  
Nonlinear Systems ◽  
Rough Sets ◽  
Estimation Procedure ◽  
New Method ◽  
Rule Based ◽  
Numerical Examples ◽  
Rule Sets ◽  
Computational Procedures ◽  
Granular Synthesis ◽  
And Function

This chapter suggests a new method to develop rule-based models using concepts about rough sets. The rules encapsulate relations among variables and give a mechanism to link granular descriptions of the models with their computational procedures. An estimation procedure is suggested to compute values from granular representations encoded by rule sets. The method is useful to develop granular models of static and dynamic nonlinear systems and processes. Numerical examples illustrate the main features and the usefulness of the method.

Fuzzy Control of Nonlinear Systems in the Presence of Noise

1995 ◽  
Author(s):  
F. Casciati ◽  
L. Faravelli
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fuzzy Control ◽  
Civil Engineering ◽  
Sensor Reading ◽  
Numerical Examples ◽  
Engineering Problems ◽  
Control Forces

Abstract Imprecise linguistic descriptions of system conditions can be used as the basis for activating control forces. In this paper, one discusses the aspects of the application of fuzzy control to civil engineering problems. Attention is focused on the presence of noise in the sensor reading and in the time delay. The results of numerical examples studying nonlinear systems subjected to random excitations are presented to illustrate some peculiar features of fuzzy control.

scholarly journals Combination of Laplace transform and residual power series techniques to solve autonomous n-dimensional fractional nonlinear systems

2021 ◽  
Vol 10 (1) ◽  
pp. 282-292
Author(s):  
Marwan Alquran ◽  
Maysa Alsukhour ◽  
Mohammed Ali ◽  
Imad Jaradat
Keyword(s):  
Nonlinear Systems ◽  
Power Series ◽  
Laplace Transform ◽  
Iterative Algorithm ◽  
Autonomous Systems ◽  
Numerical Examples ◽  
The Laplace Transform ◽  
Residual Power Series ◽  
The Impact ◽  
Residual Power

Abstract In this work, a new iterative algorithm is presented to solve autonomous n-dimensional fractional nonlinear systems analytically. The suggested scheme is combination of two methods; the Laplace transform and the residual power series. The methodology of this algorithm is presented in details. For the accuracy and effectiveness purposes, two numerical examples are discussed. Finally, the impact of the fractional order acting on these autonomous systems is investigated using graphs and tables.

Symmetric coexisting attractors and extreme multistability in chaotic system

2021 ◽  
pp. 2150458
Author(s):  
Xiaoxia Li ◽  
Chi Zheng ◽  
Xue Wang ◽  
Yingzi Cao ◽  
Guizhi Xu
Keyword(s):  
Chaotic System ◽  
Electronic Circuit ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
New Chaotic System ◽  
Initial States ◽  
Parameter Ranges ◽  
New System

In this paper, a new four-dimensional (4D) chaotic system with two cubic nonlinear terms is proposed. The most striking feature is that the new system can exhibit completely symmetric coexisting bifurcation behaviors and four symmetric coexisting attractors with the same Lyapunov exponents in all parameter ranges of the system when taking different initial states. Interestingly, these symmetric coexisting attractors can be considered as unusual symmetrical rotational coexisting attractors, which is a very fascinating phenomenon. Furthermore, by using a memristor to replace the coupling resistor of the new system, an interesting 4D memristive hyperchaotic system with one unstable origin is constructed. Of particular surprise is that it can exhibit four groups of extreme multistability phenomenon of infinitely many coexisting attractors of symmetric distribution about the origin. By using phase portraits, Lyapunov exponent spectra, and coexisting bifurcation diagrams, the dynamics of the two systems are fully analyzed and investigated. Finally, the electronic circuit model of the new system is designed for verifying the feasibility of the new chaotic system.

ŠIL'NIKOV HOMOCLINIC ORBITS IN TWO CLASSES OF 3D AUTONOMOUS NONLINEAR SYSTEMS

2011 ◽  
Vol 25 (20) ◽  
pp. 2697-2712 ◽  
Author(s):  
BAOYING CHEN ◽  
TIANSHOU ZHOU
Keyword(s):  
Computer Simulation ◽  
Nonlinear Systems ◽  
Geometric Structure ◽  
Homoclinic Orbit ◽  
Chaotic Attractor ◽  
Normal Forms ◽  
Three Dimensional ◽  
Homoclinic Orbits ◽  
Numerical Examples ◽  
Undetermined Coefficient

The Šil'nikov homoclinic theorem provides one analytic criterion for proving the existence of chaos in three-dimensional autonomous nonlinear systems. In applications of the theorem, however, the existence of a homoclinic orbit that usually determines the geometric structure of the chaotic attractor is not easily verified mainly because there are no available efficient methods. In this paper, based on the undetermined coefficient approach we present a framework of how to find homoclinic orbits in two classes of three-dimensional autonomous nonlinear systems of normal forms, including how to set a reasonable form of expanding series of the homoclinic orbit, how to determine all coefficients in the expansion, and how to find a numerical homoclinic orbit. Numerical examples show that the proposed framework in combination with computer simulation is very efficient.

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