Synchronization of fractional-order chaotic systems using adaptive linear feedback control

2014 ◽  
pp. 49-52
Author(s):  
Xian Li ◽  
Xiao Rao ◽  
Hui Zhang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Linear Feedback Control

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

FREQUENCY-DOMAIN CRITERIA FOR GLOBAL SYNCHRONIZATION OF MULTISCROLL CHAOTIC SYSTEMS UNDER LINEAR FEEDBACK CONTROL

2010 ◽  
Vol 20 (07) ◽  
pp. 2165-2177 ◽  
Author(s):  
XIAOFENG WU ◽  
ZHIFANG GUI ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Frequency Domain ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
General Mathematical Model ◽  
Linear State ◽  
Absolute Stability Theory

This paper provides a unified approach for achieving and analyzing global synchronization of a class of master-slave coupled multiscroll chaotic systems under linear state-error feedback control. A general mathematical model for such a class of multiscroll chaotic systems is first established. Based on some special properties of such systems, two less-conservative frequency-domain criteria for the desirable global synchronization are rigorously proven by means of the absolute stability theory. The analysis is then applied to two master-slave coupled modified Chua's circuits, obtaining the corresponding simple and precise algebraic criteria for global synchronization, which are finally verified by numerical simulations.

GLOBAL SYNCHRONIZATION OF MULTI-SCROLL SATURATED CHAOTIC SYSTEMS VIA SINGLE-STATE LINEAR FEEDBACK CONTROL

2013 ◽  
Vol 27 (05) ◽  
pp. 1350007 ◽  
Author(s):  
ZHIFANG GUI ◽  
XIAOFENG WU ◽  
YUN CHEN
Keyword(s):  
Feedback Control ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
Algebraic Criterion ◽  
Synchronization Problem ◽  
Single State ◽  
Conservative Result ◽  
Absolute Stability Theory

This paper investigates the global synchronization problem of master–slave coupled multi-scroll saturated chaotic systems via single-state linear feedback control. An algebraic criterion for global synchronization is rigorously proven by means of the absolute stability theory. The obtained algebraic criterion is then optimized thereby deriving a less-conservative result, which is finally verified by numerical examples.

Synchronization Controlling for the Chu Chaotic System via Linear Feedback

2011 ◽  
Vol 130-134 ◽  
pp. 2481-2484
Author(s):  
Ji Gui Jian ◽  
Xiao Lian Deng ◽  
Yan Jun Shen
Keyword(s):  
Feedback Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Simple Structure ◽  
Matrix Theory ◽  
Exponential Synchronization ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Inequality Techniques ◽  
Synchronization Scheme

Based on inequality techniques and matrix theory, linear feedback control both with one input and one state or two states and with multi-inputs is proposed to realize the globally exponential synchronization of two Chu chaotic systems. Some new sufficient algebraic criteria for the globally exponential synchronization of two chaotic systems are obtained analytically. The controllers here designed have simple structure. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

Optimal Linear and Nonlinear Control Design for Chaotic Systems

2005 ◽  
Author(s):  
Marat Rafikov ◽  
Jose´ Manoel Balthazar
Keyword(s):  
Feedback Control ◽  
Nonlinear Control ◽  
Chaotic Systems ◽  
Duffing Oscillator ◽  
Sufficient Conditions ◽  
Control Design ◽  
Linear Feedback ◽  
Nonlinear Feedback ◽  
Linear Feedback Control ◽  
Linear And Nonlinear

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Ro¨ssler system and the Duffing oscillator are provided to show the effectiveness of this method.

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