Linear feedback control, adaptive feedback control and their combination for chaos (lag) synchronization of LC chaotic systems

2007 ◽  
Vol 33 (2) ◽  
pp. 419-435 ◽  
Author(s):  
Zhenya Yan ◽  
Pei Yu
Keyword(s):  
Feedback Control ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Lag Synchronization ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control

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.

Stabilization of a Class of Chaotic Systems via Single-State Adaptive Feedback Controller

2014 ◽  
Vol 571-572 ◽  
pp. 965-968
Author(s):  
De Gang Yang ◽  
Guo Ying Qiu
Keyword(s):  
Feedback Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Feedback Controller ◽  
Control Analysis ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Feedback Control Method ◽  
Single State ◽  
System States

This paper investigates the application of the adaptive feedback control method in the chaotic system and Single-state Adaptive Feedback Controller. We divide the adaptive feedback controller into several items, each of which has only one component of the system states as feedback input into each dimension of the system. With the introduction of single-state controller, the scale of control inputs can be flexibly adjusted, the additional loading reduced, better convergence effect obtained and the application field of adaptive feedback control methods further extended in stable control analysis of chaotic systems. An example is also given to illustrate the validity of our result.

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.

Adaptive feedback control for a class of chaotic systems

2005 ◽  
Vol 23 (3) ◽  
pp. 757-765 ◽  
Author(s):  
Changchun Hua ◽  
Xinping Guan ◽  
Peng Shi
Keyword(s):  
Feedback Control ◽  
Chaotic Systems ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control

LAG SYNCHRONIZATION OF BURSTING NEURON SYSTEMS WITH STOCHASTIC PERTURBATION VIA ADAPTIVE FEEDBACK CONTROL

2014 ◽  
Vol 28 (07) ◽  
pp. 1450022 ◽  
Author(s):  
ZUO-LEI WANG ◽  
XUE-RONG SHI ◽  
YAOLIN JIANG
Keyword(s):  
Feedback Control ◽  
Stochastic Perturbation ◽  
Control Law ◽  
Lag Synchronization ◽  
Theoretical Derivation ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Bursting Neuron ◽  
Control Scheme ◽  
Adaptive Control Law

Lag synchronization of bursting neuron systems is explored when the system is subjected to stochastic perturbation. An adaptive feedback control scheme is presented when the parameters of the neuron systems are unknown. At the same time, an adaptive control law is obtained via theoretical derivation so that two slightly mismatched chaotic systems achieved asymptotically lag synchronization. The effectiveness of the proposed scheme is not only confirmed by theoretical analysis, but also verified by numerical simulations.

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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