Impulsive Control of Nonautonomous Chaotic Systems using Practical Stabilization

1998 ◽  
Vol 08 (07) ◽  
pp. 1557-1564 ◽  
Author(s):  
Tao Yang ◽  
Johan A. K. Suykens ◽  
Leon O. Chua
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Small Region ◽  
Asymptotic Stabilization ◽  
Practical Stabilization

In this paper, we use the concept of practical stabilization of impulsive differential equations for controlling nonautonomous chaotic systems. Instead of controlling a chaotic system to a point as in the case of asymptotic stabilization, the aim of practical control is to stabilize a chaotic system into a small region of phase space. This method is useful to control a chaotic system into a prescribed region. We present the theory of controlling a nonautonomous chaotic system into a small region around the origin and illustrate the method on Duffing's oscillator.

Impulsive Control and Practical Generalized Synchronization of a Class of Uncertain Chaotic System with a Given Manifold

2015 ◽  
Vol 782 ◽  
pp. 296-301
Author(s):  
Jian Xu Ding ◽  
Cheng Wang ◽  
Yong Bi
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Coupled Systems ◽  
Generalized Synchronization

In this paper, we study practical generalized synchronization of uncertain chaotic system with a given manifold Y = H(X). We construct a class of the bi-directionally coupled chaotic systems with impulsive control, and demonstrate theoretically that the bi-coupled systems could realize practical generalized synchronization on the basis of stability theory of impulsive differential equations. Numerical simulations with super-chaotic system are provided to further demonstrate the effectiveness and generality of our approach.

The Model of Liu Chaotic Synchronization with Oscillating Parameters under the Impulsive Control

2011 ◽  
Vol 480-481 ◽  
pp. 1378-1382
Author(s):  
Yan Hui Chen
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Chaotic Synchronization ◽  
Control Signal ◽  
Synchronization Control ◽  
Security Risks ◽  
Control Scheme

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with oscillating parameters approach to 0 and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.

Pinning Impulsive Synchronization of Fractional Complex Dynamical Networks

2015 ◽  
Author(s):  
Weiyuan Ma ◽  
Changpin Li ◽  
Yujiang Wu
Keyword(s):  
Differential Equations ◽  
Comparison Principle ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Impulsive Synchronization ◽  
Pinning Impulsive Control

In this paper, a class of fractional complex dynamical networks is synchronized via pinning impulsive control. At first, a comparison principle is established for fractional impulsive differential equations. Then the synchronization criterion is obtained by using the derived comparison principle. Examples are given to illustrate the results.

IMPULSIVE CONTROL FOR T–S FUZZY SYSTEM AND ITS APPLICATION TO CHAOTIC SYSTEMS

2006 ◽  
Vol 16 (08) ◽  
pp. 2417-2423 ◽  
Author(s):  
YAN-WU WANG ◽  
ZHI-HONG GUAN ◽  
HUA O. WANG ◽  
JIANG-WEN XIAO
Keyword(s):  
Chaotic System ◽  
Fuzzy System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Structure ◽  
Impulsive Control ◽  
Fuzzy Model ◽  
Chua's Circuit ◽  
Control Scheme ◽  
The Stability

An impulsive T–S fuzzy model is presented in this paper. The stability of impulsive controlled T–S fuzzy system has been analyzed theoretically. The proposed impulsive control scheme seems to have a simple control structure and may need less control energy than the normal continuous ones for the stabilization of T–S fuzzy system. Some typical chaotic systems, such as Chua's circuit, Lorenz system and Chen's chaotic system, are considered as illustrations to demonstrate the effectiveness of the proposed control scheme.

scholarly journals Impulsive Control Strategy for a Nonautonomous Food-Chain System with Multiple Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Baodan Tian ◽  
Yanhong Qiu ◽  
Yucai Ding
Keyword(s):  
Differential Equations ◽  
Food Chain ◽  
Impulsive Control ◽  
Control Strategies ◽  
Functional Differential Equations ◽  
Impulsive Differential Equations ◽  
Effective Control ◽  
Multiple Delays ◽  
Chain System ◽  
Holling Ii Functional Response

A nonautonomous food-chain system with Holling II functional response is studied, in which multiple delays of digestion are also considered. By applying techniques in differential inequalities, comparison theorem in ordinary differential equations, impulsive differential equations, and functional differential equations, some effective control strategies are obtained for the permanence of the system. Furthermore, effects of some important coefficients and delays on the permanence of the system are intuitively and clearly shown by series of numerical examples.

Impulsive Control and Synchronization of Nonlinear Dynamical Systems and Application to Secure Communication

1997 ◽  
Vol 07 (03) ◽  
pp. 645-664 ◽  
Author(s):  
Tao Yang ◽  
Leon O. Chua
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Secure Communication ◽  
Impulsive Control ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Impulsive Differential Equations ◽  
Channel Noise ◽  
Nonlinear Dynamical ◽  
Impulsive Synchronization

Impulsive control is a newly developed control theory which is based on the theory of impulsive differential equations. In this paper, we stabilize nonlinear dynamical systems using impulsive control. Based on the theory of impulsive differential equations, we present several theorems on the stability of impulsive control systems. An estimation of the upper bound of the impulse interval is given for the purpose of asymptotically controlling the nonlinear dynamical system to the origin by using impulsive control laws. In this paper, impulsive synchronization of two nonlinear dynamical systems is reformulated as impulsive control of the synchronization error system. We then present a theorem on the asymptotic synchronization of two nonlinear systems by using synchronization impulses. The robustness of impulsive synchronization to additive channel noise and parameter mismatch is also studied. We conclude that impulsive synchronization is more robust than continuous synchronization. Combining both conventional cryptographic method and impulsive synchronization of chaotic systems, we propose a new chaotic communication scheme. Computer simulation results based on Chua's oscillators are given.

scholarly journals Impulsive Control of Memristive Chaotic Systems with Impulsive Time Window

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
FuLi Chen ◽  
Hui Wang ◽  
Chuandong Li
Keyword(s):  
Numerical Simulations ◽  
Comparison Principle ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Time Window ◽  
Time Windows ◽  
Chaotic Circuit ◽  
Asymptotic Stabilization ◽  
Theoretical Results

The problem of impulsive control for memristor-based chaotic circuit systems with impulsive time windows is investigated. Based on comparison principle, several novel criteria which guarantee the asymptotic stabilization of the memristor-based chaotic circuit systems are obtained. In comparison with previous results, the present results are easily verified. Numerical simulations are given to further illustrate the effectiveness of the theoretical results.

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