Chaotic Synchronization of a Class of Nonlinear Systems via Sampled-Data State Feedback

2014 ◽  
Author(s):  
Song Yan ◽  
Chunjiang Qian ◽  
Tingwen Huang
Keyword(s):  
Chaotic System ◽  
State Feedback ◽  
Tracking Error ◽  
Practical Importance ◽  
Sampled Data ◽  
Data Feedback ◽  
Sampled Signal ◽  
System States ◽  
Data Controller ◽  
Chua Oscillator

This paper presents a control strategy for the problem of using sampled-data feedback to synchronize a slave chaotic system with a master chaotic system. The problem is of practical importance since in practice the system states is transmitted as a sampled signal. In order to solve this problem, a sampled-data controller using state feedback is designed to make the tracking error converge to zero. An application to a chaotic Chua oscillator illustrates the effectiveness of the proposed approach.

Global asymptotic synchronization of a class of non-linear systems via sampled-data feedback

2016 ◽  
Vol 40 (1) ◽  
pp. 12-21 ◽  
Author(s):  
Song Yan ◽  
Chunjiang Qian ◽  
Tingwen Huang
Keyword(s):  
State Feedback ◽  
Tracking Error ◽  
Practical Importance ◽  
Output Feedback Control ◽  
Sampled Data ◽  
Data Feedback ◽  
Driven System ◽  
Sampled Signal ◽  
Chua Oscillator ◽  
Asymptotic Synchronization

In this paper, we investigate the problem of using sampled-data feedback to synchronize a slave (driven) system with a master (driver) system. Based on the domination approach, both state-feedback and output-feedback control methods using sampled-data are proposed to make the tracking error converge to zero. The problem is of practical importance since in practice the system state is transmitted as sampled signal, and very often only the output is measurable. The effectiveness of the proposed approach is illustrated by the simulation for a chaotic Chua oscillator.

STABILIZATION OF CHAOTIC SYSTEMS USING LINEAR SAMPLED-DATA CONTROLLER

2007 ◽  
Vol 17 (06) ◽  
pp. 2021-2031 ◽  
Author(s):  
H. K. LAM ◽  
F. H. F. LEUNG
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Design Procedure ◽  
Sampling Period ◽  
Feedback Gain ◽  
Sampled Data ◽  
Lyapunov Approach ◽  
And Performance ◽  
Data Controller

This paper proposes a linear sampled-data controller for the stabilization of chaotic system. The system stabilization and performance issues will be investigated. Stability conditions will be derived based on the Lyapunov approach. The findings of the maximum sampling period and the feedback gain of controller, and the optimization of system performance will be formulated as a generalized eigenvalue minimization problem. Based on the analysis result, a stable linear sampled-data controller can be realized systematically to stabilize a chaotic system. An example of stabilizing a Lorenz system will be given to illustrate the design procedure and effectiveness of the proposed approach.

scholarly journals Control of Chaos Using Sampled-Data Feedback Control

1998 ◽  
Vol 08 (12) ◽  
pp. 2433-2438 ◽  
Author(s):  
Tao Yang
Keyword(s):  
Feedback Control ◽  
Asymptotic Stability ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Sampling Rate ◽  
Control Input ◽  
Sampled Data ◽  
Control Of Chaos ◽  
Data Feedback ◽  
Theoretical Results

In this paper we present a theory for control of chaotic systems using sampled data. The output of the chaotic system is sampled at a given sampling rate and the sampled output is used by a feedback subsystem to construct a control signal, which is held constant by a holding subsystem. Hence, during each control iteration, the control input remains unchanged. Theoretical results on the asymptotic stability of the resulting controlled chaotic systems are presented. Numerical experimental results via Chua's circuit are used to verify the theoretical results.

scholarly journals Aperiodic Sampled-Data Control for Chaotic System Based on Takagi–Sugeno Fuzzy Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Minjie Zheng ◽  
Shenhua Yang ◽  
Lina Li
Keyword(s):  
Chaotic System ◽  
Fuzzy Model ◽  
Sampling Period ◽  
Linear Matrix ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Mean Square Exponential Stability ◽  
Data Controller ◽  
Takagi Sugeno

This paper investigates the aperiodic sampled-data control for a chaotic system. Firstly, Takagi–Sugeno (T-S) fuzzy models for the chaotic systems are established. The lower and upper bounds of the sampling period are taken into consideration. Then, the criteria for mean square exponential stability analysis and aperiodic sampled-data controller synthesis are provided by means of linear matrix inequalities. And the real sampling patterns can be fully captured by constructing suitable Lyapunov functions. Finally, an illustrative example shows that the proposed method is effective to guarantee that the system’s states are stable with aperiodic sampled data.

Fault tolerant synchronization of chaotic system with sampled-data controller

2015 ◽  
pp. 29-32
Author(s):  
Tao Ren ◽  
Yan Xu ◽  
Miao Liu ◽  
Jian-xin Wen ◽  
Sen He
Keyword(s):  
Chaotic System ◽  
Fault Tolerant ◽  
Sampled Data ◽  
Data Controller

scholarly journals SAMPLED-DATA FEEDBACK CONTROL FOR CHEN'S CHAOTIC SYSTEM

2000 ◽  
Vol 49 (6) ◽  
pp. 1039
Author(s):  
YANG LIN-BAO
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Sampled Data ◽  
Data Feedback

Synchronization of Chaotic Systems Using Sampled-Data Polynomial Controller

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
H. K. Lam ◽  
Hongyi Li
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Third Party ◽  
System Stability ◽  
Stability Conditions ◽  
Sampled Data ◽  
System Matrix ◽  
Polynomial Controller ◽  
System States

This paper presents the synchronization of two chaotic systems, namely the drive and response chaotic systems, using sampled-data polynomial controllers. The sampled-data polynomial controller is employed to drive the system states of the response chaotic system to follow those of the drive chaotic system. Because of the zero-order-hold unit complicating the system dynamics by introducing discontinuity to the system, it makes the stability analysis difficult. However, the sampled-data polynomial controller can be readily implemented by a digital computer or microcontroller to lower the implementation cost and time. With the sum-of-squares (SOS) approach, the system to be handled can be in the form of nonlinear state-space equations with the system matrix depending on system states. Based on the Lyapunov stability theory, SOS-based stability conditions are obtained to guarantee the system stability and realize the chaotic synchronization subject to an H∞ performance function. The solution to the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. Simulation examples are given to illustrate the merits of the proposed sampled-data polynomial control approach for chaotic synchronization problems.

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