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.

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.

DELAYED FEEDBACK $\mathcal{H}_{\infty}$ SYNCHRONIZATION FOR TIME-DELAYED CHAOTIC SYSTEMS BASED ON T–S FUZZY MODEL

2010 ◽  
Vol 24 (02) ◽  
pp. 211-224 ◽  
Author(s):  
CHOON KI AHN ◽  
JUNG HUN PARK
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
External Disturbance ◽  
Fuzzy Model ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Linear Matrix ◽  
Control Scheme ◽  
Norm Constraint ◽  
New Formula

In this letter, we propose a new [Formula: see text] synchronization method, called a delayed feedback fuzzy [Formula: see text] synchronization (DFFHS) method, for time-delayed chaotic systems with external disturbance. Based on Lyapunov–Krasovskii theory, T–S fuzzy model, and delayed feedback control scheme, the DFFHS controller is presented to not only guarantee aymptotical synchronization but also reduce the effect of external disturbance to an [Formula: see text] norm constraint. The proposed controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed DFFHS method.

ROBUST LINEAR OUTPUT FEEDBACK CONTROL DESIGN FOR NONLINEAR CHAOTIC SYSTEMS VIA T–S FUZZY MODEL WITH H∞ SETTING

2008 ◽  
Vol 18 (11) ◽  
pp. 3375-3392 ◽  
Author(s):  
YEN-FANG LI ◽  
CHUNG-SHI TSENG
Keyword(s):  
Chaotic System ◽  
Output Feedback ◽  
Chaotic Systems ◽  
Fuzzy Model ◽  
Output Feedback Control ◽  
Control Design ◽  
Linear Controller ◽  
Control Scheme ◽  
Linear Observer ◽  
Nonlinear Chaotic System

In this paper, the problem of H∞ control design is studied for a nonlinear chaotic system via its corresponding Takagi–Sugeno (T–S) fuzzy model. It is known that many nonlinear chaotic systems can be exactly represented by their corresponding T–S fuzzy models. First, in this study, the T–S fuzzy model is proposed to represent a class of nonlinear chaotic systems. Next, a linear output feedback control scheme, where only linear controller and linear observer are considered, with H∞ setting is proposed for the nonlinear chaotic system. Then, based on the T–S fuzzy model and the proposed linear control scheme, the H∞ controller design problem for nonlinear chaotic systems is characterized in terms of minimizing the attenuation level subject to some linear matrix inequalities (LMIs), which is also called eigenvalue problem (EVP), through the scanning of a positive parameter. Finally, the proposed control scheme is applied to a chaotic system, namely Chua's circuit, to illustrate the robust performance of the proposed linear controller and linear observer.

scholarly journals Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 559 ◽  
Author(s):  
Liang Chen ◽  
Chengdai Huang ◽  
Haidong Liu ◽  
Yonghui Xia
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Unknown Parameters ◽  
Integer Order ◽  
System A ◽  
Control Scheme ◽  
Lorenz Chaotic System

The paper proves a unified analysis for finite-time anti-synchronization of a class of integer-order and fractional-order chaotic systems. We establish an effective controller to ensure that the chaotic system with unknown parameters achieves anti-synchronization in finite time under our controller. Then, we apply our results to the integer-order and fractional-order Lorenz system, respectively. Finally, numerical simulations are presented to show the feasibility of the proposed control scheme. At the same time, through the numerical simulation results, it is show that for the Lorenz chaotic system, when the order is greater, the more quickly is anti-synchronization achieved.

T-S Fuzzy Model Establishment and Control of Discrete Chaotic System

2013 ◽  
Vol 787 ◽  
pp. 846-849 ◽  
Author(s):  
Zhi Hong Yang
Keyword(s):  
Chaotic System ◽  
Sliding Mode ◽  
Fuzzy Model ◽  
Lyapunov Stability Theorem ◽  
Fuzzy Sliding Mode Control ◽  
Fuzzy Models ◽  
Control Scheme ◽  
Fuzzy Sliding Mode ◽  
The Stability ◽  
And Control

The problem of fuzzy sliding mode control of discrete chaotic system is studied. Discrete chaotic system is described based on T-S fuzzy models, and the system is translated into local linear model by fuzzy method. On the basis of Lyapunov stability theorem and approaching law method, a novel sliding mode controller is designed in the paper. The controller insures the stability of global fuzzy model. The controlled certain and uncertain Henon systems are simulated with Matlab, and the numerical results demonstrate the validity and robustness of the control scheme.

scholarly journals Time-Delayed Impulsive Control of Chaotic System Based on T-S Fuzzy Model

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Cheng Hu ◽  
Haijun Jiang
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Impulsive Control ◽  
Fuzzy Model ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
The Stability ◽  
Control And Synchronization ◽  
Time Delayed Feedback ◽  
Delayed Impulsive Control

This paper is concerned with the time-delayed impulsive control and synchronization of general chaotic system based on T-S fuzzy model. By utilizing impulsive control theory, time-delayed feedback control technique, and T-S fuzzy model, some useful and new conditions are derived to guarantee the stability and synchronization of the addressed chaotic system. Finally, some numerical simulations are given to illustrate the effectiveness of the derived results.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

scholarly journals Hybrid Passivity Based and Fuzzy Type-2 Controller for Chaotic and Hyper-Chaotic Systems

2017 ◽  
Vol 11 (2) ◽  
pp. 96-103 ◽  
Author(s):  
Fernando Serrano ◽  
Josep M. Rossell
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Law ◽  
Four Dimensions ◽  
Design Requirements ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.

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.

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