FUZZY CHAOS SYNCHRONIZATION VIA SAMPLED DRIVING SIGNALS

2004 ◽  
Vol 14 (08) ◽  
pp. 2721-2733 ◽  
Author(s):  
JUAN GONZALO BARAJAS-RAMÍREZ ◽  
GUANRONG CHEN ◽  
LEANG S. SHIEH
Keyword(s):  
Continuous Time ◽  
System Approach ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Disturbance Attenuation ◽  
Fuzzy Observer ◽  
Master System ◽  
Error Dynamics ◽  
Takagi Sugeno ◽  
Driving Signal

In this paper, a methodology to design a system that robustly synchronizes a master chaotic system from a sampled driving signal is developed. The method is based on the fuzzy Takagi–Sugeno representation of chaotic systems, from which a continuous-time fuzzy observer is designed as the solution of an LMI minimization problem such that the error dynamics have H∞disturbance attenuation performance. Then, from the dual-system approach, the fuzzy observer is digitally redesigned such that the performance is maintained for the sampled master system. The effectiveness of the proposed synchronization methodology is finally illustrated via numerical simulations of the chaotic Chen's system.

scholarly journals Observer-Based H ∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Kuan-Yi Lin ◽  
Tung-Sheng Chiang ◽  
Chian-Song Chiu ◽  
Wen-Fong Hu ◽  
Peter Liu
Keyword(s):  
Continuous Time ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Control Design ◽  
Practical Consideration ◽  
Time Varying ◽  
Fuzzy Observer ◽  
Output Tracking ◽  
Output Tracking Control

Tracking control for the output using an observer-based H ∞ fuzzy synchronization of time-varying delayed discrete- and continuous-time chaotic systems is proposed in this paper. First, from a practical point of view, the chaotic systems here consider the influence of time-varying delays, disturbances, and immeasurable states. Then, to facilitate a uniform control design approach for both discrete- and continuous-time chaotic systems, the dynamic models along with time-varying delays and disturbances are reformulated using the T-S (Takagi–Sugeno) fuzzy representation. For control design considering immeasurable states, a fuzzy observer achieves master-slave synchronization. Third, combining both a fuzzy observer for state estimation and a controller (solved from generalized kinematic constraints) output tracking can be achieved. To make the design more practical, we also consider differences of antecedent variables between the plant, observer, and controller. Finally, using Lyapunov’s stability approach, the results are sufficient conditions represented as LMIs (linear matrix inequalities). The contributions of the method proposed are threefold: (i) systemic and unified problem formulation of master-slave synchronization and tracking control for both discrete and continuous chaotic systems; (ii) practical consideration of time-varying delay, immeasurable state, different antecedent variables (of plant, observer, and controller), and disturbance in the control problem; and (iii) sufficient conditions from Lyapunov’s stability analysis represented as LMIs which are numerically solvable observer and controller gains from LMIs. We carry out numerical simulations on a chaotic three-dimensional discrete-time system and continuous-time Chua’s circuit. Satisfactory numerical results further show the validity of the theoretical derivations.

OBSERVER-BASED SYNCHRONIZATION FOR A CLASS OF FRACTIONAL CHAOTIC SYSTEMS VIA A SCALAR SIGNAL: RESULTS INVOLVING THE EXACT SOLUTION OF THE ERROR DYNAMICS

2011 ◽  
Vol 21 (03) ◽  
pp. 955-962 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Exact Analytical Solution ◽  
Fractional Order Systems ◽  
Fractional Error ◽  
Transmitted Signal ◽  
Error Dynamics

This paper deals with chaos synchronization for a class of fractional-order systems characterized by one nonlinearity. In particular, an observer-based approach is illustrated, which presents two remarkable features: (i) it provides an exact analytical solution of the fractional error dynamics, written in terms of Mittag-Leffler function; (ii) it enables synchronization to be achieved using a scalar transmitted signal. Finally, a synchronization example based on fractional Chua's system is illustrated, with the aim to show the capabilities of the developed approach.

scholarly journals Symplectic Synchronization of Lorenz-Stenflo System with Uncertain Chaotic Parameters via Adaptive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Cheng-Hsiung Yang
Keyword(s):  
Adaptive Control ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Asymptotical Stability ◽  
Sufficient Condition ◽  
Null Solution ◽  
Special Cases ◽  
Error Dynamics

A new symplectic chaos synchronization of chaotic systems with uncertain chaotic parameters is studied. The traditional chaos synchronizations are special cases of the symplectic chaos synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics and a parameter difference. The symplectic chaos synchronization with uncertain chaotic parameters may be applied to the design of secure communication systems. Finally, numerical results are studied for symplectic chaos synchronized from two identical Lorenz-Stenflo systems in three different cases.

scholarly journals LMI based fuzzy observer design for Takagi-Sugeno models containing vestigial nonlinear terms

2014 ◽  
Vol 24 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Observer Design ◽  
System Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Observer ◽  
Quadratic Inequalities ◽  
Lyapunov Stability Criterion ◽  
Takagi Sugeno

Abstract The paper deals with the problem of full order fuzzy observer design for the class of continuous-time nonlinear systems, represented by Takagi-Sugeno models containing vestigial nonlinear terms. On the basis of the Lyapunov stability criterion and the incremental quadratic inequalities, two design conditions for this kind of system model are outlined in the terms of linear matrix inequalities. A numerical example is given to illustrate the procedure and to validate the performances of the proposed approach.

scholarly journals Chaos Synchronization Based on Unknown Input Proportional Multiple-Integral Fuzzy Observer

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
T. Youssef ◽  
M. Chadli ◽  
H. R. Karimi ◽  
M. Zelmat
Keyword(s):  
Secure Communication ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Multiple Integral ◽  
Linear Matrix ◽  
Unknown Input ◽  
Matrix Inequalities ◽  
Decision Variables ◽  
Takagi Sugeno

This paper presents an unknown input Proportional Multiple-Integral Observer (PIO) for synchronization of chaotic systems based on Takagi-Sugeno (TS) fuzzy chaotic models subject to unmeasurable decision variables and unknown input. In a secure communication configuration, this unknown input is regarded as a message encoded in the chaotic system and recovered by the proposed PIO. Both states and outputs of the fuzzy chaotic models are subject to polynomial unknown input withkth derivative zero. Using Lyapunov stability theory, sufficient design conditions for synchronization are proposed. The PIO gains matrices are obtained by resolving linear matrix inequalities (LMIs) constraints. Simulation results show through two TS fuzzy chaotic models the validity of the proposed method.

scholarly journals A Simple Hybrid Synchronization for a Class of Chaotic Financial Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Jiming Zheng ◽  
Xiaoshuang Li ◽  
Yang Qiu
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Financial System ◽  
Asymptotically Stable ◽  
Financial Systems ◽  
Master System ◽  
Error System ◽  
Hybrid Synchronization ◽  
Novel Algorithm

It is an important to achieve the hybrid synchronization of the chaotic financial system. Chaos synchronization is equivalent to the error system which is asymptotically stable. The hybrid synchronization for a class of finance chaotic systems is discussed. First, a simple single variable controller is obtained to synchronize two identical chaotic financial systems with different initial conditions. Second, a novel algorithm is proposed to determine the variables of the master system that should antisynchronize with corresponding variables of the slave system and use this algorithm to determine the corresponding variables in the chaotic financial systems. The hybrid synchronization of the chaotic financial systems is realized by a simple controller. At the same time, different controllers can implement the chaotic financial system hybrid synchronization. In comparison with the existing results, the obtained controllers in this paper are simpler than those of the existing results. Finally, numerical simulations show the effectiveness of the proposed results.

HYBRID CHAOS SYNCHRONIZATION

2003 ◽  
Vol 13 (05) ◽  
pp. 1197-1216 ◽  
Author(s):  
JUAN-GONZALO BARAJAS-RAMÍREZ ◽  
GUANRONG CHEN ◽  
LEANG S. SHIEH
Keyword(s):  
Continuous Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Duffing Oscillator ◽  
The Novel ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Digital Redesign ◽  
Different Chaotic Systems ◽  
Novel Design

The problem of hybrid chaos synchronization is investigated, where a digital response subsystem is designed to synchronize with an analog drive subsystem. The approach taken is a new prediction-based digital redesign for a continuous-time observer embedded in the response via an optimal linearization approach of the nonlinear chaotic systems. Three typical but topologically quite different chaotic systems, Chua's circuit, Duffing oscillator, and Chen's system, are simulated thereby validating the novel design proposed in this paper.

scholarly journals Design of PDC Controllers by Matrix Reversibility for Synchronization ofYinandYangChaotic Takagi-Sugeno Fuzzy Henon Maps

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Chun-Yen Ho ◽  
Hsien-Keng Chen ◽  
Zheng-Ming Ge
Keyword(s):  
Chaos Synchronization ◽  
Matrix Theory ◽  
Chinese Philosophy ◽  
Fuzzy Model ◽  
Invertible Matrix ◽  
Henon Maps ◽  
Hénon Maps ◽  
Feminine Principle ◽  
Simulation Results ◽  
Takagi Sugeno

This paper investigates the synchronization ofYinandYangchaotic T-S fuzzy Henon maps via PDC controllers. Based on the Chinese philosophy,Yinis the decreasing, negative, historical, or feminine principle in nature, whileYangis the increasing, positive, contemporary, or masculine principle in nature.YinandYangare two fundamental opposites in Chinese philosophy. The Henon map is an invertible map; so the Henon maps with increasing and decreasing argument can be called theYangandYinHenon maps, respectively. Chaos synchronization ofYinandYangT-S fuzzy Henon maps is achieved by PDC controllers. The design of PDC controllers is based on the linear invertible matrix theory. The T-S fuzzy model ofYinandYangHenon maps and the design of PDC controllers are novel, and the simulation results show that the approach is effective.

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