T–S FUZZY ADAPTIVE DELAYED FEEDBACK SYNCHRONIZATION FOR TIME-DELAYED CHAOTIC SYSTEMS WITH UNCERTAIN PARAMETERS

2011 ◽  
Vol 25 (23n24) ◽  
pp. 3253-3267 ◽  
Author(s):  
CHOON KI AHN ◽  
PYUNG SOO KIM
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Fuzzy Model ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Adaptive Synchronization ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Takagi Sugeno ◽  
Fuzzy Adaptive

In this paper, we propose a new adaptive synchronization method, called a fuzzy adaptive delayed feedback synchronization (FADFS) method, for time-delayed chaotic systems with uncertain parameters. An FADFS controller that is based on the Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model, and delayed feedback control is developed to guarantee adaptive synchronization. The proposed controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example using a time-delayed Lorenz system is discussed to assess the validity of the proposed FADFS method.

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.

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

MASTER-SLAVE SYNCHRONIZATION OF NONAUTONOMOUS CHAOTIC SYSTEMS AND ITS APPLICATION TO ROTATING PENDULUMS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250147 ◽  
Author(s):  
KE DING ◽  
QING-LONG HAN
Keyword(s):  
Chaotic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Phase Locked Loops ◽  
Linear Matrix ◽  
Delayed Feedback Controller ◽  
Delay Dependent ◽  
Time Delayed Feedback

Some mathematical models in engineering and physics, such as rotating pendulums, governors and phase locked loops in circuits, can be described as nonautonomous systems in which there exist chaotic attractors. This paper investigates master-slave synchronization for two nonautonomous chaotic systems by using time-delayed feedback control. Firstly, three delay-dependent synchronization criteria, which are formulated in the form of linear matrix inequalities (LMIs), are established for complete synchronization, lag synchronization and anticipating synchronization, respectively. Secondly, sufficient conditions on the existence of a time-delayed feedback controller are derived by employing these newly-obtained synchronization criteria. The controller gain can be obtained by solving a set of LMIs. Finally, the synchronization criteria and the design method are applied to master-slave synchronization for rotating pendulum systems.

Fuzzy H∞ Synchronization for Chaotic Systems with Time-Varying Delay

2011 ◽  
Vol 66 (3-4) ◽  
pp. 151-160
Author(s):  
Choon Ki Ahn
Keyword(s):  
Chaotic Systems ◽  
External Disturbance ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Time Varying ◽  
Ts Fuzzy Model ◽  
Time Varying Delay ◽  
Norm Constraint ◽  
Takagi Sugeno ◽  
Varying Delay

In this paper, we propose a newH∞ synchronization method for fuzzy model based chaotic systems with external disturbance and time-varying delay. Based on Lyapunov-Krasovskii theory, Takagi- Sugeno (TS) fuzzy model, and linear matrix inequality (LMI) approach, the H∞ synchronization controller is presented to not only guarantee stable synchronization but also reduce the effect of external disturbance to an H∞ norm constraint. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. A simulation study is presented to demonstrate the validity of the proposed approach.

ESTIMATION OF AN ATTRACTION REGION IN ONE-DIMENSIONAL DELAYED-FEEDBACK CONTROL SYSTEMS

2005 ◽  
Vol 15 (02) ◽  
pp. 689-695
Author(s):  
KEIJI KONISHI
Keyword(s):  
Control Systems ◽  
Chaotic Systems ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
One Dimensional ◽  
Feedback Control Systems ◽  
Linear Matrix Inequality Approach ◽  
Feedback Method

This paper presents a simple numerical scheme for estimating the attraction region of a fixed point in one-dimensional discrete-time chaotic systems controlled by the delayed-feedback method. This scheme employs the well-known linear matrix inequality approach. A systematic procedure for estimating the region is provided, and numerical examples are used to validate the 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.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

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