ANTICONTROL OF CHAOS FOR A CONTINUOUS-TIME TAKAGI–SUGENO FUZZY SYSTEM VIA LOCAL TIME-DELAY FEEDBACK

2005 ◽  
Vol 15 (12) ◽  
pp. 3883-3894 ◽  
Author(s):  
TAEK RYONG KIM ◽  
YOUNG HOON JOO ◽  
JIN BAE PARK ◽  
GUANRONG CHEN
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Continuous Time ◽  
Fuzzy System ◽  
Closed Loop ◽  
Fuzzy Controller ◽  
Design Method ◽  
Fuzzy Model ◽  
Takagi Sugeno ◽  
Systematic Control

In this paper, a simple and systematic control design method is proposed for making a continuous-time Takagi–Sugeno (T–S) fuzzy system chaotic. The concept of parallel distributed compensation is employed to determine the structure of a fuzzy controller from a T–S fuzzy model. The fuzzy controller makes the T–S fuzzy model, which could be stable or unstable, bounded and chaotic. The verification of chaos in the closed-loop T–S fuzzy system is done by the following procedure. First, we establish an asymptotically approximate relationship between a continuous-time T–S fuzzy system with time-delay and a discrete-time T–S fuzzy system. Then, we verify the chaos in the closed-loop T–S fuzzy system by applying the Marotto theorem to its associated discrete-time T–S fuzzy system. The generated chaos is in the sense of Li and Yorke. Two examples are given to show that this methodology is simple and effective for anticontrol of chaos for a continuous-time T–S fuzzy system.

scholarly journals Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Wen-Jer Chang ◽  
Yu-Wei Lin ◽  
Yann-Horng Lin ◽  
Chin-Lin Pen ◽  
Ming-Hsuan Tsai
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Fuzzy Model ◽  
The Stability ◽  
Interval Type ◽  
Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

scholarly journals Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

2018 ◽  
Vol 28 (3) ◽  
pp. 457-472 ◽  
Author(s):  
José V. Salcedo ◽  
Miguél Martínez ◽  
Sergio García-Nieto ◽  
Adolfo Hilario
Keyword(s):  
Continuous Time ◽  
Closed Loop ◽  
Input Saturation ◽  
Fuzzy Model ◽  
Maximum Volume ◽  
Ts Fuzzy Model ◽  
Non Linear ◽  
Non Linear System ◽  
Takagi Sugeno ◽  
Fuzzy State

Abstract This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi-Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

Delay-Dependent H2/H∞ Control for a Class of Switched T-S Fuzzy Systems with Time-Delay

2011 ◽  
Vol 204-210 ◽  
pp. 1197-1202 ◽  
Author(s):  
Yue Quan Yang ◽  
Jian Mei Jiang ◽  
Tian Ping Zhang ◽  
Yang Yi ◽  
Qing Zhu
Keyword(s):  
Time Delay ◽  
Fuzzy System ◽  
Fuzzy Systems ◽  
Closed Loop ◽  
Fuzzy Controller ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Switching Law ◽  
And Performance ◽  
Delay Dependent

Delay-dependent H2/H∞ control is studied for a class of switched T-S fuzzy systems. The sufficient condition for delay-dependent asymptotical stability H2 and H∞ and performance of the closed-loop switched T-S fuzzy system are derived. Meanwhile, a switching law and fuzzy controller are designed respectively. Moreover, an optimal problem corresponding with time-delay is provided, and an upper bound of time-delay which ensures the system asymptotically stable is obtained using employing MatLab LMI toolbox. Finally, the effectiveness of the proposed method is demonstrated by a numerical example.

Anticontrol of Chaos for a Stable Permanent Magnet Synchronous Motor System via Time-Delay Feedback

2013 ◽  
Vol 662 ◽  
pp. 797-800
Author(s):  
Xin Sun ◽  
Li Zhao ◽  
Tong Wei Yu
Keyword(s):  
Time Delay ◽  
Permanent Magnet ◽  
Continuous Time ◽  
Fuzzy System ◽  
Motor System ◽  
Permanent Magnet Synchronous Motor ◽  
Fuzzy Model ◽  
Synchronous Motor ◽  
Feedback Controller ◽  
Simulation Results

In this paper, the chaotification problem of a stable permanent magnet synchronous motor (PMSM) system is investigated. First, the stable PMSM plant is exactly represented by a simple continuous-time T–S fuzzy model with a few IF-THEN rules. A simple time-delay feedback controller is designed by parallel distributed compensation (PDC) technique. Then, Based on the T–S fuzzy system, We realize the anticontrol of chaos for the stable PMSM system by choosing parameters properly. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by simulation results.

scholarly journals Nonlinear modelling and optimal control via Takagi-Sugeno fuzzy techniques: A quadrotor stabilization

2020 ◽  
Vol 71 (1) ◽  
pp. 1-10
Author(s):  
Miroslav Pokorný ◽  
Tomáš Dočekal ◽  
Danica Rosinová
Keyword(s):  
Closed Loop ◽  
Fuzzy Controller ◽  
Fitness Function ◽  
Fuzzy Model ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Fuzzy Aggregation ◽  
Takagi Sugeno

AbstractUsing the principles of Takagi-Sugeno fuzzy modelling allows the integration of flexible fuzzy approaches and rigorous mathematical tools of linear system theory into one common framework. The rule-based T-S fuzzy model splits a nonlinear system into several linear subsystems. Parallel Distributed Compensation (PDC) controller synthesis uses these T-S fuzzy model rules. The resulting fuzzy controller is nonlinear, based on fuzzy aggregation of state controllers of individual linear subsystems. The system is optimized by the linear quadratic control (LQC) method, its stability is analysed using the Lyapunov method. Stability conditions are guaranteed by a system of linear matrix inequalities (LMIs) formulated and solved for the closed loop system with the proposed PDC controller. The additional GA optimization procedure is introduced, and a new type of its fitness function is proposed to improve the closed-loop system performance.

scholarly journals RobustH∞Control for a Class of Uncertain Switched Fuzzy Time-Delay Systems Based on T-S Models

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Cui ◽  
Kaiqing Liu ◽  
Yang Zhao ◽  
Xue Wang
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Design Method ◽  
Fuzzy Model ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stable Theory ◽  
Time Delay Systems ◽  
Switching Law ◽  
Continuous State

The problem of robustH∞control for a class of uncertain switched fuzzy time-delay systems is discussed for system described by T-S fuzzy model with Lyapunov stable theory and linear matrix inequality approach. A sufficient condition in terms of the LMI is derived such that the stability of the closed-loop systems is guaranteed. The continuous state feedback controller is built to ensure the asymptotically stable closed-loop system for all allowable uncertainties, with the switching law designed to implement the global asymptotic stability of uncertain switched fuzzy time-delay systems. In this model, each and every subsystem of the switched systems is an uncertain fuzzy one to which the parallel distributed compensation (PDC) controller of each sub fuzzy system system is proposed with its main condition given in a more solvable form of convex combinations. Such a switched control system is highly robust to varying parameters. A simulation shows the feasibility and effectiveness of the design method.

Fuzzy Controller Design via the Inverse Solution of Lyapunov Equations

2003 ◽  
Vol 125 (1) ◽  
pp. 42-47 ◽  
Author(s):  
Wen-Jer Chang
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Design Method ◽  
Fuzzy Model ◽  
Lyapunov Equation ◽  
Inverse Solution ◽  
Lyapunov Equations ◽  
Common Lyapunov Function ◽  
Compensation Technique ◽  
Takagi Sugeno

In this paper, a fuzzy control design method is be developed for the plant model whose structure is represented by the Takagi-Sugeno fuzzy model. In each rule of the Takagi-Sugeno fuzzy model, the system is characterized by linear dynamics given in the controllability canonical form. Replacing the Lyapunov inequality with a Lyapunov equation for stability analysis, the proposed method will make use of the inverse solution of Lyapunov equations to obtain a common Lyapunov function for all the subsystems. Based on this solution, the fuzzy controller can be constructed by using the parallel distributed compensation technique.

scholarly journals Design of an Unmatching Observer-Based Controller for Discrete-Time Fuzzy Systems with Time Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zejian Zhang ◽  
Dawei Wang
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Fuzzy Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Membership Functions ◽  
Design Flexibility ◽  
Control Scheme ◽  
The Stability

The problem of an unmatching observer-based controller design for discrete-time fuzzy systems with time delay is investigated, in which the fuzzy controller shares different membership functions from the fuzzy model. The objective is to design a state observer and unmatching fuzzy controller such that the discrete closed-loop system with time delay is asymptotically stable. A sufficient condition that contains the information of the membership functions of fuzzy model and fuzzy controller for the stabilization via an unmatching observer-based output feedback is presented. The proposed control scheme is well capable of enhancing the design flexibility, and the stability condition is less conservative. Three numerical examples are given to illustrate the effectiveness and advantages of the proposed method.

scholarly journals Further results on robust fuzzy dynamic systems with LMI D-stability constraints

2014 ◽  
Vol 24 (4) ◽  
pp. 785-794 ◽  
Author(s):  
Wudhichai Assawinchaichote
Keyword(s):  
Dynamic Systems ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Local System ◽  
Linear Matrix ◽  
Fuzzy Modelling ◽  
Ts Fuzzy Model ◽  
Input Noise ◽  
Takagi Sugeno

Abstract This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

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