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.

scholarly journals T-S Fuzzy Control of Uncertain Chaotic Vibration

2012 ◽  
Vol 19 (3) ◽  
pp. 379-389 ◽  
Author(s):  
Abdelkrim Boukabou ◽  
Noura Mansouri
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Control ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Fuzzy Model ◽  
Control Approach ◽  
Chaotic Vibration ◽  
Uncertain Chaotic Systems ◽  
Simulation Results ◽  
Takagi Sugeno

We present in this paper a novel and unified control approach that combines intelligent fuzzy logic methodology with predictive method for controlling chaotic vibration of a class of uncertain chaotic systems. We first introduce prediction into each subsystem of Takagi Sugeno (T-S) fuzzy IF-THEN rules and then present a unified T-S predictive fuzzy model for chaos control. The proposed controller can successfully stabilize the chaos and track the desired targets. The simulation results illustrate its effectiveness.

scholarly journals Observer-Based Fuzzy Control for Memristive Circuit Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Qian Ye ◽  
Xuyang Lou
Keyword(s):  
Fuzzy Control ◽  
Chaotic System ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Chaotic Circuit ◽  
Control Scheme ◽  
Simulation Results ◽  
Memristive Circuit ◽  
Takagi Sugeno

This paper proposes an observer-based fuzzy control scheme for a class of memristive chaotic circuit systems. First, the Takagi-Sugeno fuzzy model is adopted to reconstruct the nonlinear chaotic circuit system. Next, based on the proposed fuzzy model, an observer-based fuzzy controller is developed to estimate the states and stabilize the origin. Third, the results are extended to explore the L∞-gain observer-based fuzzy control for the chaotic system with disturbances. Finally, simulation results are also addressed to show the effectiveness of the proposed control scheme.

scholarly journals A Takagi-Sugeno Fuzzy Model for Greenhouse Climate

2021 ◽  
Vol 11 (4) ◽  
pp. 7424-7429
Author(s):  
I. Haj Hamad ◽  
A. Chouchaine ◽  
H. Bouzaouache
Keyword(s):  
Climate Model ◽  
Fuzzy Model ◽  
Climate Data ◽  
Internal Temperature ◽  
Temperature Prediction ◽  
Greenhouse Climate ◽  
Identification Approach ◽  
Simulation Results ◽  
Takagi Sugeno ◽  
Fuzzy Logic Technique

This paper investigates the identification and modeling of a greenhouse's climate using real climate data from a greenhouse installed in the LAPER laboratory in Tunisia. The objective of this paper is to propose a solution to the problem of nonlinear time-variant inputs and outputs of greenhouse internal climate. Combining fuzzy logic technique with Least Mean Squares (LMS), a robust greenhouse climate model for internal temperature prediction is proposed. The simulation results demonstrate the effectiveness of the identification approach and the power of the implemented Takagi-Sugeno Fuzzy model-based algorithm.

Chaos synchronization of Yin and Yang T-S fuzzy models of Hénon map system

2012 ◽  
Vol 227 (7) ◽  
pp. 1535-1543
Author(s):  
Chun-Yen Ho ◽  
Hsien-Keng Chen ◽  
Zheng-Ming Ge
Keyword(s):  
System Theory ◽  
Linear System ◽  
Chaos Synchronization ◽  
Fuzzy Controller ◽  
Chinese Philosophy ◽  
Chaotic Map ◽  
Fuzzy Model ◽  
Hénon Map ◽  
Henon Map ◽  
Linear System Theory

Based on the Chinese philosophy, Yin is the decreasing, negative, historical or feminine principle in nature, while Yang is the increasing, positive, contemporary or masculine principle in nature. Yin and Yang are two fundamental opposites in Chinese philosophy. Since the discrete Hénon map system is an invertible map, Yin–Yang T-S fuzzy model of chaotic Hénon map systems with increasing and decreasing argument can be studied. The Yang T-S fuzzy model of chaotic Hénon map system is presented. The Yin T-S fuzzy model of chaotic Hénon map system and Yin T-S fuzzy rules are obtained by invertible matrix in linear system theory. Chaos synchronization of Yang T-S fuzzy model of Hénon map systems is achieved by parallel distributed compensation technique, and the fuzzy controller for chaos synchronization of Yin T-S fuzzy model of Hénon map systems is also obtained by invertible matrix in linear system theory. The design of the Yin fuzzy controller is fleetly obtained by the inverse of Yang fuzzy controller, the concern is the Yin chaotic system must be an inverse of the Yang chaotic system. T-S fuzzy model scheme is used in the nonlinear discrete chaotic map system, so the nonlinear discrete chaotic map system can be analyzed by linear system theory.

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.

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.

scholarly journals Reversible Complex Hénon Maps

2002 ◽  
Vol 11 (3) ◽  
pp. 339-347 ◽  
Author(s):  
C. R. Jordan ◽  
D. A. Jordan ◽  
J. H. Jordan
Keyword(s):  
Henon Maps ◽  
Hénon Maps

Comment on "Stability issues on Takagi-Sugeno fuzzy model-parametric approach" [with reply]

2000 ◽  
Vol 8 (3) ◽  
pp. 345-346 ◽  
Author(s):  
T.A. Johansen ◽  
O. Slupphaug ◽  
Ji-Chang Lo ◽  
Yu-Min Chen
Keyword(s):  
Fuzzy Model ◽  
Parametric Approach ◽  
Stability Issues ◽  
Takagi Sugeno

CHAOS SYNCHRONIZATION VIA UNIDIRECTIONAL COUPLING AND ITS APPLICATION TO SECURE COMMUNICATION

2009 ◽  
Vol 23 (32) ◽  
pp. 5949-5964 ◽  
Author(s):  
XINGYUAN WANG ◽  
MINGJUN WANG
Keyword(s):  
Secure Communication ◽  
Chaos Synchronization ◽  
Function Method ◽  
The Self ◽  
Largest Lyapunov Exponent ◽  
Global Synchronization ◽  
Unidirectional Coupling ◽  
Response System ◽  
Lyapunov Function Method ◽  
Simulation Results

This paper studies chaos synchronization via unidirectional coupling. The self-synchronization of Lorenz systems, modified coupled dynamos systems and hyperchaotic Chen systems is studied by three methods: the Lyapunov function method, the global synchronization method and the numerical calculation of the largest Lyapunov exponent method. In regard to application to communication, we show that via transmitting single signal the synchronization of the drive system and the response system can be achieved. An example of applying self-synchronization of hyperchaotic Chen systems to chaotic masking secure communication is presented in this paper. Simulation results show the effectiveness of the method.

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