Adaptive Fuzzy Synchronization Design and Parameter Identification for Chaotic Systems

2014 ◽  
Vol 644-650 ◽  
pp. 2514-2521
Author(s):  
Juan Meng ◽  
Hai Du ◽  
Xing Yuan Wang
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Adaptive Fuzzy Controller ◽  
Adaptive Fuzzy ◽  
Takagi Sugeno

In this paper, a new fuzzy model-based adaptive approach for synchronization of chaotic systems with unknown parameters. Theoretical analysis based on Lyapunov stability theory is provided to verify its feasibility. Takagi-Sugeno (T-S) fuzzy model is employed to express the chaotic systems. Based on this model, an adaptive fuzzy controller and the parameters update law are developed. With the proposed scheme, parameters identification and synchronization of identical or nonidentical chaotic systems can be achieved simultaneously. Numerical simulations further demonstrate the effectiveness of the proposed scheme.

scholarly journals Adaptive Anti-synchronization of Identical and Non-identical 4-D Chaotic Systems

2012 ◽  
pp. 160-164
Author(s):  
H. Najafizadegan ◽  
M. Khoeiniha ◽  
H. Zarabadipour
Keyword(s):  
Adaptive Control ◽  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Unknown Parameters ◽  
Different Chaotic Systems ◽  
Adaptive Control Law

In this paper, we investigate the chaos anti-synchronization between two identical and different chaotic systems with fully unknown parameters via adaptive control. Based on the Lyapunov stability theory, an adaptive control law and a parameter update rule for unknown parameters are designed such that the two different chaotic systems can be anti-synchronized asymptotically. Theoretical analysis and numerical simulations are shown to verify the results.

scholarly journals Adaptive multilayer T-S fuzzy controller for nonlinear SISO system optimized by differential evolution algorithm

2020 ◽  
Vol 3 (SI1) ◽  
pp. First
Author(s):  
Cao Van Kien ◽  
Ho Pham Huy Anh ◽  
Nguyen Ngoc Son
Keyword(s):  
Differential Evolution ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Algorithm ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Lyapunov Stability Theory ◽  
Uncertain Parameters ◽  
Adaptive Fuzzy ◽  
Fuzzy Models

In this paper, the authors propose a novel adaptive multilayer T-S fuzzy controller (AMTFC) with an optimized soft computing algorithm for a class of robust control uncertain nonlinear SISO systems. First, a new multilayer T-S fuzzy was created by combined multiple simple T-S fuzzy models with a sum function in the output. The multi-layer fuzzy model used in nonlinear identification has many advantages over conventional fuzzy models, but it cannot be created by the writer's experience or the trial and error method. It can only be created using an optimization algorithm. Then the parameters of the multilayer fuzzy model are optimized by the differential evolution DE algorithm is used to offline identify the nonlinear inverse system with uncertain parameters. The trained model was validated by a different dataset from the training dataset to guarantee the convergence of the training algorithm. Second, for robustly and adaptive purposes, the authors have proposed an additional adaptive fuzzy model based on Lyapunov stability theory combined with the optimized multilayer fuzzy. The adaptive fuzzy based on the sliding mode surface is designed to guarantee that the closed-loop system is asymptotically stable has been proved base on a Lyapunov stability theory. Furthermore, simulation tests are performed in the Matlab/Simulink environment that controlling a water level of a coupled tank with uncertain parameters are given to illustrate the effectiveness of the proposed control scheme. The proposed control algorithm is implemented in simulation with many different control parameters, and it is also compared with the conventional adaptive control algorithm and inverse controller. The simulation results also show the superior of the proposed controller than an adaptive fuzzy control or inverse controller when using the least mean square error standard.

scholarly journals Uncertain Fractional Order Chaotic Systems Tracking Design via Adaptive Hybrid Fuzzy Sliding Mode Control

2011 ◽  
Vol 6 (3) ◽  
pp. 418 ◽  
Author(s):  
Tsung-Chih Lin ◽  
Chia-Hao Kuo ◽  
Valentina E. Balas
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Fuzzy Controller ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Fuzzy Controller ◽  
Adaptive Fuzzy ◽  
Mode Control ◽  
And Control

In this paper, in order to achieve tracking performance of uncertain fractional order chaotic systems an adaptive hybrid fuzzy controller is proposed. During the design procedure, a hybrid learning algorithm combining sliding mode control and Lyapunov stability criterion is adopted to tune the free parameters on line by output feedback control law and adaptive law. A weighting factor, which can be adjusted by the trade-off between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive fuzzy controller and direct adaptive fuzzy controller. To confirm effectiveness of the proposed control scheme, the fractional order chaotic response system is fully illustrated to track the trajectory generated from the fractional order chaotic drive system. The numerical results show that tracking error and control effort can be made smaller and the proposed hybrid intelligent control structure is more flexible during the design process.

scholarly journals Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaobing Zhou ◽  
Lianglin Xiong ◽  
Xiaomei Cai
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Combination Synchronization ◽  
Special Cases ◽  
Complex Chaotic Systems

This paper investigates the combination-combination synchronization of four nonlinear complex chaotic systems. Based on the Lyapunov stability theory, corresponding controllers to achieve combination-combination synchronization among four different nonlinear complex chaotic systems are derived. The special cases, such as combination synchronization and projective synchronization, are studied as well. Numerical simulations are given to illustrate the theoretical analysis.

Modified Projective Synchronization of Chaotic Systems with Unknown Parameters

2011 ◽  
Vol 128-129 ◽  
pp. 1182-1185
Author(s):  
Min Xiu Yan ◽  
Li Ping Fan
Keyword(s):  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Adaptive Sliding Mode Control ◽  
Unknown Parameters ◽  
Response System ◽  
Uncertain Chaotic Systems ◽  
Modified Projective Synchronization

This paper proposes the modified projective synchronization of uncertain chaotic systems with unknown parameters via active adaptive sliding mode control (AASMC). The disturbances are considered both in the drive and the response system. The bounds of the disturbances are unknown. The adaptive updating laws are designed to tackle the unknown parameters. Moreover, the robustness and stability of the proposed AASMC is proved by the Lyapunov stability theory. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed scheme.

ADAPTIVE FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION IN THE IDENTICAL AND DIFFERENT CYQY HYPER-CHAOTIC SYSTEMS

2014 ◽  
Vol 28 (04) ◽  
pp. 1450013 ◽  
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
NA WEI ◽  
SI-HUI JIANG ◽  
XIU-KUN WANG
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Full State ◽  
Hybrid Projective Synchronization

This paper further investigates the adaptive full state hybrid projective synchronization (FSHPS) of hyper-chaotic systems — CYQY system with fully unknown parameters and perturbations. Based on the Lyapunov stability theory, adaptive controllers and updating laws of parameters can be designed for achieving the FSHPS of the CYQY hyper-chaotic systems with the same and different structures. Two groups numerical simulations are provided to verify the effectiveness of the proposed scheme.

scholarly journals Fuzzy Adaptive Controller Design for IPMSM with System Uncertainties and Disturbances Considering

2020 ◽  
Vol 30.8 (147) ◽  
pp. 22-26
Author(s):  
Nga Thi-Thuy Vu ◽  
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Sudden Change ◽  
Fuzzy Model ◽  
Lyapunov Theory ◽  
System Stability ◽  
Nonlinear Dynamic Model ◽  
Adaptive Fuzzy Controller ◽  
Adaptive Fuzzy ◽  
System Uncertainties

This paper proposed a T-S fuzzy model based adaptive fuzzy controller for the interior permanent magnet synchronous motors. Firstly, the T-S fuzzy model of the system is built based on the nonlinear dynamic model. Next, the adaptive fuzzy controller is designed to deal with the problems of system uncertainties and external disturbances. This controller includes two phases, one is for system stability and one for compensating the effect of the unknown components. The stability of the system, as well as the convergence of the adaptive law, is mathematically proven through Lyapunov theory. Finally, some simulations are done to verify the effectiveness of the presented scheme. The simulation results show that the proposed algorithm has a good response to the change of reference input, the system parameters variation, and the sudden change of the load torque.

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.

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