Fuzzy Modelling and Chaos Control in the Photogravitational Magnetic Binary Problem With Potential From a Belt

2020 ◽  
Vol 9 (3) ◽  
pp. 26-39
Author(s):  
Mohd Arif
Keyword(s):  
Chaos Control ◽  
Chaotic Systems ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Control Object ◽  
Unified Approach ◽  
Fuzzy Modelling ◽  
Binary Problem ◽  
Long Time ◽  
Material Points

Control of chaotic systems has led to many fruitful results, such as the famous OGY and feedback control. Of course, controlling chaos is not limited to the approaches above and is not specifically reviewed one by one here. The representation of chaotic systems using fuzzy models has a unified approach. The fuzzy logic controllers had been proposed for a long time and were successfully applied to control the chaos in many systems. The main purpose of this study is to presents the new fuzzy model for the photogravitational magnetic-binary problem (PMBP) where the bigger primary is a source of radiation and the smaller primary is an oblate body; and they are encompassed by a homogeneous circular cluster of material points centred at the mass centre of the system (belt). It was shown that using a new fuzzy controller, it is possible to control of chaotic behaviour of the photogravitational magnetic-binary problem (PMBP). The simulation results have demonstrated that the proposed method can satisfy the control object and enhanced stability.

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.

scholarly journals T-S Fuzzy Modelling and H∞ Attitude Control for Hypersonic Gliding Vehicles

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Weidong Zhang ◽  
Xianlin Huang ◽  
Xiao-Zhi Gao
Keyword(s):  
Attitude Control ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Attitude Dynamics ◽  
Approximation Accuracy ◽  
Fuzzy Modelling ◽  
Original Plant ◽  
Operating Points

This paper addresses the T-S fuzzy modelling and H∞ attitude control in three channels for hypersonic gliding vehicles (HGVs). First, the control-oriented affine nonlinear model has been established which is transformed from the reentry dynamics. Then, based on Taylor’s expansion approach and the fuzzy linearization approach, the homogeneous T-S local modelling technique for HGVs is proposed. Given the approximation accuracy and controller design complexity, appropriate fuzzy premise variables and operating points of interest are selected to construct the T-S homogeneous submodels. With so-called fuzzy blending, the original plant is transformed into the overall T-S fuzzy model with disturbance. By utilizing Lyapunov functional approach, a state feedback fuzzy controller has been designed based on relaxed linear matrix inequality (LMI) conditions to stable the original plants with a prescribed H∞ performance of disturbance. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed H∞ T-S fuzzy controller for the original attitude dynamics; the superiority of the designed T-S fuzzy controller compared with other local controllers based on the constructed fuzzy model is shown as well.

scholarly journals New Results on Fuzzy Synchronization for a Kind of Disturbed Memristive Chaotic System

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Wang ◽  
L. L. Chen
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Control Method ◽  
Fuzzy Controller ◽  
Fuzzy Theory ◽  
Fuzzy Model ◽  
H Infinity ◽  
The Given

This paper concerns the problem on the fuzzy synchronization for a kind of disturbed memristive chaotic system. First, based on fuzzy theory, the fuzzy model for a memristive chaotic system is presented; next, based on H-infinity technique, a multidimensional fuzzy controller and a single-dimensional fuzzy controller are designed to realize the synchronization of master-slave chaotic systems with disturbances. Finally, some typical examples are included to illuminate the correctness of the given control method.

APPLICATION AND ROBUSTNESS DESIGN OF FUZZY CONTROLLER FOR RESONANT AND CHAOTIC SYSTEMS WITH EXTERNAL DISTURBANCE

2005 ◽  
Vol 13 (03) ◽  
pp. 281-295 ◽  
Author(s):  
FENG-HSIAG HSIAO ◽  
WEI-LING CHIANG ◽  
CHENG-WU CHEN ◽  
SHENG-DONG XU ◽  
SHIH-LIN WU
Keyword(s):  
Chaotic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Design Method ◽  
Direct Method ◽  
External Disturbance ◽  
Approximation Error ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Resonant Systems

A robustness design of fuzzy control via model-based approach is proposed in this paper to overcome the effect of approximation error between nonlinear system and Takagi-Sugeno (T-S) fuzzy model. T-S fuzz model is used to model the resonant and chaotic systems and the parallel distributed compensation (PDC) is employed to determine structures of fuzzy controllers. Linear matrix inequality (LMI) based design problems are utilized to find common definite matrices P and feedback gains K satisfying stability conditions derived in terms of Lyapunov direct method. Finally, the effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic and resonant systems.

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 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.

CHAOTIC CONTROL AND CHAOTIFICATION USING FUZZY APPROACH

2008 ◽  
Vol 18 (01) ◽  
pp. 263-274
Author(s):  
KUANG-YOW LIAN ◽  
CHENG-SEA HUANG ◽  
WEN-HSIEN FANG ◽  
CHIEN-HSING SU
Keyword(s):  
State Feedback ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Feasible Solution ◽  
Fuzzy Model ◽  
Stabilization Problem ◽  
Unified Approach ◽  
Closed Loop System ◽  
Chaotic Control ◽  
The Stability

In this paper, we propose a fuzzy model-based methodology to deal with various control objectives for discrete-time chaotic systems from a unified viewpoint. With intent to unify the design process, we introduce a new design concept called virtual-desired-variable synthesis. Then, both the chaotic control and chaotification are eventually treated as a stabilization problem. Consequently, the conditions concerning the stability of the closed-loop system are formulated into LMIs. A feasible solution of the LMI problem guarantees the quadratical stability and gives the state feedback gains as well. The well-known Hénon map is used to demonstrate the unified approach.

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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