Design of Adaptive TSK Fuzzy Self-Organizing Recurrent Cerebellar Model Articulation Controller for Chaotic Systems Control

Shun-Yuan Wang,Chen-Hao Li,Chuan-Min Lin

doi:10.3390/app11041567

Abstract

The synchronization and control of chaos have been under extensive study by researchers in recent years. In this study, an adaptive Takagi–Sugeno–Kang (TSK) fuzzy self-organizing recurrent cerebellar model articulation controller (ATFSORC) is proposed, which is composed of a set of TSK fuzzy rules, a cerebellar model articulation controller (CMAC), a recurrent CMAC (RCMAC), a self-organizing CMAC (SOCMAC), and a compensation controller. Specifically, SOCMAC, RCMAC, and adaptive laws are adopted so that the association memory layers of ATFSORC can be modulated in accordance with the layer decision-making mechanism in order to reduce the structure complexity and improve the control performance of ATFSORC. Moreover, the Takagi–Sugeno–Kang fuzzy rules are introduced to increase the learning speed of ATFSORC, and the improved compensating controller is designed to dispel the errors between an ideal controller and the TFSORC. Moreover, the proposed ATFSORC is applied to chaotic systems in order to validate its performance and feasibility. Several simulation schemes are demonstrated to show the effectiveness of the proposed method. Simulation results show that the proposed ATFSORC can obtain a favorable control performance when the chaotic systems are operated at different parameters. Specifically, ATFSORC can achieve faster convergence of the tracking error than fuzzy CMAC (FCMAC) and CMAC.

Highlights

Similar self-organizing recurrent artificial neural network architecture and adaptive rules are adopted so that the cerebellar model articulation controller (CMAC) that is originally static with a fixed number of association memory layers possesses dynamic memory ability and the number of association memory layers can be changed along with the layer decision-making mechanism
The proposed ATFSORC was applied on the synchronization control of chaotic systems, and it was compared with CMAC and fuzzy CMAC (FCMAC) to validate the control performance of the proposed ATFSORC
0.01 and 1 as well as by changing the cut-in control time point of ATFSORC to 300 s after the chaotic system running, the simulation would validate the feasibility of the controller proposed in this study

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Chaos is ubiquitous and exists in various scientific fields. It has been receiving attention widely from many scholars and has been extensively studied [1,2,3,4,5]. The chaotic system is very sensitive to the initial conditions, so the behavior of a chaotic system is eventually unpredictable. If the chaotic phenomenon can be appropriately controlled, it may be of tremendous benefit in various applications because of the highly nonlinear characteristics of chaotic systems. The research overview for the synchronization and stability control of chaotic systems is discussed below

Objectives

Methods

Results