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

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.

Synthesis of Polynomial Fuzzy Model-Based Designs with Synchronization and Secure Communications for Chaos Systems with H∞ Performance

“…Let the Lyapunov function V(x) = xT (x)P( x) x(x), where P( x) = R −1 ( x) ∈ N × N is a polynomial matrix whose eigenvalues are greater than zero. This indicates that the polynomial Lyapunov function will be positive except for the states at the original point when (11) is held. Performing the differentiation of V(x) with respect to time obtains…”

“…Theorem 1. If the SOS-based stability criteria (11) and ( 12) are satisfied for a polynomial symmetric matrix R( x) ∈ N×N and a polynomial matrix O i (x) with prescribed ξ in (10), the system (7) will be H ∞ stable.…”

“…Furthermore, solving LMI-based stability conditions can secure the state feedback gain. Thus, chaotic systems have been synchronized through T-S fuzzy modeling and control [9][10][11][12]. In [9], the LMI-based fuzzy control was applied to synchronization of chaotic systems.…”

“…In [10], the perturbation observer-based LMI was engaged for the synchronization of T-S fuzzy chaos systems. In [11], the design of an adaptive TSK fuzzy self-organizing compensator was proposed for chaotic systems. An exact linearization (EL) technique, which was employed to synchronize the chaotic systems via the PDC, has been discussed [12].…”

A Type‐3 Fuzzy Approach for Stabilization and Synchronization of Chaotic Systems: Applicable for Financial and Physical Chaotic Systems

“…In [23], based on reinforcement learning and FLSs, a synchronization scheme is developed. e performance of FLS-based synchronization methods is evaluated and analyzed in [24]. In [25], improvement of the synchronization accuracy and the convergence speed is studied by the use of FLSs.…”