Function-Link Fuzzy Cerebellar Model Articulation Controller Design for Nonlinear Chaotic Systems Using TOPSIS Multiple Attribute Decision-Making Method

Abstract

This paper aims to propose a more efficient control algorithm to select suitable firing nodes, improve the computational efficiency, reduce the number of firing rules and achieve good performance for nonlinear chaotic systems. A novel function-link fuzzy cerebellar model articulation controller (FLFCMAC) is designed by using a multiple attribute decision-making method named as technique for order of preference by similarity to ideal solution (TOPSIS). The TOPSIS is used to determine the optimal threshold values for receptive-field basis function in association memory space such that the firing fuzzy rules can be effectively reduced. In the TOPSIS design, the Shannon entropy index is used to derive the objective weights of the evaluation attribute. The proposed control system is composed of a TOPSIS-based FLCMAC (TFLFCMAC) and a fuzzy compensator. The TFLFCMAC is the main tracking controller employed to mimic an ideal controller, and the fuzzy compensator can eliminate the approximation error between the TFLFCMAC and the ideal controller. The parameters of the proposed TFLFCMAC are tuned online using the adaptation laws that are derived from a Lyapunov stability theorem, so that the system’s stability is guaranteed. Finally, the proposed control system is applied to a Duffing–Holmes chaotic system and a gyro chaotic system to illustrate its favorable control performance and to show its superiority to the other control techniques.