Design of an adaptive self-organizing fuzzy neural network controller for uncertain nonlinear chaotic systems

Abstract

Though the control performances of the fuzzy neural network controller are acceptable in many previous published papers, the applications are only parameter learning in which the parameters of fuzzy rules are adjusted but the number of fuzzy rules should be determined by some trials. In this paper, a Takagi–Sugeno-Kang (TSK)-type self-organizing fuzzy neural network (TSK-SOFNN) is studied. The learning algorithm of the proposed TSK-SOFNN not only automatically generates and prunes the fuzzy rules of TSK-SOFNN but also adjusts the parameters of existing fuzzy rules in TSK-SOFNN. Then, an adaptive self-organizing fuzzy neural network controller (ASOFNNC) system composed of a neural controller and a smooth compensator is proposed. The neural controller using the TSK-SOFNN is designed to approximate an ideal controller, and the smooth compensator is designed to dispel the approximation error between the ideal controller and the neural controller. Moreover, a proportional-integral (PI) type parameter tuning mechanism is derived based on the Lyapunov stability theory, thus not only the system stability can be achieved but also the convergence of tracking error can be speeded up. Finally, the proposed ASOFNNC system is applied to a chaotic system. The simulation results verify the system stabilization, favorable tracking performance, and no chattering phenomena can be achieved using the proposed ASOFNNC system.