H∞ tracking control for nonlinear multivariable systems using wavelet-type TSK fuzzy brain emotional learning with particle swarm optimization

Abstract This paper studies the H ∞ tracking control for uncertain nonlinear multivariable systems. We propose a control strategy, which combines the adaptive wavelet-type Takagi-Sugeno-Kang (TSK) fuzzy brain emotional learning controller (WTFBELC) and the H ∞ robust tracking compensator. As for the adaptive WTFBELC, it is a main controller designed to mimic the ideal controller. The proposed WTFBELC is to obtain much better ability of handling nonlinearities and uncertainties, but the proposed H ∞ robust tracking compensator is to compensate the residual error between the adaptive WTFBELC and the ideal controller. Furthermore, the optimal learning rates of the adaptive WTFBELC are searched quickly by using the particle swarm optimization (PSO) algorithm, and the parameter updated laws are derived based on the steepest descent gradient method. The robust tracking performance of this novel control scheme is guaranteed based on Lyapunov stability theory. The mass-spring-damper mechanical system and the three-link robot manipulator, are used to verify the effectiveness of the proposed adaptive PSO-WTFBELC H ∞ control scheme.