This paper studies the ${\mathit{H}}_{\infty }$ 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 $H_{\infty }$ 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 $H_{\infty }$ 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 $H_{\infty }$ control scheme.

本文研究了 ${\mathit{H}}_{\infty }$不确定非线性多变量系统的跟踪控制。我们提出了一种控制策略，该策略结合了自适应小波型Takagi-Sugeno-Kang（TSK）模糊脑情感学习控制器（WTFBELC）和$H_{\infty }$强大的跟踪补偿器。对于自适应WTFBELC，它是一个主控制器，旨在模仿理想控制器。提出的WTFBELC是为了获得更好的处理非线性和不确定性的能力，但是提出的$H_{\infty }$鲁棒的跟踪补偿器用于补偿自适应WTFBELC和理想控制器之间的残留误差。此外，通过使用粒子群优化（PSO）算法快速搜索自适应WTFBELC的最佳学习率，并基于最速下降梯度法推导参数更新定律。基于Lyapunov稳定性理论，可以保证这种新颖控制方案的鲁棒跟踪性能。质量弹簧阻尼器机械系统和三连杆机器人操纵器用于验证所提出的自适应PSO-WTFBELC的有效性$H_{\infty }$ 控制方案。