This paper presents a new Takagi-Sugeno-Kang fuzzy Echo State Neural Network (TSKFESN) structure to design a direct adaptive control for uncertain SISO nonlinear systems. The proposed TSKFESN structure is based on the echo state neural network framework containing multiple sub-reservoirs. Each sub-reservoir is weighted with a TSK fuzzy rule. The adaptive law of the TSKFESN-based direct adaptive controller is derived by using a fractional-order sliding mode learning algorithm. Moreover, the Lyapunov stability criterion is employed to verify the convergence of the fractional-order adaptive law of the controller parameters. The evaluation of the proposed direct adaptive control scheme is verified using two case studies, the regulation problem of a torsional pendulum and the speed control of a direct current (DC) machine as a real-time application. The simulation and the experimental results show the effectiveness of the proposed control scheme.

本文提出了一种新的 Takagi-Sugeno-Kang 模糊回声状态神经网络 (TSKFESN) 结构，以设计不确定 SISO 非线性系统的直接自适应控制。所提出的 TSKFESN 结构基于包含多个子水库的回声状态神经网络框架。每个子水库都用 TSK 模糊规则加权。基于 TSKFESN 的直接自适应控制器的自适应律是通过使用分数阶滑模学习算法推导出来的。此外，采用Lyapunov稳定性判据来验证控制器参数分数阶自适应律的收敛性。所提出的直接自适应控制方案的评估通过两个案例研究得到验证，扭摆的调节问题和作为实时应用的直流 (DC) 电机的速度控制。