Direct adaptive control for nonlinear systems using a TSK fuzzy echo state network based on fractional-order learning algorithm

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.