Fuzzy Echo State Neural Networks and Funnel Dynamic Surface Control for Prescribed Performance of a Nonlinear Dynamic System

This paper presents a funnel dynamic surface control combined with fuzzy echo state networks (FESNs) for the prescribed tracking performance of a strict feedback multi-input–multi-output (MIMO) nonlinear dynamic system. A new funnel variable is defined so that the funnel virtual control forces the tracking error to fall within funnel boundary, and adaptive FESN method is also proposed to improve the approximation performance in conventional neural network algorithms. A strict feedback controller and adaptive laws for estimating the uncertainties were derived using the recursive steps of dynamic surface control based on the Lyapunov stability theory. Lyapunov stability analysis confirmed the boundedness and convergence of the closed-loop system. The performance of the proposed control scheme was validated by simulations and experimental applications to the tracking control of a MIMO nonlinear system and a robot manipulator.