Design of Fast Variable Structure Adaptive Fuzzy Control for Nonlinear State-Delay Systems with Uncertainty

Abstract

In this study, a new fast variable structure adaptive fuzzy controller is presented for nonlinear state-delay systems which are subjected to external disturbances and uncertainties. The undesirable chattering and singularity of the variable structure scheme are eliminated by using a novel fast robust high-precision continuous nonsingular control law which is able to accelerate the finite-time convergence both in reaching and sliding phases of the motion. A fuzzy logic system with a neural network adaptive law is used to approximate the dynamics of the nonlinear system containing the current state and the delayed state. The superiority of the proposed fuzzy neural network in online adjusting the weights of the network is the fast convergence rate of the approximation error to the optimum value in a very short time. The stability of the closed-loop system is proved by using an extended finite-time Lyapunov criterion such that the convergence of the position tracking error, velocity tracking error, and the estimation error to the bounded region is guaranteed in a very short time. Two second-order uncertain nonlinear simulation examples with external disturbances are given to evaluate the efficacy of the proposed control technique. The simulation results show that faster and high-precision tracking performance is obtained compared with the existing recent works focused on robust control of nonlinear state-delay systems with uncertainties.