Adaptive Fuzzy Control for Nonlinear Time-Delay Systems with Dynamical Uncertainties

Abstract

In this paper, an adaptive fuzzy backstepping robust control approach is proposed for a class of SISO nonlinear strict-feedback systems. The nonlinear systems addressed in this paper are assumed to possess three uncertainties: (i) the unstructured uncertainties; (ii) the time delays; and (iii) the dynamics uncertainties. In adaptive backstepping recursive design, fuzzy logic systems are used to approximate the unstructured uncertainties. A nonlinear damping technique and Lyapunov–Krasovskii functions are introduced to cancel the effects of the dynamics uncertainties and deal with the time delays, respectively. Combining the backstepping technique and a small gain approach, a stable adaptive fuzzy robust control approach is developed. It is proved that all the signals of the closed-loop system are semi-golablly uniformaly ultimately bounded (SUUB). The effectiveness of the proposed approach is illustrated by a simulation example.