Observer-based Adaptive Fuzzy Backstepping Control for Strict-feedback Nonlinear Systems with Unknown Time Delays

In this paper, an adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time delays and unmeasured states. By using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed for estimating the unmeasured states. By combining the adaptive backstepping technique with adaptive fuzzy control design, an adaptive fuzzy output feedback backstepping control approach is developed. It is mathematically proved that the proposed adaptive fuzzy control approach is able to guarantee that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded (SUUB) and that the tracking error converges to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the proposed approach.