Observer-based adaptive fuzzy backstepping dynamic surface control for a class of non-linear systems with unknown time delays

An adaptive fuzzy backstepping control approach is considered for a class of non-linear systems with unknown time delays and immeasurable states. Fuzzy logic systems are used to approximate the unknown non-linear functions, and a fuzzy state observer is designed for estimating the immeasurable states. By combining the adaptive backstepping technique and dynamic surface control technique, an adaptive fuzzy output-feedback backstepping control approach is developed. The proposed control method not only overcomes the problem of `explosion of complexity` inherent in typical backstepping design approaches but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed-loop adaptive control system are semi-globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighbourhood of the origin with appropriate choice of design parameters. Simulation results are provided to show the effectiveness of the proposed approach.