Adaptive fuzzy tracking control for a class of pure-feedback nonlinear systems with time-varying delay and unknown dead zone

This paper investigates the problem of adaptive fuzzy tracking control for a category of pure-feedback nonlinear systems with time-varying delay and unknown dead zone. Fuzzy logic systems are used to identify unknown functions existing in systems. Mean-value theorem is introduced to overcome the difficulty arising from the pure-feedback structure in designing controller. Based on the information of dead-zone slopes, dead zone is handled. Only one adaptive parameter needs updating online by considering the norm of membership function vectors rather than all sub-vectors. Moreover, utilizing the adaptive backstepping technique, a novel adaptive fuzzy tracking control scheme is developed to guarantee all signals of the closed-loop systems are semi-globally uniformly ultimately bounded, and the tracking error can be regulated to the origin with a small neighborhood. The stability of the closed-loop system is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach.