Delay Nonlinear Pure - Feedback Adaptive Fuzzy Tracking Control System

The nonlinear phenomenon and time delay are widespread in the industrial systems control and the objective world. The uncertainty, Internal or external interference and time delays and so on often lead down the stability and the performances of the control systems. They also bring inconvenience to the analysis and synthesis of systems. Therefore, the study of the control problem of the nonlinear time-daley systems has been a very active topic in the field of intelligent control subjects.Based on the above issues,this paper addresses the problem of adaptive fuzzy control for a class of uncertain nonlinear pure-feedback systems with time-varying delays.The unknown nonlinear functions are approximated by the fuzzy logic systems and then the adaptive fuzzy tracking controller is presented by using the back-stepping method and Lyapunov functionals.In addition, the work in the paper provides a new sufficient condition for the tracking control of nonlinear pure-feedback systems with time delays.1.Adaptive fuzzy control for a class of uncertain nonlinear pure-feedback systems.This section proposes a control scheme of adaptive fuzzy control for a class of uncertain nonlinear pure-feedback systems.Fuzzy logic systems and the backstepping techniques method are utilized to analy the system and construct adaptive fuzzy controller,and the Lyapunov stability theorem has proved that the desighed adaptive fuzzy tracking controller can ensure that the system output track the reference signal while the. tracking error converges to a small area around the origin.Simulation results show that the proposed adaptive controller guarantees that all the variables in the closed-loop system are bounded while the system’s output follows the given reference signal well.2.Adaptive fuzzy control for a class of uncertain nonlinear pure-feedback systems with time delays.This section proposes a control scheme of adaptive fuzzy control for a class of uncertain nonlinear pure-feedback systems with time delays. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and then adaptive technique and back stepping method are utilized to construct adaptive fuzzy controller that has a simpler structure and fewer learning parameters.Simulation results show that the proposed adaptive controller guarantees all the singles in the closed-loop system remain bounded in probability.