Adaptive Fuzzy Control For Nonlinear Systems With Constraints

In recent years,some progress has been made in the research of nonlinear systems control,but there are still a lot of problems need to be studied in depth.Firstly,most of the existing adaptive control research for nonlinear systems are based on state unconstrained conditions.While constraints exist in actual systems,and violation of constraints will result in systems performance degradation or system instability.Secondly,most of the existing research on constrained nonlinear systems are based on the measurable states,and then we design an adaptive controller to achieve systems stability.But the states of the actual systems are often unmeasurable.Furthermore,the existing research of constrained nonlinear systems are always focus on constant constraints,but there are few researches focus on time-varying constraints.This paper mainly deals with the problem of tracking control of constrained nonlinear systems with unmeasurable states.In this paper,we study the constrained control problems of the pure feedback systems and the non-strict feedback systems.Details are listed as follows.1.Firstly,this paper investigated the tracking control problem for nonlinear pure feedback systems with full state constraints and the controlled systems states can not be measured.By constructing barrier Lyapunov functions and using fuzzy logic systems to approximate the unknown nonlinear functions,the fuzzy states observer is designed to estimate the immeasurable states of the controlled systems.Through taking the barrier Lyapunov functions into account in every step of Backstepping process,an output feedback controller satisfying the full state constraints is designed.The designed control strategy ensures that the tracking error is uniformly ultimately bounded.2.Secondly,this paper investigated the tracking control problem for nonlinear nonstrict feedback systems with full state constraints.The linear high gain observer is designed to estimate the immeasurable systems states.By the technique of variable separation,the Backstepping design difficulty caused by the non-strict feedback structure is solved.The fuzzy logic system is used to approximate the unknown nonlinear function.And then by considering the barrier Lyapunov functions in every step of Backstepping process,the output feedback controller is designed and the tracking error is uniformly ultimately bounded.At the same time,full state constraints are not violated.3.Finally,this paper deals with the tracking control problem for a class of nonlinear time-varying time-delay systems with time-varying output constraints and input saturation.Fuzzy observer is applied to estimate the immeasurable states of the systems.The auxiliary dynamic system is used to compensate the input saturation,and the asymmetrical barrier Lyapunov function is considered to ensure that the time-varying output constraints are not violated.In this part,we also ensured that the states constant constraints are not violated.Based on adaptive Backstepping control and Lyapunov stability theorem,and then we can prove that the proposed adaptive fuzzy output feedback controller satisfying the constraints.And then all the closed-loop systems signals are uniformly ultimately bounded.