Adaptive Backstepping Control And Analysis For Uncertain Nonliner Systems

In recent years,the control field has studied nonlinear systems and obtained many valuable results on the stability,controllability,observability,switching stabilization and other synthesis problems.The Backstepping method is widely used in the control problems of nonlinear systems,especially the smooth nonlinear systems with lower triangular form.As an effective method,it has been paid more and more attention.In many practical systems,uncertainties often exist,and fuzzy systems are powerful tools for dealing with uncertain nonlinear systems due to their general approximation properties.Therefore,this thesis combines Backstepping technology with fuzzy adaptive control design,an adaptive fuzzy control method is proposed to solve the problem of state feedback for uncertain switched systems and output feedback control for uncertain non-smooth systems.The main contents of the study are as follows:(1)This thesis is concerned with the problem of adaptive tracking control for a class of uncertain switched nonlinear systems with completely unknown backlash-like hysteresis control input.By combining adaptive Backstepping technique with fuzzy systems approximation ability,an adaptive neural control algorithm is presented for the systems under consideration.The explosion of complexity in traditional Backstepping design is avoided by using dynamic surface control.It is demonstrated that the practical output tracking performance is achieved by using the proposed state-feedback controllers,and all the signals remain bounded.Finally,simulation results are given to show the effectiveness of the theoretical approaches.(2)The problem of adaptive output-feedback control for a class of non-smooth nonlinear systems is studied.First,the concept of semi-globally uniformly ultimately bounded(SGUUB)stability that has been widely used for smooth nonlinear systems with lower triangular systems is extended to the non-smooth systems.Then by resorting to set-valued maps and set-valued derivatives,a new Lyapunov criterion ensuring the SGUUB stability is developed for non-smooth nonlinear systems,which establishes the theory foundation for the subsequent Backstepping control design.With the help of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions,the system under investigation is first transformed into an equivalent model.In the sequel,exploring some efficient techniques,an adaptive fuzzy output-feedback controller is constructed for the systems under consideration by utilizing an appropriate observer and the approximation ability of fuzzy systems.