Small-Gain Technique-Based Adaptive Control Design For Switched Pure-Feedback Nonlinear Systems

As a typical class of hybrid systems,switched systems have attracted a great deal of attention because of their importance from both theoretical and practical points of view.Many practical systems can be modeled as switched systems,such as chemical processes,mechatronic and mechanical systems,switching power converters,and so on.Unlike non-switched systems,the study of switched systems is a challenging topic in the modern engineering literature because switched systems are characterized by intertwined continuous dynamics and discrete dynamics.On the other hand,compared with strict-feedback nonlinear systems,switched pure-feedback nonlinear systems have a more general structure,and such system has no affine appearance of the state variables to be used as virtual controls and actual control in the backstepping recursive design procedure.Therefore,the study of pure feedback switched systems has important significance both in theory development and engineering applications.Based on the current research status of switched pure-feedback nonlinear systems,the problems of stabilization,tracking control and output-feedback control are investigated by exploiting switched systems theory,backstepping,the common Lyapunov function(CLF)method,the average dwell time(ADT)method,input-to-state stability(ISS)analysis and a small-gain technique.The main results of this thesis are summarized as follows:(1)The problem of adaptive neural networks(NNs)tracking control is investigated for a class of completely non-affine switched pure-feedback uncertain nonlinear systems with switched reference model.A sufficient and necessary condition for the control problem to be solvable is derived by exploiting the common Lyapunov function(CLF)method,backstepping,input-to-state stability(ISS)analysis and the small-gain technique.Also,a small-gain technique based adaptive NN control scheme is provided to avoid the designed difficulty caused by the construction of an overall CLF for the switched closed-loop system,which is usually required when studying the switched pure-feedback system.Adaptive NN controllers of individual subsystems are constructed to guarantee that all of the signals in the closed-loop system are semi-globally uniformly ultimately bounded under arbitrary switchings,and the tracking error converges to a small neighborhood of the origin.Two examples,which include a continuously stirred tank reactor(CSTR)system,are presented to demonstrate the effectiveness of the proposed design approach.(2)The problem of adaptive output-feedback neural networks control is addressed for a class of switched pure-feedback uncertain nonlinear systems.A switched observer is first constructed to estimate the unmeasurable states.Next,with help of NN to approximate the unknown nonlinear terms,a switched small-gain technique-based adaptive output-feedback NN control scheme is developed by exploiting the backstepping recursive design scheme,input-to-state stability(ISS)analysis,the common Lyapunov function(CLF)method and the average dwell time(ADT)method.The proposed controllers for individual subsystems guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded under a class of switching signals with ADT,and finally two examples illustrate the effectiveness of theoretical results.The conclusions and perspectives are presented in the end of the thesis.