Prescribed Performance Control Design For Switched Nonlinear Systems

With the improvement of complexity of the systems,non-switched models can no longer meet the needs of application and research,so switched model emerges.At the beginning of the study,scholars focused on the stability of switched systems,so abundant research results have been achieved on stability properties of switched systems,and several methods,such as common Lyapunov function,multiple Lyapunov functions,average dwell time,and so forth,have been proposed.However,for practical systems,such as aircraft systems and traffic control,it is incomplete only to consider the stability of a system,transient performance and steady state performance and other properties are also of great importance.In this case,the prescribed performance which can pay attention to the stability of systems as well as the transient performance of systems has been provided.However,in the aforementioned literature,most works developed on the prescribed performance control technique focus on non-switched nonlinear systems,less attention about how to develop the prescribed performance control technique has been paid to switched nonlinear systems.In this thesis,several control schemes are proposed for several classes of switched systems with prescribed performance.The main contributions are summarized as follows:First,a partial state feedback control design scheme with average dwell time is proposed for a class of switched cascaded nonlinear systems with dynamic uncertainty,unknown nonlinearities and time-varying disturbances.By introducing an equivalent system,the problem of prescribed performance of the original switched system is transformed into the problem of stabilization of the equivalent system,and the inequality constraint of the tracking error required by the prescribed performance is transformed into the equality constraint.For this equivalent unconstrained switched system,the average dwell time method is introduced into the backstepping design approach.Then for the unmeasurable state,a method of resetting the average dwell time is proposed,which proves that the state is bounded under a certain average dwell time.For the measurable state,the Lyapunov function is constructed to prove the boundedness of the state,and the Nussbaum function is employed to solve the unknown symbol problem of the unknown control gain.The controllers of subsystems are designed to guarantee prescribed bounds on the transient and steady-state performance of the output tracking errors,plus the boundedness of all other signals in the resulting closed-loop system under a class of switching signals with average dwell time.Simulation results demonstrate the effectiveness of the proposed approach.Second,a state feedback control scheme under arbitrary switching signals is proposed for a class of uncertain switched nonlinear pure feedback systems,capable of guaranteeing,for any initial system condition,output tracking with prescribed performance and bounded closed loop signals.The proposed state feedback controller isolates the output performance characteristics from control gains selection and exhibits strong robustness against model uncertainties.At the same time,the constructed controller avoids using the high-order derivative of the desired trajectory and reduces the complexity of the controller.Simulation results demonstrate the effectiveness of the proposed approach.The conclusions and perspectives are presented in the end of the thesis.