Research On Robust Hybrid Control Of Switched Nonlinear Systems

In recent years,the stability theory and application of switched linear systems are gradually improved while there are still many challenging problems remaining in the control of switched nonlinear system which is a universal system in practical application.Switched nonlinear system is mainly composed of several switched nonlinear subsystems and a switching function.The complex dynamic characteristics,which mainly come from nonlinear characteristics of the nonlinear subsystems and discrete dynamics of the switching function,make the traditional continuous control and discrete control fail to achieve ideal control properties when applied on the switched nonlinear system.In this paper,the control problems of two important switched nonlinear systems are studied based on hybrid control theory.The contents of this thesis include the following three points:1.A switched affine system model based on DC-DC buck converter is established.Considering all subsystems probably generated from switched action,the closed-loop hybrid system is established.According to the properties of the proposed Lyapunov function and its derivatives along switched subsystems,a robust switched control strategy based on state feedback is designed.Based on the stability theory of hybrid system,the stability of the closed-loop system is analyzed in order to obtain the control parameters reasonably.A sufficient condition for the asymptotic stability of a particular equilibrium point is derived.Since the switching frequency of the switching actuator is limited in practice,the robustness properties of both general disturbance and spatial regularization are proposed.The results exclude zeno behaviour of the closed-loop system when reaching the equilibrium point.Finally,the effectiveness of the proposed control strategy is verified by numerical simulation.2.Considering a perturbed model of the general uncertain switched affine system,a robust switching control strategy based on output feedback is designed when parts of the system state are unavailable.Firstly,a robust switching control based on static output feedback is designed.The common Lyapunov function is introduced to derive a sufficient condition assuring the asymptotic stability of a particular equilibrium point.The sufficient condition takes form of linear matrix inequalities.Then,the dynamic output feedback is introduced to reduce the conservatism of the control parameters derived from the static output feedback.The asymptotic stability of a particular equilibrium point is also guaranteed by a common Lyapunov function.The results show that the proposed switched control strategy can achieve robustness property under parameter uncertainty and external disturbance,and drive the state of the system from any initial point to the desired equilibrium point.Finally,the effectiveness of the proposed control strategy is verified by numerical simulation and experimental platform.3.For switched Lurie systems,an event-triggered state feedback control law based on boundary constraint is designed under given switching function.Firstly,a continuous state feedback control is proposed to achieve asymptotic stability of switched Lurie system under given switching function by solving the linear matrix inequalities proposed.Based on the above continuous state feedback control,the event-triggered control is introduced to reduce the update of the control input.The basic idea is to introduce two auxiliary systems as the boundary,which limits the evolution of the system state.Then,the whole closedloop system is modeled as a hybrid system with dwell-time.The stability and robustness of the closed-loop system are analyzed based on the hybrid control theory.Finally,the effectiveness of the proposed control strategy is verified by a numerical simulation.