Study On Passivity And Constrained Control For Switched Nonlinear Systems

Switched systems consist of finite subsystems and a switching law determining the instant when some subsystem is activated.Switched systems have very complex dynamic behavior.In particular,switching laws directly affect dynamic behavior of switched systems.Benefiting from the importance in engineering applications and theory analysis,switched systems have become a hot topic in the field of control study and also attracted a lot of interests of many researchers.Nevertheless,due to the interaction of discrete dynamics and continuous dynamics,switched systems,generally speaking,have more complicated dynamic behavior than non-switched systems.In addition,passivity,as an important system property,has been widely used in analysis and control for nonlinear systems.However,the research on passivity for switched nonlinear systems is still immature,and there are many problems which deserve further study.This thesis studies passivity and constrained control problems for switched nonlinear systems.The main contributions of this thesis are as follows.(1)The issue of adaptive output tracking control for a class of switched nonlinear systems with uncertain parameters is investigated,where the solvability of the corresponding control problem for each subsystem is unnecessary.Individual update laws corresponding to different unknown parameters are designed in order to reduce the conservativeness produced from the adoption of a common update law.First,we feedback passivate each subsystem of switched systems in the associated subregions.Then,by passivity obtained,the dual design of the adaptive controllers and a state-dependent switching law is constructed to solve the adaptive output tracking control problem for the resulting closed-loop system.(2)A framework of regional passivity theory for switched systems is set up using multiple barrier storage functions.First,by introducing the barrier storage function,the notion of regional passivity for non-switched systems is presented and an associated switching version is also given subsequently.Then,a sufficient condition is provided under which a switched system is regionally passive.Second,regional passivity is shown to be preserved under feedback interconnection,and asymptotic stability can be reached if a switched system is strictly regionally passive or regionally passive plus asymptotic detectability,and meanwhile the system trajectory remains in the corresponding open region.Third,as an application of the theory provided,the stabilization problem for state-constrained strict-feedback switched nonlinear systems is solved,where no subsystem is required to be stabilizable.Finally,the notion of adaptive feedback regional passivation is introduced,and a co-design of controllers and a switching law is also provided to guarantee that the adaptive stabilization issue for a class of state-constrained strict-feedback switched nonlinear systems with unknown parameters is solvable.(3)The problem of finite-time H? control for switched nonlinear systems is studied.This problem is studied in two parts.First,the notion of finite-time H? control for switched systems is introduced.The solvability condition of the finite-time H? control problem for a class of switched nonlinear systems is presented,where the powers of chained integrators associated with individual subsystems can be different positive odd rational numbers from each other.Moreover,based on the method of multiple Lyapunov functions and the technique of adding a power integrator,a family of controllers and a proper switching law are designed such that the finite-time H? control problem of the resulting closed-loop system is solvable.Second,the issue of passivity-based finite-time H? control for switched nonlinear systems with more general structure is investigated.Specially,when the nominal system corresponding to each subsystem in some associated subregion is finite-time passive,the solvability of the issue under study is obtained via a co-design of output controllers and a switching law.In addition,if each nominal system does not possess the finite-time passivity property,a control strategy based on finite-time feedback passivation is also estabilished.Furthermore,it is shown that,in finite-time H? control,control behavior gives rise to the result that the system still has the practical stability property even suffering some special forms of exogenous disturbances,which is difficult to be assured in traditional H? control no matter how small exogenous disturbances are.(4)The passivity-based mean square exponential stabilization problem for switched stochastic nonlinear systems is studied.First,a concept of generalized small-time norm-observability is presented and an appropriate test condition is also provided.Additionally,design of controllers is also provided such that the resulting closed-loop system is mean-square exponentially stable with respect to an average dwell time and a passivity rate given in prior,where there is at least one stochastic subsystem which is passive.(5)The stabilization issues for state-constrained high-order switched nonlinear systems are investigated.This study is composed of two parts as follows:(i)the robust stabilization issue for a class of state-constrained high-order switched nonlinear systems is addressed,where all subsystems are allowed to be unstabilizable.On the basis of effective coupling of the technique of adding a power integrator and the method of multiple barrier Lyapunov functions,the co-design of robust controllers and a switching law is carried out such that the resulting closed-loop system is asymptotically stable and meanwhile the violation of the constraints does not happen.Moreover,the requirement of the connection of barrier Lyapunov functions for two adjacent subsystems on the switching instants,and even a certain amount of jump is also allowed;(ii)the adaptive stabilization issue for a class of state-constrained high-order switched nonlinear systems with known parameters is concerned.A sufficient condition guaranteeing the solvability of the adaptive stabilization issue for state-constrained high-order switched nonlinear systems is provided,where no subsystem is required to be stabilizable.Further,based on multiple barrier Lyapunov functions constructed,a design strategy of adaptive controllers and a state-dependent switching law is presented.Finally,the conclusions and perspectives are presented.