Research On Model Reference Adaptive Constraints And Tracking Control Of Switched Systems

Many complex systems established according to the development needs in real life are accompanied by time-varying and unstable,and only one equation of motion expressed in the form of differential equations is not enough to fully describe the dynamics of the system.Moreover,for a discrete system or continuous system,the control effect of single control is not ideal.The switched systems can overcome the shortcomings of such problems effectively.On the one hand,the switched systems can describe some complex systems with multiple modes.On the other hand,the control of complex systems by the switched systems theory can achieve control effects that cannot be achieved by a single control.In recent years,switched systems have gained extensive research.Modeling uncertainties usually exist in switched systems.The coexistence and interaction of continuous dynamics,discrete dynamics and uncertainties make the behavior of the system extremely complex,and the operating mechanism of the system unclear.Many control problems need to be solved.In addition,in practice,the switched systems must be constrained,including state constraints and output constraints and so on.These constraints will directly affect the control design of the switched systems.At present,the research on this aspect is quite limited.Aiming at the above problems,this thesis mainly studies the model reference adaptive control problem of switched systems with state constraints under arbitrary switching and the model reference adaptive tracking control problems of switched systems with unstable subsystems under slow switching.The uncertainties,state constraints and switching conditions of the system are analyzed and assumed,and the switching adaptive controller and switching signals are designed to ensure the stability of the switched systems.The main work of this thesis is as follows:(1)According to the given switched system models,the switched reference models are established,and the stability of the switched reference models is analyzed under the condition of state constraints and unstable subsystems,respectively.(2)The model reference adaptive control problem for switched systems with state constraints under arbitrary switching conditions.Firstly,a reasonable assumption is put forward for the uncertainties,and a switching adaptive controller is design to counteract the influence of the uncertainties.Secondly,a common limited Lyapunov function is constructed and sufficient conditions guaranteeing the stability of the switched systems with state constraints are given,and finally complete the proof.(3)Under slow switching,the problem of adaptive tracking control of the switched system with unstable subsystems is studied.Firstly,the adaptive controller is designed to eliminate the influence of uncertainties on switched systems.Secondly,a class of average dwell time that can ensure the stability of the switched systems is found.Finally,by constructing the multiple Lyapunov function,sufficient conditions for the stability of the switched error system with unstable subsystem are given and the proof is completed.(4)The example of Jet Cat SPT5 aero-engine is used for testing and simulation,and the simulation results are presented.The simulation results show that the designed controller can guarantee the stability of the system,which verifies the correctness of the aforementioned design theory.