Research On Sliding Mode Control Method Of Markovian Jump Systems Based On Event-triggered Mechanism

Markovian jump systems can be used to describe the dynamic characteristics of jump between subsystems caused by various external random factors.The system is widely used in industrial manufacturing,communication networks,aerospace and other systems.On the one hand,in the practical system modeling process,uncertainty and external disturbance are inevitably introduced into the system with the control input,and sliding mode control has significant advantages in the research of related problems.On the other hand,since the event-triggered control strategy conforms to the law of"on-demand transmission",the event-triggered sliding mode control can reduce the waste of computing and communication resources.It is worth noting that there exist still some urgent problems to be solved in using event-triggered sliding mode control method to study the robust stabilization of Markovian jump systems,for example,how to reasonably and effectively introduce the event-triggered mechanism and design the sliding mode controller for piecewise homogeneous Markovian jump systems with time-varying transition rate,and how to realize the reachability and stochastic admissibility analysis of sliding mode dynamics for singular Markovian jump systems.Based on the above analysis,the specific research work of this thesis is as follows:(1)The design of event-triggered linear sliding mode controller for piecewise homogeneous Markovian jump systems is studied.Firstly,the system is transformed into two low-order subsystems by linear transformation,and an appropriate linear sliding mode surface function is proposed.On this basis,the event-triggered mechanism is introduced.Then,the sliding mode control law is designed such that the system trajectory can be driven and remained on the specified sliding surface.In addition,a set of new sufficient conditions are proposed by using Lyapunov function method to ensure the random stability of sliding mode.Finally,the proposed results are applied to the single link flexible manipulator system to verify the effectiveness of the theoretical results.(2)The design of event-triggered integral sliding mode controller for Markovian jump systems is studied.Firstly,under the event-triggered condition,the time-varying trigger threshold is adopted to ensure that the system trajectory enters the bounded region.Two integral sliding surface functions are established for Markovian jump systems.One is the continuous-state-dependent sliding surface function,which is used to analyze the reachability of sliding surface.The other is the sliding surface function based on the trigger state,which is used to design the event-triggered integral sliding mode controller.Then,a sufficient condition for the ultimate boundedness of the sliding mode dynamics is established,and the existence of a positive lower bound of the internal execution time is guaranteed.Finally,two simulation examples are given to illustrate the effectiveness of the theoretical results.(3)The design of event-triggered linear sliding mode controller for singular Markovian jump systems is studied.Firstly,in order to ensure the reachability of sliding surface,an event-triggered sliding mode control law is designed.For singular Markovian jump systems,aiming at the difficulties caused by event-triggered sliding mode control strategy,a lemma for dealing with s(t)sgn s(i _k)is given.Then,a set of new sufficient conditions are given by using Lyapunov function method to ensure the random admissibility of sliding modes.In addition,the positive lower limit of execution time can be ensured,and Zeno phenomenon will not occur.Finally,two simulation examples are given to verify the effectiveness of the theoretical results in this thesis.