Research On Event-driven Control For Markov Jump Systems

With the advent of the era of intelligent manufacturing industry,the scale of control system is increasing and the structure is becoming more and more complex.It is difficult to fully express large-scale system and complex system with traditional modeling methods.As a typical hybrid dynamic system,Markov jump system has powerful modeling ability and can be used to describe the actual system.Therefore the research on Markov jump system has become a hot spot in the control field.At the same time,with the increasing of system complexity,utilization of traditional time-driven control strategy in the system will cause the waste of limited bandwidth resources.Therefore,in order to save the communication resources and avoid the waste of bandwidth resources,the system based on event-driven control strategy has attracted more and more scholars’ attention.In this paper,the stochastic stabilization of Markov jump systems under event-driven control is investigated.Firstly,this paper researches the Markov jump systems based on the event-driven control strategy,and obtains the stochastic stabilization conditions of Markov jump system with completely known transition probabilities.According to this result and the nature of the system transition probability matrix,the stochastic stabilization conditions of Markov jump system with partially known transition probabilities are obtained.Secondly,event-triggered stabilization for Markov jump systems with time-varying delay is researched.By constructing the delay-dependent Lyapunov function and combining with the relevant event-driven conditions,the stochastic stabilization conditions of Markov jump systems with completely known and partially known transition probabilities are derived by Jensen inequality,the properties of transition probability matrix and Schur complement lemma.Thirdly,under event-driven strategy,saturating Markov jump systems are considered.When the state transition probabilities of the Markov jump systems are completely unknown,the stochastic stabilization conditions of the system are obtained.The estimation of domain of attraction is obtained according to the optimization algorithm.At the same time,the minimum time interval of event triggering is given,then the Zeno behavior can be avoided.Finally,under event-driven control strategy,the design of the quantization feedback controller for saturating Markov jump systems is considered.According to the selected logarithmic quantizer,the signals of the input channel and the output channel are quantized,and the stabilization conditions of Markov jump systems are obtained with partially known transition probabilities.The domain of attraction in mean square sense are estimated by using the convex optimization algorithm.The effectiveness of the above results is verified by corresponding numerical examples.