Control Of Markov Jump Systems With Mismatched Modes

Most results of Markov jump systems are based on an implicit assumption,that is,the modes of controller are the same as modes of original system.However,the imperfection of physical devices may impair this ideal assumption.On the one hand,the controller may not receive ac-curate system modes information due to package loss or delays.On the other hand,the failure and low efficiency of mode switching devices may also prevent the controller from switching to the corresponding system mode timely.Researchers proposed a statistical method called hidden Markov model,which can weaken the tough requirement of physical devices so that it is more prac-tical compared with absolute match case,to deal with the modes mismatch problem.In this model,controller modes are obtained by a conditional transition probability from modes of system to con-troller.By adjusting the conditional transition probability,we can handle three different modes match scenarios,which are completely matched,partially matched and completely mismatched,respectively,which means the hidden Markov model is a unified framework.In this paper,we will discuss the control problems of Markov jump systems with mismatched modes.The main contributions are listed as follows.(1)Considering a class of Markov jump Lur'e systems with mismatched modes information,we design an asynchronous controller which is composed of linear state feedback and nonlinear(the same as system)output feedback,based on hidden Markov model.The unique controller structure is more flexible than the state feedback ones and will have better results.Then,the stability and l2 performance are discussed,a sufficient condition presented in LMI is obtained to guarantee the system is stochastically stable with a l2 performance from disturbance to output.Finally,a numerical example is provided to illustrate the effectiveness of obtained results.(2)Considering a class of nonlinear 2D-Markov jump systems in Roesser model,we study the sliding mode control problems of it.Noting the special properties of 2D systems,a novel 2D sliding surface is constructed.In order to handle the mismatched modes between system and controller,the hidden Markov model is introduced to design the sliding mode control law.Then,we discuss the system stability with an H? performance and the reachability of states to the slid-ing surface,respectively.A sufficient condition is obtained which can guarantee the system is asymptotically mean square stable with an H? performance and the reachability of sliding mode dynamics,simultaneously.Finally,we summaries the sliding mode controller design procedures into to an algorithm whose effectiveness is verified by a numerical example.(3)Considering a class of 2D-Markov jump systems in Roesser model,we study the asyn-chronous quadric control problems of it.Noting the mismatched modes between controller and system,we introduce a hidden Markov model to design an asynchronous state feedback controller.Then,a quadric cost function is defined and the system stability is discussed.The guaranteed cost performance is studied under three different initial conditions·Both initial system states and initial system modes are known,·Initial system states satisfy a bounded condition and initial system modes are known,·Initial system states satisfy a bounded condition and initial system modes are unknown.Finally,sufficient conditions that can make sure system is stable with a optimal guaranteed cost performance under different initial conditions are obtained.