| With the rapid development of science and technology,a large amount of complex dynamic systems such as space systems,integrated systems,manufacturing systems are arised.Such systems are naturally subjected to abrupt changes in structures which may arise from the sudden variation of environment,the damaged components of systems,or failure of subsystems ’ connection,etc.Among the different approaches to model the concerned phenomena,Markovian Jump Systems(MJSs)are well suited to describe such dynamics.Since the MJSs models come into stage,we have successfully witnessed the widely application in manufacturing systems,network control systems,etc.Gener-ally speaking,an MJS is composed of several subsystems where the dynamics of each subsystem is named a mode.The dynamics of the MJLS jumps among these modes and the jumping rule is governed by a Markov chain.The mode transition probability matrix(MTPM)which determines the switching probability of each mode are impor-tant parameters of Markov chain.Further,MTPM are related to the state variations.It is well worth pointing out that existing work mainly focuses on the research of MJSs based on the invariable MTPM and stability and controller design problems of MJSs have been intensively studied.Nevertheless in many practical MJSs,the MTPM can be adjusted by human artificial action.If control is performed on MTPM,the occurrence probability of system mode will be changed and it is possible to improve the system performance.Thus,this paper performs research on a class of discrete-time Markovian Jump Systems(MJSs)in the view of stochastic switching rule of modes will have influ-ence on system stability and performance.The proposed control mechanism not only guarantees system stability,but also decreases system cost effectively by adjusting the occurrence probability of modes.The main work of this dissertation is as follows:(1)The optimal control strategy is investigated for discrete-time MJLSs with con-trollable MTPM.Due to the introduction of mode feedback control,a new quadratic performance index,which contains both mode control cost and state control cost is es-tablished.Based on this,the optimal mode feedback controller which can adjust the occurrence probability of modes can be designed together with its admissible value set discussed.(2)The state and mode feedback control strategy for a class of discrete-time MJLs with controllable MTPM is discussed.The strategy consisting of two parts:the finite-pathdependent state feedback controller design with which uniform stability of MJLSs can be ensure,and the optimal mode feedback controller which aims to decrease system cost.Compared with the traditional state feedback control strategy,the introduction of state and mode feedback control pair helps to decrease system cost on the basis of ensuring stability.This paper investigates the optimal mode control strategy and the state and mode feendback control strategy for a class of discrete-time MJLs with controllable MTPM.The corresponding controllers design is introduced in details.The effectiveness of the proposed control strategy is illustrated via numerical examples. |
