Optimization Strategy Of A Class Of Markov Jump Systems

Markovian jump systems (MJSs) are a kind of stochastic hybrid system with Markovian jump parameters, whose dynamic evolution is modeled by not only continuous time but also discrete events. The discrete events are called system modes in MJSs and stochastic jump among these system modes is governed by a Markov process. In practical, MJSs have enjoyed great success in fully describing systems subject to random abrupt changes resulting from faulty communication links, failures in structures, or sudden variations of environment. There has been increasing interest of scholars in MJSs. Therefore, the research of MJSs has profound theoretical and practical significance.The stochastic switch law between different modes in MJSs is described by a Markov chain. In continuous-time MJSs, the occurrence probability of each mode is totally determined by mode transition rate matrix (MTRM). Meanwhile, discrete-time MJSs correspond to mode transition probability matrix (MTPM). Considerable literature shows that there exists a close relation between system performance and MTRM or MTRM. It’s worth noting that almost of the works concerning MJSs was done on basis of invariable MTRM or MTPM. However, in practical systems, MTRM or MTPM is always controllable and artificial control of MTRM or MTPM can further improve system stability as well as system performance. In addition, MJSs usually model dynamic systems working in noisy environment. Therefore, the existence of noise can’t be neglected. It is worth reminding that noise not only disturbs system states but also brings adverse effects to system performance. For MJSs with controllable Markov chain, we investigate the optimization strategy of system performance in presence of noises. According to different system states and system modes, the optimization strategy is divided into two parts:continuous-time MJSs and discrete time MJSs. The main contributions of this dissertation are as follows:(1) A decision-control strategy is proposed for continuous-time MJSs with Gaussian noises and controllable MTRM. The proposed strategy consists of two parts: decision, which means the artificial actions to govern MTRM, and controller to govern system state. For this strategy, a joint index is put forward to evaluate system cost, which is a combination of traditional JLQG cost and additional decision cost. With the assumption of new MTRM obtained with a desired decision, optimal controller as well as Markovian filter is designed with the application of separation principle. The problem of seeking optimal decision-control pair is deduced to the issue to find the optimal decision. Meanwhile, an iterative algorithm is developed to obtain the optimal decision as well as its convergence proved.(2) An optimization strategy of system performance is investigated for discrete-time MJSs with Gaussian noises and controllable MTPM. Based on controllable MTPM, a novel decision-control strategy is proposed. Then a joint index is given due to extra expenses of decision. By assuming that optimal decision has been introduced to MTPM, an optimal controller is designed with the application of separation principle. Then joint index can be represented as a function of decision. Finally, to minimize joint index, an iterative algorithm is given for the seeking of optimal decision.This paper investigates the optimization strategy for continuous-time and discrete-time MJSs with controllable Markov chain and Gaussian noise respectively. The corresponding controller is designed in theory and numerical examples have been simulated to prove decision-control strategy’s effectiveness. All the contents are concluded at last and the future study topics are discussed.