一类马尔可夫跳变系统优化策略

发布时间：2019-04-28 06:45

【摘要】：马尔可夫跳变系统是一类具有马尔可夫参数的随机混合系统,其动态演化由连续时间和离散事件共同描述,离散事件被称为系统模态,并且该系统在各个模态的随机跳变由马尔可夫过程控制。在实际中,马尔可夫跳变系统能够有效建模内部结构易受到环境突变、设备故障、连接失败等影响而发生突变的动态系统,并取得重大成功,引起学者不断关注。因而,研究马尔可夫跳变系统具有深远的理论和实际意义。马尔可夫跳变系统不同模态间随机切换规律由马尔可夫链描述。在连续时间马尔可夫跳变系统中,切换概率由模态转移速率矩阵(MTRM)决定,而离散时间马尔可夫跳变系统则由模态转移概率矩阵(MTPM)决定。大量文献表明马尔可夫跳变系统其性能与MTRM、MTPM关系密切,并且其中绝大多数研究基于MTRM、MTPM为定值的情况。然而真实系统中,MTRM和MTPM往往是可控的,且人为控制MTRM、MTPM能够改善动态系统的稳定性和性能。另外,马尔可夫跳变系统常用于建模多噪声系统,因此噪声也是不可忽略的因素。值得注意的是,噪声不仅会干扰系统状态,而且会对系统性能产生不利影响。本文针对马尔可夫链可控的马尔可夫跳变系统,研究高斯噪声存在下系统性能的优化策略。根据系统状态和系统模态的不同,分别研究连续时间马尔可夫跳变系统和离散时间马尔可夫跳变系统的优化策略。具体工作如下：(1)针对高斯噪声下可控MTRM的连续时间马尔可夫跳变系统,研究了系统性能的决策-控制策略,其中决策代表对MTRM的控制,控制则表示状态控制器。对于上述决策-控制策略,提出包含跳变线性二次高斯最优控制的代价和决策代价的混合性能指标。假设最优决策已引入MTRM,利用分离定理分别设计最优状态反馈控制器和最优马尔可夫滤波器,将设计最优决策-控制对简化为寻找最优决策。最后提出一个能够寻找最优决策量的迭代算法,并进一步证明其收敛性和存在性。(2)针对高斯噪声下MTPM可控的离散时间马尔可夫跳变系统,研究系统性能的优化策略。基于能控的MTPM,提出了一种决策-控制策略。由于决策的引入不可避免产生额外控制代价,因此本文引入一种混合性能指标。假设最优决策已引入MTPM,利用分离定理设计了最优控制器,将混合性能指标转化为决策量的函数。为了最小化混合性能指标,本文进一步提出了一个寻找最优决策量的迭代算法。本文给出了基于高斯噪声和可控MTRM/MTPM的马尔可夫跳变系统决策-控制策略,从理论上给出了相关控制器的设计方案,并通过仿真实验验证了决策-控制策略的有效性。论文结尾,给出了研究总结,并讨论了下一步的研究方向。
[Abstract]:Markov jump system is a class of stochastic hybrid systems with Markov parameters. Its dynamic evolution is described by continuous time and discrete events. Discrete events are called system modes. The random jump of the system in each mode is controlled by Markov process. In practice, Markov jump systems can effectively model dynamic systems whose internal structures are susceptible to sudden changes in the environment, equipment failures, connection failures, etc., and have achieved great success, which has attracted scholars' constant attention. Therefore, the study of Markov jump system has far-reaching theoretical and practical significance. The stochastic switching law between different modes of Markov jump system is described by Markov chain. In the continuous-time Markov jump system, the switching probability is determined by the modal transfer rate matrix (MTRM), while the discrete-time Markov jump system is determined by the modal transition probability matrix (MTPM). A large number of literatures have shown that the performance of Markov jump systems is closely related to MTRM,MTPM, and most of the studies are based on the case of MTRM,MTPM as a constant value. However, in real systems, MTRM and MTPM are usually controllable, and artificial control of MTRM,MTPM can improve the stability and performance of dynamic systems. In addition, Markov jump systems are often used to model multi-noise systems, so noise can not be ignored. It is worth noting that noise not only interferes with the state of the system, but also adversely affects the performance of the system. In this paper, the optimization strategy of system performance in the presence of Gao Si noise is studied for Markov jump systems controlled by Markov chains. The optimization strategies of continuous-time Markov jump system and discrete-time Markov jump system are studied according to the difference of system state and system mode. The specific work is as follows: (1) for the continuous-time Markov jump system with controllable MTRM under Gao Si noise, the decision-control strategy of the system performance is studied, in which the decision-making representative controls the MTRM and the control represents the state controller. For the above-mentioned decision-control strategy, a mixed performance index including the cost of the linear quadratic Gao Si optimal control and the cost of the decision-making is proposed. It is assumed that MTRM, has been introduced to design the optimal state feedback controller and the optimal Markov filter respectively by using the separation theorem. The optimal decision-control pair is simplified to find the optimal decision. Finally, an iterative algorithm which can find the optimal decision quantity is proposed, and its convergence and existence are further proved. (2) for the MTPM-controllable discrete-time Markov jump system with Gao Si noise, the optimization strategy of the system performance is studied. A decision-control strategy based on controllable MTPM, is proposed. Since the introduction of decision-making inevitably results in additional control costs, a hybrid performance index is introduced in this paper. It is assumed that MTPM, has been introduced into the optimal decision making to design the optimal controller by using the separation theorem, and the mixed performance index is transformed into a function of the decision quantity. In order to minimize the mixed performance index, an iterative algorithm is proposed to find the optimal decision quantity. In this paper, the decision-control strategy of Markov jump system based on Gao Si noise and controllable MTRM/MTPM is given, and the design scheme of related controller is given theoretically. The validity of decision-control strategy is verified by simulation experiment. At the end of the paper, a summary of the research is given, and the future research direction is discussed.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O211.62

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