發(fā)布時間：2019-04-28 06:45

【摘要】：馬爾可夫跳變系統(tǒng)是一類具有馬爾可夫參數(shù)的隨機(jī)混合系統(tǒng),其動態(tài)演化由連續(xù)時間和離散事件共同描述,離散事件被稱為系統(tǒng)模態(tài),并且該系統(tǒng)在各個模態(tài)的隨機(jī)跳變由馬爾可夫過程控制。在實際中,馬爾可夫跳變系統(tǒng)能夠有效建模內(nèi)部結(jié)構(gòu)易受到環(huán)境突變、設(shè)備故障、連接失敗等影響而發(fā)生突變的動態(tài)系統(tǒng),并取得重大成功,引起學(xué)者不斷關(guān)注。因而,研究馬爾可夫跳變系統(tǒng)具有深遠(yuǎn)的理論和實際意義。馬爾可夫跳變系統(tǒng)不同模態(tài)間隨機(jī)切換規(guī)律由馬爾可夫鏈描述。在連續(xù)時間馬爾可夫跳變系統(tǒng)中,切換概率由模態(tài)轉(zhuǎn)移速率矩陣(MTRM)決定,而離散時間馬爾可夫跳變系統(tǒng)則由模態(tài)轉(zhuǎn)移概率矩陣(MTPM)決定。大量文獻(xiàn)表明馬爾可夫跳變系統(tǒng)其性能與MTRM、MTPM關(guān)系密切,并且其中絕大多數(shù)研究基于MTRM、MTPM為定值的情況。然而真實系統(tǒng)中,MTRM和MTPM往往是可控的,且人為控制MTRM、MTPM能夠改善動態(tài)系統(tǒng)的穩(wěn)定性和性能。另外,馬爾可夫跳變系統(tǒng)常用于建模多噪聲系統(tǒng),因此噪聲也是不可忽略的因素。值得注意的是,噪聲不僅會干擾系統(tǒng)狀態(tài),而且會對系統(tǒng)性能產(chǎn)生不利影響。本文針對馬爾可夫鏈可控的馬爾可夫跳變系統(tǒng),研究高斯噪聲存在下系統(tǒng)性能的優(yōu)化策略。根據(jù)系統(tǒng)狀態(tài)和系統(tǒng)模態(tài)的不同,分別研究連續(xù)時間馬爾可夫跳變系統(tǒng)和離散時間馬爾可夫跳變系統(tǒng)的優(yōu)化策略。具體工作如下：(1)針對高斯噪聲下可控MTRM的連續(xù)時間馬爾可夫跳變系統(tǒng),研究了系統(tǒng)性能的決策-控制策略,其中決策代表對MTRM的控制,控制則表示狀態(tài)控制器。對于上述決策-控制策略,提出包含跳變線性二次高斯最優(yōu)控制的代價和決策代價的混合性能指標(biāo)。假設(shè)最優(yōu)決策已引入MTRM,利用分離定理分別設(shè)計最優(yōu)狀態(tài)反饋控制器和最優(yōu)馬爾可夫濾波器,將設(shè)計最優(yōu)決策-控制對簡化為尋找最優(yōu)決策。最后提出一個能夠?qū)ふ易顑?yōu)決策量的迭代算法,并進(jìn)一步證明其收斂性和存在性。(2)針對高斯噪聲下MTPM可控的離散時間馬爾可夫跳變系統(tǒng),研究系統(tǒng)性能的優(yōu)化策略�；谀芸氐腗TPM,提出了一種決策-控制策略。由于決策的引入不可避免產(chǎn)生額外控制代價,因此本文引入一種混合性能指標(biāo)。假設(shè)最優(yōu)決策已引入MTPM,利用分離定理設(shè)計了最優(yōu)控制器,將混合性能指標(biāo)轉(zhuǎn)化為決策量的函數(shù)。為了最小化混合性能指標(biāo),本文進(jìn)一步提出了一個尋找最優(yōu)決策量的迭代算法。本文給出了基于高斯噪聲和可控MTRM/MTPM的馬爾可夫跳變系統(tǒng)決策-控制策略,從理論上給出了相關(guān)控制器的設(shè)計方案,并通過仿真實驗驗證了決策-控制策略的有效性。論文結(jié)尾,給出了研究總結(jié),并討論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.
【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O211.62

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