离散Markov与semi-Markov随机切换系统的分析与控制

发布时间：2018-03-02 03:01

本文关键词： Markov切换系统 semi-Markov切换系统时变转移概率 σ均方稳定时变李亚普诺夫函数方法时变控制策略　出处：《哈尔滨工业大学》2016年博士论文　论文类型：学位论文

【摘要】：随机切换现象(如工作环境变化、系统零部件损坏、系统时滞、非线性系统工作点转变等)普遍存在于各类实际系统中。随机切换系统,鉴于其在描述随机切换现象中的优势,在过去的几十年中得到了广泛的研究。作为最重要的-类随机切换系统,Markov切换系统的相关控制问题取得了丰硕的研究成果。但是目前,仍存在一些具有挑战性的问题亟待解决,例如异步切换现象、非线性Markov切换系统的研究等,同时,一些已有结果在保守性方面仍有待改进。另一方面,semi-markov切换系统放松了Markov切换系统的无后效性(Markov特性),因而扩展了Markov随机切换系统的应用范围,成为该领域新的研究重点。但是,因为semi-Markov切换系统每一时刻的转移概率依赖于切换序列的所有历史信息,使得semi-Markov切换系统的研究更加复杂,甚至对于基本的稳定性分析和镇定问题也很难得到理想的结果。本文不仅改进了已有Markov切换系统的相关结果,而且基于时变李亚普诺夫函数方法得到了semi-Markov切换系统易检测的稳定性分析和控制器存在条件。此外,为验证所提出的相关理论的正确性,本文在单连杆单连杆机械臂系统、汽车悬架系统、单摆系统、直升机垂直升降系统、小车倒立摆系统、种群生态系统等实际系统的控制问题中进行了相关的仿真验证。本文第一章介绍了切换系统,尤其是随机切换系统的研究背景和意义,以及Markov切换系统和semi-Markov切换系统的研究现状。第二章基于扩增系统模态维数的方法,研究了一类具有系统状态时滞和模态检测时滞的Markov线性切换系统的时滞异步切换控制问题。首先,本章提出了一种新的系统模态维数扩增方法,并成功将原系统建模为一类新的具有更多系统模态的Markov切换系统,得到其转移概率矩阵；其次,通过随机李亚普诺夫函数方法建立了适用于原系统的时滞异步控制器设计方法。本章所提出的系统模态维数扩增方法使得新建立的系统其模态个数不随模态检测时滞增大而增加,从而有效解决了现有方法中新构建的Markov切换系统的模态个数随模态检测时滞的增加而指数增加的问题。第三章研究了具有部分未知转移概率矩阵的模糊Markov切换系统的H°°控制和模型预测控制问题。首先,本章研究了一类模糊规则前件部分模态依赖的模糊Markov切换系统,即,不同模态对应于不同的前件变量或模糊划分,在转移概率部分未知情况下的H°°控制器设计方法。较模糊规则前件部分不依赖于系统模态的模糊Marrkov切换系统而言,所研究的系统在保证建模精度的条件下减少了模糊规则的个数,从而降低了稳定性分析和控制器设计过程中的计算量。其次,本章研究了一类具有输入输出约束的模糊Markov切换系统的模型预测控制方法。通过引入外部变量,使得所提出的方法有效降低了已有结果的保守性。第四章在σ均方稳定的定义下研究了semi-Markov随机切换系统的状态反馈控制和H°°控制问题。首先,不同于已有的基于离散时间转移概率的研究方法,本章利用semi-Markov核分析了semi-Markov线性切换系统的稳定性,从而避免了求解离散时间转移概率上界或近似值的复杂计算过程；其次,本章提出了一类时变李亚普诺夫函数方法,并且详细对比了基于时不变和时变李亚普诺夫函数方法所得结果的保守性；再次,本章将所得的稳定性条件拓展到系统镇定问题,提出了时变状态反馈控制器设计方法；最后,基于时变李亚普诺夫函数方法和时变控制策略,本章进一步研究了模糊semi-Markov切换系统的状态反馈控制和H°°控制问题。需要指出的是,本章通过引入外部变量成功解决了以切换时刻为单位分析semi-Markov切换系统稳定性和控制器设计过程中出现的消除矩阵幂问题。较已有的研究方法,本章提出的方法不仅能够利用驻留时间概率分布函数扩展系统的建模范围,同时具有更低的保守性。第五章在均方稳定的基础上研究了一类驻留时间概率分布函数符合指数调节周期分布的离散时间semi-Markov线性切换系统的稳定性分析和镇定间题。本章首先给出一般semi-Markov线性切换系统均方稳定的充要条件；其次,针对具有指数调节周期类型的驻留时间概率分布的semi-Markov线性切换系统,给出了可求解的均方稳定的充分条件；同时,采用驻留时间依赖的李亚普诺夫函数方法,建立了驻留时间依赖的控制器存在条件。相比一般semi-Markov线性切换系统的已有研究仅局限于充分性条件,本章所给出的结果具有阶段性的进展。同时,本章利用指数调节周期分布的特性近似不同类型的驻留时间分布的方法也为semi-Markov切换系统均方稳定的研究提供了新的思路。
[Abstract]:Random switching phenomena (such as the change of the operating environment, system of damaged parts, system delay, the working point of nonlinear system transformation etc.) are ubiquitous in all kinds of actual system. The random switching system, in view of its description of stochastic switching phenomena in the advantages, has been widely studied in the past few decades. As a random switching system important - related control problem of Markov switched system has achieved fruitful results. However, there are still some challenging problems to be solved, such as asynchronous switching phenomenon of Markov switched nonlinear systems, at the same time, some results in conservative aspects still need to be improved. On the other hand, semi-Markov switching system relax after effectless Markov switching system (Markov characteristics), and expand the scope of application of Markov random switching system, has become a new focus in this field. Is that because all information transfer probability every time semi-Markov switching system depends on the switching sequence, which makes the research of semi-Markov switching system is more complex, even for the basic stability analysis and stabilization problem is difficult to get ideal results. This paper not only improve the related existing Markov switching system, and based on the time-varying Lyapunov function method of stability analysis and controller semi-Markov switching system to detect the existence condition. In addition, the correctness of the theory for the validation of the proposed, based on a single link single link manipulator system, suspension system, pendulum system, helicopter vertical lift system, inverted pendulum system, the actual control problem of population ecology system in the simulated related. The first chapter introduces the switching system, especially stochastic switching system The research background and significance, and research status of Markov switching system and semi-Markov switching system. The second chapter is based on the method of amplification system modal dimension, time delay of asynchronous switching control problem is studied for a class of Markov linear switched systems with state time-delay system and modal detection delay. Firstly, this chapter proposes a system modal dimension the new amplification method, and the success of the original system is modeled as a new mode of Markov system has more switching system, the transtion-probablity matrix; secondly, the design method of delay asynchronous controller through stochastic Lyapunov function method was established for the original system. The system modal dimension is proposed in this chapter the amplification method makes the system the newly established the modal number with the modal detection delay increases, thereby effectively solving the Markov switching system of new construction in the existing method The number of modes with increasing delay and increase the index of modal detection problems. The third chapter studies the Markov switching system with fuzzy partially unknown transtion-probablity matrix of the H degree degree control and model predictive control problem. Firstly, this chapter studies a kind of fuzzy rules of former part of mode dependent fuzzy and Markov switching system that is, different modes, corresponding to the antecedent variables of different or fuzzy partition, design method of controller H degrees degrees in case of partly unknown transition probabilities. A fuzzy Marrkov rules in system switching system depends on the former part of the modal words, the system can reduce the number of fuzzy rules model under the condition of precision, thereby reducing the computation of stability analysis and controller design process. Secondly, this chapter studies a class of input and output constraints of fuzzy and Markov switching system model prediction Control method. By introducing external variables, makes the proposed method effectively reduces the conservativeness of the existing results. In the fourth chapter, a definition of mean square stability of semi-Markov random switched systems with state feedback control and H degrees degrees control. Firstly, research methods based on discrete time transfer probability are different from this. Semi-Markov makes use of the semi-Markov nuclear stability of switched linear systems is analyzed, so as to avoid the complicated calculation process of solving discrete time transfer probability bounds or approximations; secondly, this chapter proposes a class of time-varying Li Yapu Lyapunov function method, and the results were compared with variable Lyapunov function method based on time invariant and conservative; again, this chapter will expand to the stability condition of stabilization system, put forward the time-varying state feedback controller design method; finally, based on the When the change of control strategy of Lyapunov function method and, this chapter further studies the problem of fuzzy and semi-Markov switching system state feedback control and H control. The degree degree should be pointed out that this chapter by introducing external variables is solved successfully by switching time for analysis to eliminate the problem of matrix power stability and controller design of semi-Markov switching system in the unit. Compared with the existing research methods, modeling the scope of this chapter the proposed method not only can use the dwell time of the probability distribution function of the expansion of the system, at the same time is less conservative. The stability analysis of the fifth chapter based on the mean square stability is studied for a class of dwell time probability distribution function with exponential distribution adjustment cycle discrete time linear semi-Markov switching system and stabilization problem. This chapter first presents the general semi-Markov linear switching system mean square stable charge Secondly, according to the conditions; with index adjustment cycle type of probability distribution of the dwell time of semi-Markov switched linear systems, the sufficient condition for the mean square stability can be solved is given; at the same time, the Lyapunov function method with dwell time dependence, existence condition dependent controller is established. Compared with the existing dwell times of general linear semi-Markov switched systems are only limited to the sufficient conditions, in this chapter the results with the stage. At the same time, provides a new idea of this chapter uses the index adjustment characteristic of periodic distribution of different types of approximate dwell time distribution method for semi-Markov switching stability of the system.

【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP13

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