本文關(guān)鍵詞： Markov切換系統(tǒng) semi-Markov切換系統(tǒng) 時(shí)變轉(zhuǎn)移概率 σ均方穩(wěn)定 時(shí)變李亞普諾夫函數(shù)方法 時(shí)變控制策略　出處：《哈爾濱工業(yè)大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：隨機(jī)切換現(xiàn)象(如工作環(huán)境變化、系統(tǒng)零部件損壞、系統(tǒng)時(shí)滯、非線性系統(tǒng)工作點(diǎn)轉(zhuǎn)變等)普遍存在于各類實(shí)際系統(tǒng)中。隨機(jī)切換系統(tǒng),鑒于其在描述隨機(jī)切換現(xiàn)象中的優(yōu)勢,在過去的幾十年中得到了廣泛的研究。作為最重要的-類隨機(jī)切換系統(tǒng),Markov切換系統(tǒng)的相關(guān)控制問題取得了豐碩的研究成果。但是目前,仍存在一些具有挑戰(zhàn)性的問題亟待解決,例如異步切換現(xiàn)象、非線性Markov切換系統(tǒng)的研究等,同時(shí),一些已有結(jié)果在保守性方面仍有待改進(jìn)。另一方面,semi-markov切換系統(tǒng)放松了Markov切換系統(tǒng)的無后效性(Markov特性),因而擴(kuò)展了Markov隨機(jī)切換系統(tǒng)的應(yīng)用范圍,成為該領(lǐng)域新的研究重點(diǎn)。但是,因?yàn)閟emi-Markov切換系統(tǒng)每一時(shí)刻的轉(zhuǎn)移概率依賴于切換序列的所有歷史信息,使得semi-Markov切換系統(tǒng)的研究更加復(fù)雜,甚至對于基本的穩(wěn)定性分析和鎮(zhèn)定問題也很難得到理想的結(jié)果。本文不僅改進(jìn)了已有Markov切換系統(tǒng)的相關(guān)結(jié)果,而且基于時(shí)變李亞普諾夫函數(shù)方法得到了semi-Markov切換系統(tǒng)易檢測的穩(wěn)定性分析和控制器存在條件。此外,為驗(yàn)證所提出的相關(guān)理論的正確性,本文在單連桿單連桿機(jī)械臂系統(tǒng)、汽車懸架系統(tǒng)、單擺系統(tǒng)、直升機(jī)垂直升降系統(tǒng)、小車倒立擺系統(tǒng)、種群生態(tài)系統(tǒng)等實(shí)際系統(tǒng)的控制問題中進(jìn)行了相關(guān)的仿真驗(yàn)證。本文第一章介紹了切換系統(tǒng),尤其是隨機(jī)切換系統(tǒng)的研究背景和意義,以及Markov切換系統(tǒng)和semi-Markov切換系統(tǒng)的研究現(xiàn)狀。第二章基于擴(kuò)增系統(tǒng)模態(tài)維數(shù)的方法,研究了一類具有系統(tǒng)狀態(tài)時(shí)滯和模態(tài)檢測時(shí)滯的Markov線性切換系統(tǒng)的時(shí)滯異步切換控制問題。首先,本章提出了一種新的系統(tǒng)模態(tài)維數(shù)擴(kuò)增方法,并成功將原系統(tǒng)建模為一類新的具有更多系統(tǒng)模態(tài)的Markov切換系統(tǒng),得到其轉(zhuǎn)移概率矩陣；其次,通過隨機(jī)李亞普諾夫函數(shù)方法建立了適用于原系統(tǒng)的時(shí)滯異步控制器設(shè)計(jì)方法。本章所提出的系統(tǒng)模態(tài)維數(shù)擴(kuò)增方法使得新建立的系統(tǒng)其模態(tài)個(gè)數(shù)不隨模態(tài)檢測時(shí)滯增大而增加,從而有效解決了現(xiàn)有方法中新構(gòu)建的Markov切換系統(tǒng)的模態(tài)個(gè)數(shù)隨模態(tài)檢測時(shí)滯的增加而指數(shù)增加的問題。第三章研究了具有部分未知轉(zhuǎn)移概率矩陣的模糊Markov切換系統(tǒng)的H°°控制和模型預(yù)測控制問題。首先,本章研究了一類模糊規(guī)則前件部分模態(tài)依賴的模糊Markov切換系統(tǒng),即,不同模態(tài)對應(yīng)于不同的前件變量或模糊劃分,在轉(zhuǎn)移概率部分未知情況下的H°°控制器設(shè)計(jì)方法。較模糊規(guī)則前件部分不依賴于系統(tǒng)模態(tài)的模糊Marrkov切換系統(tǒng)而言,所研究的系統(tǒng)在保證建模精度的條件下減少了模糊規(guī)則的個(gè)數(shù),從而降低了穩(wěn)定性分析和控制器設(shè)計(jì)過程中的計(jì)算量。其次,本章研究了一類具有輸入輸出約束的模糊Markov切換系統(tǒng)的模型預(yù)測控制方法。通過引入外部變量,使得所提出的方法有效降低了已有結(jié)果的保守性。第四章在σ均方穩(wěn)定的定義下研究了semi-Markov隨機(jī)切換系統(tǒng)的狀態(tài)反饋控制和H°°控制問題。首先,不同于已有的基于離散時(shí)間轉(zhuǎn)移概率的研究方法,本章利用semi-Markov核分析了semi-Markov線性切換系統(tǒng)的穩(wěn)定性,從而避免了求解離散時(shí)間轉(zhuǎn)移概率上界或近似值的復(fù)雜計(jì)算過程；其次,本章提出了一類時(shí)變李亞普諾夫函數(shù)方法,并且詳細(xì)對比了基于時(shí)不變和時(shí)變李亞普諾夫函數(shù)方法所得結(jié)果的保守性；再次,本章將所得的穩(wěn)定性條件拓展到系統(tǒng)鎮(zhèn)定問題,提出了時(shí)變狀態(tài)反饋控制器設(shè)計(jì)方法；最后,基于時(shí)變李亞普諾夫函數(shù)方法和時(shí)變控制策略,本章進(jìn)一步研究了模糊semi-Markov切換系統(tǒng)的狀態(tài)反饋控制和H°°控制問題。需要指出的是,本章通過引入外部變量成功解決了以切換時(shí)刻為單位分析semi-Markov切換系統(tǒng)穩(wěn)定性和控制器設(shè)計(jì)過程中出現(xiàn)的消除矩陣冪問題。較已有的研究方法,本章提出的方法不僅能夠利用駐留時(shí)間概率分布函數(shù)擴(kuò)展系統(tǒng)的建模范圍,同時(shí)具有更低的保守性。第五章在均方穩(wěn)定的基礎(chǔ)上研究了一類駐留時(shí)間概率分布函數(shù)符合指數(shù)調(diào)節(jié)周期分布的離散時(shí)間semi-Markov線性切換系統(tǒng)的穩(wěn)定性分析和鎮(zhèn)定間題。本章首先給出一般semi-Markov線性切換系統(tǒng)均方穩(wěn)定的充要條件；其次,針對具有指數(shù)調(diào)節(jié)周期類型的駐留時(shí)間概率分布的semi-Markov線性切換系統(tǒng),給出了可求解的均方穩(wěn)定的充分條件；同時(shí),采用駐留時(shí)間依賴的李亞普諾夫函數(shù)方法,建立了駐留時(shí)間依賴的控制器存在條件。相比一般semi-Markov線性切換系統(tǒng)的已有研究僅局限于充分性條件,本章所給出的結(jié)果具有階段性的進(jìn)展。同時(shí),本章利用指數(shù)調(diào)節(jié)周期分布的特性近似不同類型的駐留時(shí)間分布的方法也為semi-Markov切換系統(tǒng)均方穩(wěn)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.

【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP13

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