本文選題：Markov切換系統(tǒng) + 約束控制與濾波　； 參考：《安徽工業(yè)大學》2017年碩士論文

【摘要】：作為混雜系統(tǒng)的一種重要分支,Markov切換系統(tǒng)由于其數(shù)學表達方式簡便,又在電力系統(tǒng)、電路網(wǎng)絡系統(tǒng)、航空航天、機器人機械系統(tǒng)、經(jīng)濟學系統(tǒng)、制造業(yè)等領域有著廣泛的應用,從而吸引了國內(nèi)外許多學者的關注。本文在已有的研究結(jié)果基礎上,針對Markov切換系統(tǒng)模態(tài)獲取受到約束和網(wǎng)絡傳輸受到約束情況下的控制和濾波問題進行相關研究,主要內(nèi)容集中在有限時間l_2-l_∞跟蹤控制器設計、有限時間異步H_∞濾波器設計、有限時間異步l_2-l_∞濾波器設計等方面。具體內(nèi)容為:1.針對一類具有Markov切換的重復標量非線性系統(tǒng),研究其有限時間l_2-l_∞跟蹤控制問題。所考慮系統(tǒng)的模態(tài)信息獲取是不完整的,且服從一個確定的伯努利分布的白噪聲序列。主要目的是設計一個狀態(tài)反饋控制器使得所考慮的系統(tǒng)在模態(tài)部分可獲取時仍然在有限時間內(nèi)跟蹤給定的信號且滿足一定的l_2-l_∞性能指標。通過利用模態(tài)依賴的對角占優(yōu)Lyapunov泛函方法,得到了可行的狀態(tài)反饋控制器存在的一些充分條件。在此基礎上,通過改進的矩陣解耦方法可以求得可行的控制器參數(shù)。最后,通過一個數(shù)值例子和一個經(jīng)濟模型驗證了所提方法的有效性。2.研究了一類不確定通信連接的網(wǎng)絡化離散Markov切換系統(tǒng)有限時間異步H_∞濾波器設計問題。其中,網(wǎng)絡傳輸約束問題被充分考慮到系統(tǒng)的輸出端,其會導致數(shù)據(jù)包丟失、時延等現(xiàn)象。此外,傳感器非線性以及系統(tǒng)模態(tài)切換和濾波器模態(tài)切換存在異步現(xiàn)象在設計過程中也給予了考慮,兩個隨機變量用來描述其隨機發(fā)生現(xiàn)象。這使得我們的系統(tǒng)模型比其他文獻更具有通用性�；谟邢迺r間隨機分析理論,得到了使得濾波誤差系統(tǒng)是有限時間均方隨機有界且滿足期望的H_∞性能指標的異步濾波器存在的相應判據(jù)。借助于該判據(jù)并且將第三章中改進的求解控制器的矩陣解耦方法運用到濾波器求解問題中,使得所提出的相應異步濾波器設計方法具有更低的保守性。最后,所給的數(shù)值例子和PWM驅(qū)動的升壓轉(zhuǎn)換器模型說明了所提出方法的優(yōu)越性和可行性。3.基于2中的結(jié)果,進一步將其推廣到網(wǎng)絡化的非線性Markov切換系統(tǒng),探討了其有限時間異步l_2-l_∞濾波器設計問題。在進行異步l_2-l_∞濾波器設計時,也同時考慮了網(wǎng)絡的傳輸約束問題、傳感器非線性以及系統(tǒng)模態(tài)與濾波器模態(tài)之間的異步現(xiàn)象。在有限時間穩(wěn)定理論框架下,結(jié)合Takagi-Sugeno模糊模型,深入剖析了該類非線性系統(tǒng)的特點,并分析了濾波誤差系統(tǒng)有限時間有界性以及l(fā)_2-l_∞性能,給出了所考慮系統(tǒng)的異步l_2-l_∞濾波器設計方法。最后通過數(shù)值例子和一個倒立擺模型說明了所提出設計方法是可用的。
[Abstract]:As an important branch of hybrid system, Markov switching system because of its mathematical expression is simple, and in the electric power system, electric network system, aerospace, robot system, economics, manufacturing and other fields have a wide range of applications, which has attracted the attention of many scholars at home and abroad. Based on the existing research results on the mode of Markov switching system for access is restricted and controlled by the network transmission and filtering problem constraints were studied, the main contents focus tracking controller design in finite time robust l_2-l_ design, asynchronous H_ filter limited time, limited time asynchronous l_2-l_ filter design. The specific contents are as follows: repeated scalar 1. for a class of nonlinear systems with Markov switching, study the finite time robust l_2-l_ tracking control problem. The modal information system under consideration Access is not complete, and subject to a determination of the distribution of Bernoulli white noise sequence. The main purpose is to design a state feedback controller can be obtained in the modal part still in finite time tracking of the given signal and satisfy the l_2-l_ for certain performance index makes the system. By using the Lyapunov functional method diagonally dominant the mode dependent, we get some sufficient conditions for the existence of the state feedback controller is feasible. On this basis, the controller parameters can be obtained by decoupling matrix method and feasible improvement. Finally, the validity of.2. through a number of examples and an economic model show that the proposed method is studied for a class of uncertain network communication the connection of Markov discrete finite time switching system of asynchronous H_ filter design problem. The network transmission constraints by considering output system , which will lead to packet loss, delay and so on. In addition, the sensor nonlinearity and system mode switching and mode switching filter exist asynchronous phenomenon in the design process is considered, two random variables are used to describe the random phenomena. This system makes our model is more general than other finite time literature. Based on the stochastic analysis theory, has been such that the filtering error system is mean square random finite time bounded and satisfy the corresponding criterion of existence of asynchronous H_ filter 2 performance of the expected. With the help of the criterion and the decoupling method of matrix controller is improved in Chapter third to solve the problem of using the filter, the corresponding asynchronous filter design the proposed method is less conservative. Finally, a numerical example and the PWM boost converter to drive the model to illustrate the proposed method The superiority and feasibility of.3. 2 based on the results, further extended to nonlinear Markov switching network system, discusses the finite time asynchronous l_2-l_ filter design. In the design of asynchronous l_2-l_ filter, also considering transmission constraints of the network, as well as between modal and sensor nonlinear modal filter the asynchronous phenomenon. In the framework of finite time stability, combined with the Takagi-Sugeno fuzzy model, in-depth analysis of the characteristics of the nonlinear system, and analyzes the filtering error system finite time boundedness and robust l_2-l_ filter performance, design method of asynchronous l_2-l_ systems are considered. Finally through the model to illustrate the proposed design the method is available for a numerical example and an inverted pendulum.

【學位授予單位】：安徽工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN713;TP273

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