發(fā)布時間：2018-08-30 15:42

【摘要】：作為一類特殊的混雜系統(tǒng),切換系統(tǒng)是研究混雜系統(tǒng)理論的一種重要模型。切換系統(tǒng)是由一系列連續(xù)時間或者離散時間子系統(tǒng)及一條作用在其中的切換規(guī)則組成的。由于切換的存在,系統(tǒng)的動態(tài)行為會變得十分復(fù)雜,從而為切換系統(tǒng)及相關(guān)領(lǐng)域提供了很多具有研究價值的課題。另外,實際系統(tǒng)由于存在著生產(chǎn)設(shè)備本身物理極限的問題而具有狀態(tài)受限,因此研究具有狀態(tài)約束的切換系統(tǒng)就更加具有實際意義。同時,線性切換正系統(tǒng)在網(wǎng)絡(luò)擁塞控制、傳染病控制等領(lǐng)域的廣泛應(yīng)用也引起了眾多學(xué)者的關(guān)注。本論文的主要研究內(nèi)容如下:本文首先介紹切換系統(tǒng)、切換正系統(tǒng)以及具有狀態(tài)約束的切換系統(tǒng)的概念。其中包括切換系統(tǒng)的研究背景、主要研究問題以及主要研究方法。在此基礎(chǔ)上,從連續(xù)時間和離散時間的角度,分別研究具有狀態(tài)約束的切換系統(tǒng)的鎮(zhèn)定問題。針對系統(tǒng)飽和發(fā)生與飽和不發(fā)生時每一個子系統(tǒng)所對應(yīng)的Lyapunov函數(shù)的衰減率都不相同的特點,提出一種同時具有飽和依賴型和模型依賴型的平均駐留時間方法。另外,給出切換系統(tǒng)的穩(wěn)定與鎮(zhèn)定的充分條件并且設(shè)計狀態(tài)反饋控制器。此外,本文設(shè)計的這種模型依賴型的改進的平均駐留時間比標準的平均駐留時間要小,且與飽和依賴型的改進的平均駐留時間方法相比,在一定程度上降低了保守性。然后,研究具有狀態(tài)約束的連續(xù)時間切換正系統(tǒng)鎮(zhèn)定問題。首先給出連續(xù)時間切換正系統(tǒng)的數(shù)學(xué)模型,利用前面提出的同時具有飽和依賴型和模型依賴型的改進的平均駐留時間方法,通過推導(dǎo)證明得到了切換正系統(tǒng)鎮(zhèn)定的充分條件以及相應(yīng)的狀態(tài)反饋控制器。最后,通過數(shù)值仿真例子來說明本章所提出方法的有效性。最后,對本文所做的研究工作進行總結(jié)并探討接下來需要繼續(xù)深入研究的問題,即對未來工作的展望。
[Abstract]:As a special class of hybrid systems, switched systems are an important model to study the theory of hybrid systems. Switched systems are composed of a series of continuous-time or discrete time subsystems and a switching rule acting on them. Because of the existence of handoff, the dynamic behavior of the system will become very complex, which provides a lot of valuable research topics for switched systems and related fields. In addition, the actual system has the state limitation because of the physical limit of the production equipment itself, so it is more meaningful to study the switching system with state constraints. At the same time, the extensive application of linear switched forward system in network congestion control, infectious disease control and other fields has attracted many scholars' attention. The main contents of this thesis are as follows: firstly, the concepts of switched systems, switched positive systems and switched systems with state constraints are introduced. It includes the research background, the main research problems and the main research methods of switched systems. On this basis, the stabilization problem of switched systems with state constraints is studied from the point of view of continuous time and discrete time respectively. In view of the fact that the attenuation rate of Lyapunov functions corresponding to each subsystem is different when saturation occurs and does not occur, an average resident time method with both saturation-dependent and model-dependent is proposed. In addition, sufficient conditions for stability and stabilization of switched systems are given and a state feedback controller is designed. In addition, the improved average residence time of the model dependent type is smaller than that of the standard one, and compared with the improved average residence time method of the saturated dependent type, it reduces the conservatism to some extent. Then, the stabilization problem of continuous-time switched positive systems with state constraints is studied. Firstly, the mathematical model of continuous time switching positive system is given, and the improved average dwell time method with both saturation and model dependence is used. The sufficient conditions for stabilization of switched positive systems and the corresponding state feedback controllers are proved by derivation. Finally, numerical simulation examples are given to illustrate the effectiveness of the proposed method. Finally, the research work done in this paper is summarized and the problems that need to be further studied are discussed, that is, the prospect of future work.
【學(xué)位授予單位】：東北電力大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP13

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本文編號：2213528