發(fā)布時(shí)間：2018-11-08 15:09

【摘要】：近年來,動(dòng)力學(xué)系統(tǒng)的能控性理論在生物、物理、金融、醫(yī)學(xué)等方面都得到了廣泛的研究與應(yīng)用.基于此原因,本文主要利用分?jǐn)?shù)階微積分的相關(guān)知識(shí)與控制理論討論了幾類分?jǐn)?shù)階微分系統(tǒng)的控制問題.全文共分為六章.第一章,簡要介紹了分?jǐn)?shù)階微分方程、脈沖微分方程及控制理論的發(fā)展背景,國內(nèi)外研究現(xiàn)狀及本文的主要工作.第二章,歸納本文所需要的預(yù)備知識(shí),包括函數(shù)空間與Borel可測(cè),分?jǐn)?shù)階導(dǎo)數(shù)的定義和一些基本性質(zhì)以及本文用到的集值映射相關(guān)引理.第三章,研究了帶阻尼的線性和非線性脈沖分?jǐn)?shù)階微分系統(tǒng)的解的存在性與完全能控性.利用Mittag-Leffler矩陣函數(shù)以及Schauder不動(dòng)點(diǎn)定理證明解的存在性以及脈沖微分方程能控性存在的充分必要條件。第四章,研究了一類帶有非局部邊值條件的脈沖分?jǐn)?shù)階微分方程的最優(yōu)反饋控制.在前人的工作基礎(chǔ)上,利用Filippove引理以及一些相關(guān)的引理考慮了拉格朗日型問題的最優(yōu)控制.第五章,研究了一類Riemann-Liouville中立型分?jǐn)?shù)階代數(shù)系統(tǒng)的最優(yōu)反饋控制.通過利用Schaefer不動(dòng)點(diǎn)定理得到該系統(tǒng)的解的唯一性和存在性,再利用Filippove引理證明了可行集的非空性,最后討論了拉格朗日型問題的最優(yōu)控制對(duì)的存在性.第六章,總結(jié)目前的研究工作,并提出未來的研究設(shè)想.
[Abstract]:In recent years, the controllability theory of dynamic systems has been widely studied and applied in biology, physics, finance, medicine and so on. For this reason, this paper mainly discusses the control problems of several kinds of fractional differential systems by using the relevant knowledge of fractional calculus and control theory. The full text is divided into six chapters. In the first chapter, the development background of fractional differential equation, impulsive differential equation and control theory, the current research situation at home and abroad and the main work of this paper are briefly introduced. In the second chapter, we summarize the preparatory knowledge needed in this paper, including the definition of function space and Borel measurability, the definition of fractional derivative and some basic properties, and the relevant Lemma of set-valued mapping used in this paper. In chapter 3, the existence and complete controllability of solutions for linear and nonlinear impulsive fractional differential systems with damping are studied. By using Mittag-Leffler matrix function and Schauder fixed point theorem, the existence of solutions and the existence of controllability of impulsive differential equations are proved. In chapter 4, the optimal feedback control for a class of impulsive fractional differential equations with nonlocal boundary value conditions is studied. On the basis of previous work, the optimal control of Lagrange type problem is considered by using Filippove Lemma and some related Lemma. In chapter 5, the optimal feedback control for a class of Riemann-Liouville neutral fractional algebraic systems is studied. By using the Schaefer fixed point theorem, the uniqueness and existence of the solution of the system are obtained, and the nonempty property of the feasible set is proved by using the Filippove Lemma. Finally, the existence of the optimal control pair for the Lagrange type problem is discussed. The sixth chapter summarizes the current research work and puts forward the future research ideas.
【學(xué)位授予單位】：廣西民族大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 韋維;項(xiàng)筱玲;;一類非線性脈沖發(fā)展方程的最優(yōu)反饋控制(英文)[J];工程數(shù)學(xué)學(xué)報(bào);2006年02期

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本文編號(hào)：2318851