几类分数阶微分系统的能控性的研究
发布时间：2018-11-08 15:09
【摘要】：近年来,动力学系统的能控性理论在生物、物理、金融、医学等方面都得到了广泛的研究与应用.基于此原因,本文主要利用分数阶微积分的相关知识与控制理论讨论了几类分数阶微分系统的控制问题.全文共分为六章.第一章,简要介绍了分数阶微分方程、脉冲微分方程及控制理论的发展背景,国内外研究现状及本文的主要工作.第二章,归纳本文所需要的预备知识,包括函数空间与Borel可测,分数阶导数的定义和一些基本性质以及本文用到的集值映射相关引理.第三章,研究了带阻尼的线性和非线性脉冲分数阶微分系统的解的存在性与完全能控性.利用Mittag-Leffler矩阵函数以及Schauder不动点定理证明解的存在性以及脉冲微分方程能控性存在的充分必要条件。第四章,研究了一类带有非局部边值条件的脉冲分数阶微分方程的最优反馈控制.在前人的工作基础上,利用Filippove引理以及一些相关的引理考虑了拉格朗日型问题的最优控制.第五章,研究了一类Riemann-Liouville中立型分数阶代数系统的最优反馈控制.通过利用Schaefer不动点定理得到该系统的解的唯一性和存在性,再利用Filippove引理证明了可行集的非空性,最后讨论了拉格朗日型问题的最优控制对的存在性.第六章,总结目前的研究工作,并提出未来的研究设想.
[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.
【学位授予单位】：广西民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2318851
[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.
【学位授予单位】：广西民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关期刊论文 前1条
1 韦维;项筱玲;;一类非线性脉冲发展方程的最优反馈控制(英文)[J];工程数学学报;2006年02期
，本文编号：2318851
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