双弹性弦空间半离散化的一致边界可观性
发布时间：2018-09-07 18:31
【摘要】：近几年,弹性系统的边界观测和边界控制得到广泛研究。多数情况下,描述分布参数系统的偏微分方程组求其解析解是不可能的或是相当复杂的。因此,在实际应用中,为了便于计算和工程上的实现,利用近似计算方法求解偏微分方程和处理分布参数控制系统具有重要的理论意义和实用价值。本文用乘子法和滤波法研究了双弹性弦空间半离散的边界一致可观性。首先,利用有限差分格式对双弹性弦方程进行空间半离散化,给出离散系统的能量及其分析,得到系统是能量守恒系统;其次,对离散系统的特征值和特征向量进行分析,给出特征值和特征向量的基本性质;再次,通过对特征向量的边界观测,指出离散系统不具有一致可观性;最后,利用乘子法,通过选取合适的滤波空间,得到系统的一致边界可观性。本文结构如下,第一章是绪论部分,简单介绍本文背景,方程可观性的发展概述,本文主要研究工作。第二章是预备知识,介绍无穷为控制理论,应用程序的例子,空间半离散化类型。第三章,研究双弹性弦空间半离散化的一致性,离散化系统的谱分析,观测不等式的证明,离散化系统一致同时可观性。
[Abstract]:In recent years, boundary observation and boundary control of elastic systems have been extensively studied. In most cases, it is impossible or rather complex for a system of partial differential equations describing distributed parameter systems to find its analytical solution. Therefore, in practical applications, in order to facilitate the calculation and engineering realization, it is of great theoretical significance and practical value to solve partial differential equations and deal with distributed parameter control system by approximate calculation method. In this paper, the boundary uniform observability of semi-discrete space with two elastic strings is studied by means of multiplier method and filtering method. Firstly, the space semi-discretization of the bielastic chord equation is carried out by using finite difference scheme, and the energy of the discrete system and its analysis are given, the energy conservation system is obtained, and the eigenvalue and eigenvector of the discrete system are analyzed. The basic properties of eigenvalues and Eigenvectors are given. Thirdly, by observing the boundary of Eigenvectors, it is pointed out that the discrete systems are not uniformly observable. Finally, by means of the multiplier method, the proper filtering space is selected. The uniform boundary observability of the system is obtained. The structure of this paper is as follows. The first chapter is the introduction part, briefly introduces the background of this paper, the development of the equation observability, the main research work of this paper. The second chapter is the preparatory knowledge. It introduces the control theory of infinity, the example of application program, and the type of space semi-discretization. In chapter 3, we study the consistency of semi-discretization in bielastic chord space, the spectral analysis of discretized systems, the proof of observational inequalities, and the uniform simultaneous observability of discretized systems.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
本文编号：2229080
[Abstract]:In recent years, boundary observation and boundary control of elastic systems have been extensively studied. In most cases, it is impossible or rather complex for a system of partial differential equations describing distributed parameter systems to find its analytical solution. Therefore, in practical applications, in order to facilitate the calculation and engineering realization, it is of great theoretical significance and practical value to solve partial differential equations and deal with distributed parameter control system by approximate calculation method. In this paper, the boundary uniform observability of semi-discrete space with two elastic strings is studied by means of multiplier method and filtering method. Firstly, the space semi-discretization of the bielastic chord equation is carried out by using finite difference scheme, and the energy of the discrete system and its analysis are given, the energy conservation system is obtained, and the eigenvalue and eigenvector of the discrete system are analyzed. The basic properties of eigenvalues and Eigenvectors are given. Thirdly, by observing the boundary of Eigenvectors, it is pointed out that the discrete systems are not uniformly observable. Finally, by means of the multiplier method, the proper filtering space is selected. The uniform boundary observability of the system is obtained. The structure of this paper is as follows. The first chapter is the introduction part, briefly introduces the background of this paper, the development of the equation observability, the main research work of this paper. The second chapter is the preparatory knowledge. It introduces the control theory of infinity, the example of application program, and the type of space semi-discretization. In chapter 3, we study the consistency of semi-discretization in bielastic chord space, the spectral analysis of discretized systems, the proof of observational inequalities, and the uniform simultaneous observability of discretized systems.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
【参考文献】
相关期刊论文 前1条
1 Xiu-ling LI;Jun-jie WEI;;Stability and Bifurcation Analysis in a System of Four Coupled Neurons with Multiple Delays[J];Acta Mathematicae Applicatae Sinica(English Series);2013年02期
，本文编号：2229080
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