【摘要】：近幾年,彈性系統(tǒng)的邊界觀測和邊界控制得到廣泛研究。多數(shù)情況下,描述分布參數(shù)系統(tǒng)的偏微分方程組求其解析解是不可能的或是相當復雜的。因此,在實際應用中,為了便于計算和工程上的實現(xiàn),利用近似計算方法求解偏微分方程和處理分布參數(shù)控制系統(tǒng)具有重要的理論意義和實用價值。本文用乘子法和濾波法研究了雙彈性弦空間半離散的邊界一致可觀性。首先,利用有限差分格式對雙彈性弦方程進行空間半離散化,給出離散系統(tǒng)的能量及其分析,得到系統(tǒng)是能量守恒系統(tǒng);其次,對離散系統(tǒng)的特征值和特征向量進行分析,給出特征值和特征向量的基本性質(zhì);再次,通過對特征向量的邊界觀測,指出離散系統(tǒng)不具有一致可觀性;最后,利用乘子法,通過選取合適的濾波空間,得到系統(tǒng)的一致邊界可觀性。本文結構如下,第一章是緒論部分,簡單介紹本文背景,方程可觀性的發(fā)展概述,本文主要研究工作。第二章是預備知識,介紹無窮為控制理論,應用程序的例子,空間半離散化類型。第三章,研究雙彈性弦空間半離散化的一致性,離散化系統(tǒng)的譜分析,觀測不等式的證明,離散化系統(tǒng)一致同時可觀性。
[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.
【學位授予單位】：渤海大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O241.8

【參考文獻】

相關期刊論文 前1條

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

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本文編號：2229080