本文選題：精確能控性 + 同時(shí)能控性　； 參考：《山西大學(xué)》2017年碩士論文

【摘要】：能控性是分布參數(shù)控制理論的一個(gè)重要問(wèn)題。本文研究波方程系統(tǒng)的能控性問(wèn)題.在第一章中,我們簡(jiǎn)要地介紹了分布參數(shù)控制理論的研究進(jìn)展和本文的主要內(nèi)容。在第二章中,我們研究由若干個(gè)具有不同傳播速度的線性阻尼波解耦形成的方程組的同時(shí)精確能控性,證明可以用同一控制將所有波系統(tǒng)同時(shí)精確控制(這一性質(zhì)被稱為同時(shí)精確能控性).主要方法是,采用經(jīng)典的Hilbert唯一方法,建立原系統(tǒng)的能控性與其對(duì)偶系統(tǒng)的能觀測(cè)性的等價(jià)關(guān)系,通過(guò)證明能觀性不等式,得到原系統(tǒng)的同時(shí)精確能控性.在第三章中,我們考慮下列一維非線性波方程yu-yxx+g(y)yt=hlw的內(nèi)部精確能控性,其中,g(·)是非負(fù)連續(xù)函數(shù),g(Y)Yt稱為退化阻尼項(xiàng),h是施加在方程內(nèi)部的控制函數(shù).假設(shè)g(·)滿足(?)γ(γ為充分小的正數(shù))時(shí),我們應(yīng)用線性化原理和對(duì)線性化阻尼波方程的顯式能觀性不等式估計(jì),證明在齊次狄利克雷邊界條件下退化阻尼波系統(tǒng)是整體精確能控的;假設(shè)g(s)=|s|,利用Banach不動(dòng)點(diǎn)定理,我們得到退化阻尼波系統(tǒng)的局部精確能控性.在第四章中,我們討論了半線性波方程的兩個(gè)脫敏控制問(wèn)題.假設(shè)非線性項(xiàng)f滿足(?)=(?)=0,證明了紐曼邊界觀測(cè)量對(duì)于初始擾動(dòng)可以實(shí)現(xiàn)脫敏控制;假設(shè)非線性項(xiàng)f是整體Lipschitz連續(xù)性的,我們證明內(nèi)部觀測(cè)量對(duì)于初始擾動(dòng)可以實(shí)現(xiàn)近似脫敏控制.
[Abstract]:Controllability is an important problem in distributed parameter control theory. In this paper, we study the controllability of wave equation systems. In the first chapter, we briefly introduce the research progress of distributed parameter control theory and the main contents of this paper. In the second chapter, we study the simultaneous exact controllability of several linear damped wave decoupling equations with different propagation velocities. It is proved that all wave systems can be controlled precisely at the same time by the same control (this property is called simultaneous precise controllability). The main method is to establish the equivalent relation between the controllability of the original system and the observability of the dual system by using the classical Hilbert unique method. By proving the observability inequality, the simultaneous exact controllability of the original system is obtained. In chapter 3, we consider the following internal exact controllability of yu-yxx g(y)yt=hlw, where g () is a nonnegative continuous function called degenerate damping term h is a control function applied within the equation. Assuming that g () satisfies (緯) 緯 (緯 is a sufficiently small positive number), we apply the linearization principle and estimate the explicit observability inequality for the linearized damped wave equation, and prove that the degenerate damped wave system is globally accurately controllable under the homogeneous Delikley boundary condition. By using the Banach fixed point theorem, we obtain the locally exact controllability of degenerate damped wave systems. In chapter 4, we discuss two desensitization control problems for semilinear wave equations. Assuming that the nonlinear term f is satisfied, it is proved that the Newman boundary observation can realize desensitization control for the initial disturbance, and assuming that the nonlinear term f is global Lipschitz continuity, we prove that the internal observation can realize the approximate desensitization control for the initial disturbance.
【學(xué)位授予單位】：山西大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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本文編號(hào)：1793234