發(fā)布時(shí)間：2018-03-09 04:09

  本文選題：隨機(jī)拋物型方程　切入點(diǎn)：能控性　出處：《東北師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：本篇學(xué)位論文主要研究了耦合線性隨機(jī)拋物型方程組在單個(gè)控制下的能控性,以及在單個(gè)觀測下的能觀性問題.能控性和能觀性是現(xiàn)代控制論兩個(gè)基本的研究問題.能控性主要研究可行性問題.為了建立耦合隨機(jī)拋物系統(tǒng)的零能控性,本文采用了Lebeau-Robbiano方法.關(guān)鍵是證明當(dāng)終端值在有限維空間取值時(shí),某個(gè)倒向隨機(jī)耦合拋物型方程組的能觀性估計(jì).同時(shí),給出了一個(gè)反例,說明與確定性系統(tǒng)不同的是,對于隨機(jī)耦合拋物系統(tǒng)的零能控性,Kalman秩條件不再成立.另一方面,還證明了由多個(gè)隨機(jī)拋物型方程構(gòu)成的線性耦合方程組在單個(gè)觀測下的能觀性不等式和唯一延拓性質(zhì).本文采用了Carleman估計(jì)的方法.證明了在一定條件下,解向量的某一分量的局部信息可以決定所有解分量的整體信息.與已有的結(jié)果相比,本篇論文中的能觀性結(jié)論不僅對方程的個(gè)數(shù)沒有限制,對系數(shù)的正則性要求也較低。
[Abstract]:The controllability of coupled linear stochastic parabolic equations under a single control is studied in this dissertation. Controllability and observability are two basic problems in modern cybernetics. Controllability is the main feasibility problem. In order to establish zero controllability of coupled stochastic parabolic systems, In this paper, the Lebeau-Robbiano method is used. The key point is to prove the observability estimation of a backward stochastic coupled parabolic system when the terminal value is taken in a finite dimensional space. At the same time, a counterexample is given to show that different from the deterministic system, For stochastic coupled parabolic systems, the zero controllability Kalman rank condition no longer holds. On the other hand, In this paper, we also prove the observability inequality and the unique continuation property of linear coupled equations composed of multiple stochastic parabolic equations under a single observation. In this paper, we use the method of Carleman estimation to prove that under certain conditions, The local information of one component of the solution vector can determine the global information of all solution components. Compared with the existing results, the observability conclusion in this paper not only has no limit on the number of equations, but also requires less regularity of coefficients.
【學(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.26

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 Hongheng LI;Qi L;;Null Controllability for Some Systems of Two Backward Stochastic Heat Equations with One Control Force[J];Chinese Annals of Mathematics(Series B);2012年06期

，

本文編號：1586913