耦合随机抛物系统的能控性和能观性

发布时间：2018-03-09 04:09

本文选题：随机抛物型方程　切入点：能控性　出处：《东北师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：本篇学位论文主要研究了耦合线性随机抛物型方程组在单个控制下的能控性,以及在单个观测下的能观性问题.能控性和能观性是现代控制论两个基本的研究问题.能控性主要研究可行性问题.为了建立耦合随机抛物系统的零能控性,本文采用了Lebeau-Robbiano方法.关键是证明当终端值在有限维空间取值时,某个倒向随机耦合抛物型方程组的能观性估计.同时,给出了一个反例,说明与确定性系统不同的是,对于随机耦合抛物系统的零能控性,Kalman秩条件不再成立.另一方面,还证明了由多个随机抛物型方程构成的线性耦合方程组在单个观测下的能观性不等式和唯一延拓性质.本文采用了Carleman估计的方法.证明了在一定条件下,解向量的某一分量的局部信息可以决定所有解分量的整体信息.与已有的结果相比,本篇论文中的能观性结论不仅对方程的个数没有限制,对系数的正则性要求也较低。
[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.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.26

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