A control problem under incomplete information for a linear stochastic differential equation

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• 作者：V. L. Rozenberg
• 关键词：guidance problem ; guaranteed closed ; loop control ; linear stochastic differential equation
• 刊名：Proceedings of the Steklov Institute of Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：295
• 期：1-supp
• 页码：145-155
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Pleiades Publishing
• ISSN：1531-8605
• 卷排序：295

文摘

A problem of guaranteed closed-loop control under incomplete information is considered for a linear stochastic differential equation (SDE) from the viewpoint of the method of open-loop control packages worked out earlier for the guidance of a linear control system of ordinary differential equations (ODEs) to a convex target set. The problem consists in designing a deterministic open-loop control providing (irrespective of a realized initial state from a given finite set) prescribed properties of the solution (being a random process) at a terminal point in time. It is assumed that a linear signal on some number of realizations is observed. By the equations of the method of moments, the problem for the SDE is reduced to an equivalent problem for systems of ODEs describing the mathematical expectation and covariance matrix of the original process. Solvability conditions for the problems in question are written.