随机微分方程及相关Kolmogorov方程的最优控制

IF 1.3 4区数学 Q1 MATHEMATICS Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI:10.3934/eect.2022023

Ștefana-Lucia Aniţa

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引用次数: 0

摘要

本文研究了一个反馈马尔可夫输入的随机最优控制问题。该问题被简化为一个Kolmogorov方程的确定性最优控制问题，其中确定性问题的控制是开环型的。在一个特殊情况下，证明了确定性控制问题的最优控制的存在性。导出了一个极大值原理和若干一阶必要最优性条件。讨论了一些例子和评论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Optimal control for stochastic differential equations and related Kolmogorov equations

This paper concerns a stochastic optimal control problem with feedback Markov inputs. The problem is reduced to a deterministic optimal control problem for a Kolmogorov equation where the control for the deterministic problem is of open-loop type. The existence of an optimal control is proved for the deterministic control problem in a particular case. A maximum principle and some first order necessary optimality conditions are derived. Some examples and comments are discussed.

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology