随机偏微分方程控制理论的简明介绍

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-26 DOI:10.3934/MCRF.2021020

Qi Lu, Xu Zhang

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引用次数: 6

摘要

本讲义的目的是对随机偏微分方程控制系统的控制理论作一个简明的介绍。我们将主要关注这些系统的可控性和最优控制问题。对于第一个问题，我们给出了随机输运方程的精确可控性、随机抛物方程的零可控性和近似可控性以及随机双曲方程的缺乏精确可控性的结果。对于随机线性二次最优控制问题，我们首先介绍了随机线性二次最优控制问题，然后介绍了一般最优控制问题的庞特里亚金型极大值原理。值得一提的是，为了解决这一领域的一些难题，人们不得不开发新的工具，比如我们之前的工作中介绍的随机换位法。

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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A concise introduction to control theory for stochastic partial differential equations

The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the first one, we present results for the exact controllability of stochastic transport equations, null and approximate controllability of stochastic parabolic equations and lack of exact controllability of stochastic hyperbolic equations. For the second one, we first introduce the stochastic linear quadratic optimal control problems and then the Pontryagin type maximum principle for general optimal control problems. It deserves mentioning that, in order to solve some difficult problems in this field, one has to develop new tools, say, the stochastic transposition method introduced in our previous works.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.