具有期望路径约束的SDEs及相关约束FBSDEs的最优控制

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-02 DOI:10.3934/puqr.2022020

Ying Hu, Shanjian Tang, Z. Xu

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引用次数: 0

摘要

本文研究具有期望路径约束的随机微分方程的最优控制问题。给出了约束FBSDEs的一般最优随机控制的随机极大值原理。特别是伴随方程中的补偿过程是确定性的，这在文献中似乎是新的。对于线性随机系统和二次代价函数的典型情况(即所谓的LQ最优随机控制)，建立了验证定理，并给出了约束反射FBSDEs的存在唯一性。

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Optimal control of SDEs with expected path constraints and related constrained FBSDEs

In this paper, we consider optimal control of stochastic diﬀerential equations subject to an expected path constraint. The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs. In particular, the compensated process in our adjoint equation is deterministic, which seems to be new in the literature. For the typical case of linear stochastic systems and quadratic cost functionals (i.e., the so-called LQ optimal stochastic control), a veriﬁcation theorem is established, and the existence and uniqueness of the constrained reﬂected FBSDEs are also given.

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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.