SDE控制的随机线性二次控制问题离散化的误差分析

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS IMA Journal of Mathematical Control and Information Pub Date : 2021-08-01 DOI:10.1093/imamci/dnab031

Yanqing Wang

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引用次数: 3

摘要

本文对具有控制相关噪声的随机微分方程随机线性二次型问题提出了一种时间隐式离散化方法，并证明了该离散化方法的收敛速度。与现有结果相比，控制变量是随机过程，可以包含在系统的扩散项中。在此基础上，提出了一种梯度下降算法及其收敛速度。最后，给出了一个数值例子来支持理论发现。

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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Error analysis of a discretization for stochastic linear quadratic control problems governed by SDEs

In this work, a time-implicit discretization for stochastic linear quadratic problems subject to stochastic differential equations with control-dependence noises is proposed, and the convergence rate of this discretization is proved. Compared to the existing results, the control variables are stochastic processes and can be contained in systems’ diffusion term. Based on this discretization, a gradient descent algorithm and its convergence rate are presented. Finally, a numerical example is provided to support the theoretical finding.

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来源期刊

IMA Journal of Mathematical Control and Information 工程技术-应用数学

CiteScore

3.30

自引率

6.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal is to provide an outlet for papers which are original and of high quality in mathematical control theory, systems theory, and applied information sciences. Short papers and mathematical correspondence or technical notes will be welcome, although the primary function of the journal is to publish papers of substantial length and coverage. The emphasis will be upon relevance, originality and clarify of presentation, although timeliness may well be an important feature in acceptable papers. Speculative papers that suggest new avenues for research or potential solutions to unsolved problems of control and information theory will be particularly welcome. Specific application papers will not normally be within the remit of the journal. Applications that illustrate techniques or theories will be acceptable. A prime function of the journal is to encourage the interplay between control and information theory and other mathematical sciences. All submitted papers will be judged on their merits by at least two referees and a full paper report will be available to the intending authors. Submitted articles will in general be published in an issue within six months of submission. Papers should not have previously published, nor should they be undes consideration for publication in another journal. This Journal takes publication ethics very seriously. If misconduct is found or suspected after the manuscript is published, the journal will investigate the matter and this may result in the article subsequently being retracted.