Accuracy Estimates for Bilinear Optimal Control Problems Governed by Ordinary Differential Equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-03-31 DOI:10.1080/01630563.2023.2192776

Jacob Körner, A. Borzì

引用次数: 0

Abstract

Abstract First- and second-order accuracy estimates for an optimal control problem governed by a system of ordinary differential equations with a bilinear control mechanism are presented. The numerical time discretization scheme under consideration is the finite element method with continuous piecewise linear functions. Central to this work is a first- and second-order analysis of optimality of the continuous and approximated optimal control problems. In the case of box constraints on the control, first-order error estimates for the control function are obtained assuming a piecewise constant approximation of the control, whereas second-order accuracy can be obtained in the case of a continuous, piecewise polynomial approximation. Numerical evidence is presented that supports the theoretical findings.

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常微分方程双线性最优控制问题的精度估计

摘要给出了一类具有双线性控制机构的常微分方程组最优控制问题的一阶和二阶精度估计。所考虑的数值时间离散方案是具有连续分段线性函数的有限元法。这项工作的核心是连续和近似最优控制问题的一阶和二阶最优性分析。在控制框约束的情况下，控制函数的一阶误差估计是在假设控制的分段常数近似值的情况下得到的，而在连续的、分段多项式近似值的情况下可以得到二阶精度。数值证据支持理论发现。

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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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.