Optimal Control Duality and the Douglas–Rachford Algorithm

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-02-12 DOI:10.1137/23m1558549

Regina S. Burachik, Bethany I. Caldwell, C. Yalçin Kaya, Walaa M. Moursi

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 680-698, February 2024.
Abstract. We explore the relationship between the dual of a weighted minimum-energy control problem, a special case of linear-quadratic optimal control problems, and the Douglas–Rachford (DR) algorithm. We obtain an expression for the fixed point of the DR operator as applied to solving the optimal control problem, which in turn devises a certificate of optimality that can be employed for numerical verification. The fixed point and the optimality check are illustrated in two example optimal control problems.

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最优控制对偶性和道格拉斯-拉赫福德算法

SIAM 控制与优化期刊》第 62 卷第 1 期第 680-698 页，2024 年 2 月。摘要我们探讨了加权最小能量控制问题（线性二次优化控制问题的一种特例）的对偶与道格拉斯-拉赫福德（DR）算法之间的关系。我们得到了 DR 算子用于求解最优控制问题的定点表达式，进而设计出了可用于数值检验的最优性证书。固定点和最优性检验在两个优化控制问题示例中进行了说明。

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

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.