Existence of Optimal Pairs for Optimal Control Problems with States Constrained to Riemannian Manifolds

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-07-12 DOI:10.1137/23m1584095

Li Deng, Xu Zhang

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2098-2114, August 2024.
Abstract. In this paper, we investigate the existence of optimal pairs for optimal control problems with their states constrained pointwise to Riemannian manifolds. For this purpose, by means of the Riemannian geometric tool, we introduce a crucial Cesari-type property, which is an extension of the classical Cesari property (see Definition 3.3, p. 51 in [L. D. Berkovitz, Optimal Control Theory, Appl. Math. Sci. 12, Springer-Verlag, New York, Heidelberg, 1974]) from the setting of Euclidean spaces to that of Riemannian manifolds. Moreover, we show the efficiency of our result by a concrete example.

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状态受限于黎曼曼曲面的最优控制问题的最优对的存在性

SIAM 控制与优化期刊》，第 62 卷第 4 期，第 2098-2114 页，2024 年 8 月。摘要在本文中，我们研究了最优控制问题的最优对的存在性，这些问题的状态点约束于黎曼流形。为此，我们借助黎曼几何工具，引入了一个关键的 Cesari 型属性，它是经典 Cesari 属性的扩展（见 [L. D. Berkovitz, Optimal Control Problems, Riemannian Manifolds] 中的定义 3.3, 第 51 页）。D. Berkovitz, Optimal Control Theory, Appl.Sci. 12, Springer-Verlag, New York, Heidelberg, 1974]）中的定义 3.3）。此外，我们还通过一个具体的例子来说明我们的结果的效率。

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.