EXISTENCE OF OPTIMAL PAIRS FOR OPTIMAL CONTROL PROBLEMS WITH STATES CONSTRAINED TO RIEMANNIAN MANIFOLDS

被引：0
作者：
Deng, Li [1 ]
Zhang, Xu [2 ,3 ]
机构：
[1] Southwest Jiaotong Univ, Sch Math, Chengdu 611756, Peoples R China
[2] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China
[3] Sichuan Univ, New Cornerstone Sci Lab, Chengdu, Peoples R China
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2024年 / 62卷 / 04期
基金：
美国国家科学基金会;
关键词：
existence of optimal pairs; optimal controls; Cesari-type property; Riemannian manifolds; THEOREMS;
D O I：
10.1137/23M1584095
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
引用
收藏
页码：2098 / 2114
页数：17
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