Existence of optimal pairs for optimal control problems with states constrained to Riemannian manifolds

2024/01/13 by Li Deng, Xu Zhang, Deng, Li +1 · 1 citation
Computer Science · Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2401.07006

openalex publication_date 2024/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 [3, Definition 3.3, p. 51]) from the setting of Euclidean spaces to that of Riemannian manifolds. Moreover, we show the efficiency of our result by a concrete example.

Cited by

• Inexact calculus of variations on the hyperspherical tangent bundle with connections to the attention mechanism

Related

• Second Order Necessary Conditions for Endpoints-Constrained Optimal Control Problems on Riemannian manifolds
• Second Order Necessary Conditions for Optimal Control Problems on Riemannian Manifolds
• On the Reinhardt Conjecture and Formal Foundations of Optimal Control
• Riemannian optimal control
• The optimal control related to Riemannian manifolds and the viscosity solutions to H-J-B equations