2020/07/10 by Li Deng, Xu Zhang, Deng, Li +1
Engineering · Mathematics · #Elasticity and Material Modeling #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2007.05178
openalex publication_date 2020/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we are concerned with optimal control problems evolved on Riemannian manifolds, where the initial and final states satisfy some inequality and equality type constraints, and the control set is a separable metric space. We obtain the second order necessary conditions of integral and quasi-pointwise forms, both of which work for Pontryagin type critical controls and involve the curvature tensor. Also, we apply the condition of integral form to the Bolza problem, where the initial and final states are subject to equality's type constraint.