Year: 2022
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 3 : pp. 351–382
Abstract
In this paper, we present our optimality results on optimal control problems for ordinary differential equations on Riemannian manifolds. For the problems with free states at the terminal time, we obtain the first and second-order necessary conditions, dynamical programming principle, and their relations. Then, we consider the problems with the initial and final states satisfying some inequality-type and equality-type constraints, and establish the corresponding first and second-order necessary conditions of optimal pairs in the sense of either spike or convex variations. For each of the above results concerning second-order optimality conditions, the curvature tensor of the underlying manifold plays a crucial role.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2021-0018
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 3 : pp. 351–382
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Optimal control necessary condition dynamical programming principle Riemannian manifold curvature tensor.