Comptes Rendus
no. 2
Optimal control
Pointwise second-order necessary conditions for optimal control problems evolved on Riemannian manifolds

Presented by: Jean-Michel Coron

Qing Cui1; Li Deng1; Xu Zhang2
1 School of Mathematics, Southwest Jiaotong University, Chengdu 611756, Sichuan Province, China
2 School of Mathematics, Sichuan University, Chengdu 610064, Sichuan Province, China
Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 191-194.

In this Note, we study an optimal control problem on a Riemannian manifold. The control set in our problem is assumed to be a general Polish space, and therefore the classical variation technique fails. We obtain a pointwise second-order optimality condition, for which the curvature tensor of the manifold appears explicitly in the second-order dual equation.

Dans cette Note, nous étudions un problème du contrôle optimal sur une variété riemannienne. Dans ce problème, l'ensemble des contrôles est un espace de Polish général ; ainsi, la technique de variation classique ne s'applique pas ici. On obtient une condition d'optimalité ponctuelle du second ordre, pour laquelle le tenseur de courbure de la variété apparaît explicitement dans l'équation duale du second ordre.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.09.032

Qing Cui 1; Li Deng 1; Xu Zhang 2

1 School of Mathematics, Southwest Jiaotong University, Chengdu 611756, Sichuan Province, China
2 School of Mathematics, Sichuan University, Chengdu 610064, Sichuan Province, China 
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Qing Cui; Li Deng; Xu Zhang. Pointwise second-order necessary conditions for optimal control problems evolved on Riemannian manifolds. Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 191-194. doi : 10.1016/j.crma.2015.09.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.032/

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