黎曼流形上具有凸约束最优控制问题的必要条件

Necessary Conditions for Optimal Control Problems with Convex Constraints on Riemannian Manifolds

本文讨论黎曼流形上的最优控制问题,主要考虑的是初始状态固定,终止状态无约束,控制具有凸约束的情况。对于这种情况,通过引入适当的对偶方程,且它依赖于流形中的曲率张量,从而建立二阶必要条件。本文给出了黎曼流形上具有凸约束最优控制问题的一阶和二阶必要条件。

This paper mainly discusses the optimal control problem on the Riemannian manifold. The main considerations are the fixed initial state, the endpoint is free, and the control set is assumed to be convex in a Euclidian space. In this case, a second-order necessary condition is established by introducing an appropriate dual equation, which depends on the curvature tensor in the manifold. In this paper, first- and second-order necessary conditions for optimal control problems with convex constraints on Riemannian manifolds are given.