论文标题
端点受约束最佳控制问题的二阶必需条件
Second Order Necessary Conditions for Endpoints-Constrained Optimal Control Problems on Riemannian manifolds
论文作者
论文摘要
在本文中，我们关注的是在Riemannian歧管上演变的最佳控制问题，在Riemannian歧管上，初始状态和最终状态满足某些不平等和平等类型的约束，而控制集则是可分离的度量空间。我们获得了积分和准点形式的二阶必需条件，两者都适用于Pontryagin型临界控制，并涉及曲率张量。此外，我们将整体形式的条件应用于Bolza问题，在Bolza问题中，初始状态和最终状态受到平等类型的约束。
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.
