A Connection Between the Maximum Principle and Dynamic Programming for Constrained Control Problems
A Connection Between the Maximum Principle and Dynamic Programming for Constrained Control Problems
复制标题
约束控制问题的极大值原理与动态规划的联系
DOI：
10.1137/s0363012903430585
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
H. Frankowska
中科院分区：
文献类型：
--
作者：
A. Cernea;H. Frankowska
我们考虑了由非凸微分包含给出的具有动力学的Mayer最优控制问题，其轨迹被约束在一个闭集上，得到了以极大值原理的形式的必要的最优性条件以及余态与值函数之间的关系。这一附加关系依次被应用来证明最大值原理是非退化的。我们还给出了最大断裂原理正规性的一个充分条件。
为了得到这些结果，我们使用了微分包含的凸线性化和沿最优轨迹的约束的凸线性化。然后应用凸分析的对偶理论推导出最优性的必要条件。这样，我们将极大值原理和动态规划之间的已知关系从无约束问题推广到有约束情况。
We consider the Mayer optimal control problem with dynamics given by a nonconvex differential inclusion, whose trajectories are constrained to a closed set and obtain necessary optimality conditions in the form of the maximum principle together with a relation between the costate and the value function. This additional relation is applied in turn to show that the maximum principle is nondegenerate. We also provide a sufficient condition for the normality of the maximum\break principle.
To derive these results we use convex linearizations of differential inclusions and convex linearizations of constraints along optimal trajectories. Then duality theory of convex analysis is applied to derive necessary conditions for optimality. In this way we extend the known relations between the maximum principle and dynamic programming from the unconstrained problems to the constrained case.