论文标题
网络上的随机控制：弱DPP和验证定理
Stochastic control on networks: weak DPP, and verification theorem
论文作者
论文摘要
本文的目的是研究连接处的随机控制问题，并在接线点进行控制。控制问题是在弱意义上提出的，使用放松的控制，即控制在紧凑型集合上的概率度量空间中的控制。我们首先证明了可接受规则的紧凑性和动态编程原则（DPP）。我们通过对问题的价值函数进行验证定理来完成本文，并使用在交界处提出的准线性非退化PDE的最新结果，并在接口点具有非线性neumann边界条件。给出了一个示例，其中接口点的最佳控制是与线性约束的凸二次优化问题的解决方案。
The purpose of this article is to study a stochastic control problem on a junction, with control at the junction point. The problem of control is formulated in the weak sense, using a relaxed control, namely a control which takes values in the space of probability measures on a compact set. We prove first the compactness of the admissible rules and the dynamic programming principle (DPP). We complete this article by giving a verification Theorem for the value function of the problem, using some recent results on quasi linear non degenerate PDE posed on a junction, with non linear Neumann boundary condition at the junction point. An example is given, where the optimal control at the junction point is solution of a convex quadratic optimization problem with linear constraints.
