Necessary condition for optimal control of doubly stochastic systems
Necessary condition for optimal control of doubly stochastic systems
复制标题
双随机系统最优控制的必要条件
DOI：
10.3934/mcrf.2020002
复制
发表时间：
2020
影响因子：
1.2
通讯作者：
Yang Juan
中科院分区：
文献类型：
--
作者：
Zhang Liangquan;Zhou Qing;Yang Juan
本文的目的是建立由前向后双随机微分方程控制的系统的最优随机控制的一个必要条件。控制约束不需要是凸的。用两种包含两个布朗运动的新伴随过程来描述这一条件，对应于前向和后向分量以及哈密顿量的极大值条件。主要结果的证明是基于spike变分原理、对偶技术以及对控制变量的状态和伴随过程的精细估计。提供了一个示例来说明。
The aim of this paper is to establish a necessary condition for optimal stochastic controls where the systems governed by forward-backward doubly stochastic differential equations (FBDSDEs in short). The control constraints need not to be convex. This condition is described by two kinds of new adjoint processes containing two Brownian motions, corresponding to the forward and backward components and a maximum condition on the Hamiltonian. The proof of the main result is based on spike's variational principle, duality technique and delicate estimates on the state and the adjoint processes with respect to the control variable. An example is provided for illustration.