Constrained and Unconstrained Optimal Discounted Control of Piecewise Deterministic Markov Processes
Constrained and Unconstrained Optimal Discounted Control of Piecewise Deterministic Markov Processes
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DOI：
10.1137/140996380
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发表时间：
2016-06
期刊：
影响因子：
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通讯作者：
O. Costa;F. Dufour;A. Piunovskiy
中科院分区：
文献类型：
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作者：
O. Costa;F. Dufour;A. Piunovskiy
本文的主要目标是研究分段确定性马尔可夫过程的无限视野期望贴现连续时间最优控制问题，其中控制连续作用于过程的跳跃强度 $\lambda$ 和过程的转移测度 $Q$，但不作用于确定性流 $\phi$。本文的贡献适用于无约束和约束情况。假设可接受的控制策略集是由策略形成的，策略可能是随机的，并且取决于过程的历史，在设定值的动作空间中取值。对于无约束情况，我们根据过程 $\phi$、$\lambda$、$Q$ 的三个局部特征以及集值动作空间的半连续性性质提供充分条件，以保证积分微分最优方程（即所谓的 Bellman--Hamilton--Jacobi 方程）的存在性和唯一性以及最优（和 $\delta$-也是最优的）...
The main goal of this paper is to study the infinite-horizon expected discounted continuous-time optimal control problem of piecewise deterministic Markov processes with the control acting continuously on the jump intensity $\lambda$ and on the transition measure $Q$ of the process but not on the deterministic flow $\phi$. The contributions of the paper are for the unconstrained as well as the constrained cases. The set of admissible control strategies is assumed to be formed by policies, possibly randomized and depending on the history of the process, taking values in a set valued action space. For the unconstrained case we provide sufficient conditions based on the three local characteristics of the process $\phi$, $\lambda$, $Q$ and the semicontinuity properties of the set valued action space, to guarantee the existence and uniqueness of the integro-differential optimality equation (the so-called Bellman--Hamilton--Jacobi equation) as well as the existence of an optimal (and $\delta$-optimal, as well) ...