Bang-bang controls of point processes
Bang-bang controls of point processes
复制标题
点过程的 Bang-Bang 控制
DOI：
10.2307/1425910
复制
发表时间：
1976
影响因子：
1.2
通讯作者：
P. Brémaud
中科院分区：
文献类型：
--
作者：
P. Brémaud
本文考虑了在强度属于R ~+的某个闭区间的约束下，控制点过程的强度，使其在一个固定区间内的点数等于给定整数的概率最大化的问题.该问题被称为点过程的基本可测空间上的概率集的优化问题，并被证明是等价于确定性控制问题。给出了关于最优解集的结构结果。后者的存在性被证明;控制被证明是邦邦和一个完整的解决方案，可以通过应用庞特里亚金的最大值原理。
In this paper, we consider the problem of controlling the intensity of a point process in order to maximize the probability that the number of points in a fixed interval equals a given integer, under the constraint that the intensity belong to some closed interval of R +. The problem is stated as a problem of optimization on the set of probabilities over the basic measurable space of point processes, and shown to be equivalent to a problem of deterministic control. Structural results concerning the set of optimal solutions are given. The existence of the latter is proven; the control is shown to be bang-bang and a complete solution can be obtained by application of Pontryagin's Maximum Principle.