Optimal impulsive control of piecewise deterministic Markov processes



Dufour, F, Horiguchi, M and Piunovskiy, AB
(2016) Optimal impulsive control of piecewise deterministic Markov processes. Stochastics: An International Journal of Probability and Stochastic Processes, 88 (7). 1073 - 1098.

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Abstract

In this paper, we study the infinite-horizon expected discounted continuous-time optimal control problem for Piecewise Deterministic Markov Processes with both impulsive and gradual (also called continuous) controls. The set of admissible control strategies is supposed to be formed by policies possibly randomized and depending on the past-history of the process. We assume that the gradual control acts on the jump intensity and on the transition measure, but not on the flow. The so-called Hamilton–Jacobi–Bellman (HJB) equation associated to this optimization problem is analyzed. We provide sufficient conditions for the existence of a solution to the HJB equation and show that the solution is in fact unique and coincides with the value function of the control problem. Moreover, the existence of an optimal control strategy is proven having the property to be stationary and non-randomized.

Item Type: Article
Uncontrolled Keywords: Optimal control, piecewise deterministic Markov process, impulsive control, discounted cost AMS Subject Classifications, Primary, 90C40, Secondary, 60J25
Depositing User: Symplectic Admin
Date Deposited: 01 Jul 2016 15:35
Last Modified: 14 Jan 2021 01:12
DOI: 10.1080/17442508.2016.1197925
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3001993