DUFOUR, François; HORIGUCHI, Masayuki; PIUNOVSKIY, Alexei

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Licence d’utilisation du document

DUFOUR, François
Institut Polytechnique de Bordeaux [Bordeaux INP]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]

HORIGUCHI, Masayuki
Department of Mathematics

PIUNOVSKIY, Alexei
Department of Mathematical Sciences [Liverpool]

Langue

Article de revue

Ce document a été publié dans

Stochastics: An International Journal of Probability and Stochastic Processes. 2016, vol. 88, n° 7, p. 1073-1098

Taylor & Francis: STM, Behavioural Science and Public Health Titles

Résumé en anglais

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.< Réduire

Mots clés en anglais

Optimal control

Piecewise deterministic Markov process

Impulsive control

Discounted cost

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193826

Project ANR

Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251