Optimal strategies for impulse control of piecewise deterministic Markov processes. (March 2017)

• Record Type: Journal Article
• Authors: de Saporta, Benoîte; Dufour, François; Geeraert, Alizée
• Is Part Of: Automatica. Volume 77(2017)
• Page Start: 219
• Page End: 229
• Publication Date: 2017-03
• Subjects: Impulse control -- Piecewise deterministic Markov processes -- Optimal strategy -- Long-run average cost -- Dynamic programming; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.11.039
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper deals with the general discounted impulse control problem of a piecewise deterministic Markov process. We investigate a new family of ϵ -optimal strategies. The construction of such strategies is explicit and only necessitates the previous knowledge of the cost of the no-impulse strategy. In particular, it does not require the resolution of auxiliary optimal stopping problem or the computation of the value function at each point of the state space. This approach is based on the iteration of a single-jump-or-intervention operator associated to the piecewise deterministic Markov process.