Optimal Control of Piecewise Deterministic Markov Processes

O. L. V. Costa () and F. Dufour ()
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O. L. V. Costa: Escola Politécnica da Universidade de São Paulo, Departamento de Engenharia de Telecomunicações e Controle
F. Dufour: Université de Bordeaux, Institut Polytechnique de Bordeaux INRIA Bordeaux Sud Ouest, Team: ASTRAL IMB, Institut de Mathématiques de Bordeaux

A chapter in Stochastic Analysis, Filtering, and Stochastic Optimization, 2022, pp 53-77 from Springer

Abstract: Abstract This chapter studies the infinite-horizon continuous-time optimal control problem of piecewise deterministic Markov processes (PDMPs) with the control acting continuously on the jump intensity λ and on the transition measure Q of the process. Two optimality criteria are considered, the discounted cost case and the long run average cost case. We provide conditions for the existence of a solution to an integro-differential optimality equality, the so called Hamilton-Jacobi-Bellman HJB) equation, for the discounted cost case, and a solution to an HJB inequality for the long run average cost case, aswell as conditions for the existence of a deterministic stationary optimal policy. From the results for the discounted cost case and under some continuity and compactness hypothesis on the parameters and non-explosive assumptions for the process, we derive the conditions for the long run average cost case by employing the so-called vanishing discount approach.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-98519-6_3

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DOI: 10.1007/978-3-030-98519-6_3

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