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Optimal Control of Piecewise Deterministic Markov Processes

In: Stochastic Analysis, Filtering, and Stochastic Optimization

Author

Listed:
  • 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)

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.

Suggested Citation

  • O. L. V. Costa & F. Dufour, 2022. "Optimal Control of Piecewise Deterministic Markov Processes," Springer Books, in: George Yin & Thaleia Zariphopoulou (ed.), Stochastic Analysis, Filtering, and Stochastic Optimization, pages 53-77, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98519-6_3
    DOI: 10.1007/978-3-030-98519-6_3
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