Continuous Control of Piecewise Deterministic Markov Processes with Long Run Average Cost

Oswaldo Costa (1) , François Dufour (2, 3)

1 USP - Universidade de São Paulo = University of São Paulo
2 IMB - Institut de Mathématiques de Bordeaux
3 CQFD - Quality control and dynamic reliability

The main goal of this work is to derive sufficient conditions for the existence of an optimal control strategy for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we apply the so-called vanishing discount approach to obtain a solution to an average cost optimality inequality (ACOI) associated to the long run average cost problem. Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP.

Domaines: Optimisation et contrôle [math.OC]

Oswaldo Costa, François Dufour. Continuous Control of Piecewise Deterministic Markov Processes with Long Run Average Cost. Stochastic Processes, Finance and Control. A Festschrift in Honor of Robert J. Elliott., World Scientific, pp.120-154, 2012. ⟨hal-00759726⟩