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This papers deals with the constrained discounted control of piecewise deterministic Markov process (PDMPs) in general Borel spaces. The control variable acts on the jump rate and transition measure, and the goal is to minimize the total expected discounted cost, composed of positive running and boundary costs, while satisfying some constraints also in this form. The basic idea is, by using the special features of the PDMPs, to re-write the problem via an embedded discrete-time Markov chain associated to the PDMP and re-formulate the problem as an infinite dimensional linear programming (LP) problem, via the occupation measures associated to the discrete-time process. It is important to stress however that our new discrete-time problem is not in the same framework of a general constrained discrete-time Markov Decision Process and, due to that, some conditions are required to get the equivalence between the continuous-time problem and the LP formulation. We provide in the sequel sufficient conditions for the solvability of the associated LP problem, based on a generalization of Theorem 4.1 in [8]. In the Appendix we present the proof of this generalization which, we believe, is of interest on its own. The paper is concluded with some examples to illustrate the obtained results.
This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts
The main goal of this paper 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 (PDMPs) taking values in a general Borel s
The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact act
We study discrete-time discounted constrained Markov decision processes (CMDPs) on Borel spaces with unbounded reward functions. In our approach the transition probability functions are weakly or set-wise continuous. The reward functions are upper se
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled process is shown