## Section: New Results

### The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

Participant : François Dufour.

The main goal of this work is to apply the so-called policy iteration algorithm (PIA) 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 first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form. These results have been obtained in collaboration with Oswaldo Luis Do Valle Costa from Escola Politécnica da Universidade de São Paulo, Brazil. It has been published in Applied Mathematics and Optimization [19] .