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

## Abstract

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 (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.

- Authors:

- Escola Politecnica da Universidade de Sao Paulo, Departamento de Engenharia de Telecomunicacoes e Controle (Brazil)
- Universite Bordeaux I, IMB, Institut Mathematiques de Bordeaux, INRIA Bordeaux Sud Ouest, Team: CQFD (France)

- Publication Date:

- OSTI Identifier:
- 21480258

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Applied Mathematics and Optimization; Journal Volume: 62; Journal Issue: 2; Other Information: DOI: 10.1007/s00245-010-9099-4; Copyright (c) 2010 Springer Science+Business Media, LLC

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; CONTROL THEORY; CONVERGENCE; MARKOV PROCESS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; OPTIMAL CONTROL; POISSON EQUATION; CONTROL; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL LOGIC; PARTIAL DIFFERENTIAL EQUATIONS; SPACE; STOCHASTIC PROCESSES

### Citation Formats

```
Costa, O. L. V., E-mail: oswaldo@lac.usp.b, and Dufour, F., E-mail: dufour@math.u-bordeaux1.f.
```*The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes*. United States: N. p., 2010.
Web. doi:10.1007/S00245-010-9099-4.

```
Costa, O. L. V., E-mail: oswaldo@lac.usp.b, & Dufour, F., E-mail: dufour@math.u-bordeaux1.f.
```*The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes*. United States. doi:10.1007/S00245-010-9099-4.

```
Costa, O. L. V., E-mail: oswaldo@lac.usp.b, and Dufour, F., E-mail: dufour@math.u-bordeaux1.f. Fri .
"The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes". United States. doi:10.1007/S00245-010-9099-4.
```

```
@article{osti_21480258,
```

title = {The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes},

author = {Costa, O. L. V., E-mail: oswaldo@lac.usp.b and Dufour, F., E-mail: dufour@math.u-bordeaux1.f},

abstractNote = {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 (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.},

doi = {10.1007/S00245-010-9099-4},

journal = {Applied Mathematics and Optimization},

number = 2,

volume = 62,

place = {United States},

year = {Fri Oct 15 00:00:00 EDT 2010},

month = {Fri Oct 15 00:00:00 EDT 2010}

}

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