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

Journal Article · Fri Oct 15 04:00:00 EDT 2010 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-010-9099-4· OSTI ID:21480258

Costa, O L. V., ^[1]; Dufour, F ^[2]

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

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.

• OSTI ID: 21480258
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 62; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGORITHMS
CONTROL
CONTROL THEORY
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
MARKOV PROCESS
MATHEMATICAL LOGIC
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
OPTIMAL CONTROL
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
SPACE
STOCHASTIC PROCESSES