THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

Autor(es)

Costa, O. L. V. ^[1] ; Dufour, F. ^{[2, 3]}

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Engn Telecomunicacoes & Controle, Escola Politecn, BR-05508900 Sao Paulo - Brazil

^[2] Univ Bordeaux 1, F-33405 Talence - France

^[3] INRIA Bordeaux Sud Ouest, Bordeaux - France

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF APPLIED PROBABILITY; v. 46, n. 4, p. 1157-1183, DEC 2009.
• Citações Web of Science: 4

Resumo

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). 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. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper. (AU)

• Processo FAPESP: 03/06736-7 - Controle e filtragem de sistemas estocásticos markovianos com saltos nos parâmetros
• Beneficiário: João Bosco Ribeiro do Val
• Modalidade de apoio: Auxílio à Pesquisa - Temático