Hamilton-Jacobi-Bellman inequality for the average control of piecewise deterministic Markov processes

Autor(es)

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

Afiliação do(s) autor(es)

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

^[2] Univ Bordeaux, INRIA Bordeaux Sud Ouest, Inst Polytech Bordeaux, Team CQFD, IMB, Bordeaux - France

• Tipo de documento: Artigo Científico
• Fonte: STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES; v. 91, n. 6, p. 817-835, AUG 18 2019.
• Citações Web of Science: 0

Resumo

The main goal of this paper is to study the infinite-horizon long run average continuous-time optimal control problem of piecewise deterministic Markov processes (PDMPs) with the control acting continuously on the jump intensity lambda and on the transition measure Q of the process. We provide conditions for the existence of a solution to an integro-differential optimality inequality, the so called Hamilton-Jacobi-Bellman (HJB) equation, and for the existence of a deterministic stationary optimal policy. These results are obtained by using the so-called vanishing discount approach, under some continuity and compactness assumptions on the parameters of the problem, as well as some non-explosive conditions for the process. (AU)

• Processo FAPESP: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Beneficiário: Julio Romano Meneghini
• Modalidade de apoio: Auxílio à Pesquisa - Programa Centros de Pesquisa em Engenharia
• Processo FAPESP: 14/50851-0 - INCT 2014: Instituto Nacional de Ciência e Tecnologia para Sistemas Autônomos Cooperativos Aplicados em Segurança e Meio Ambiente
• Beneficiário: Marco Henrique Terra
• Modalidade de apoio: Auxílio à Pesquisa - Temático