Optimal impulsive control of piecewise deterministic Markov processes
| hal.structure.identifier | Institut Polytechnique de Bordeaux [Bordeaux INP] | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DUFOUR, François | |
| hal.structure.identifier | Department of Mathematics | |
| dc.contributor.author | HORIGUCHI, Masayuki | |
| hal.structure.identifier | Department of Mathematical Sciences [Liverpool] | |
| dc.contributor.author | PIUNOVSKIY, Alexei | |
| dc.date.accessioned | 2024-04-04T03:12:02Z | |
| dc.date.available | 2024-04-04T03:12:02Z | |
| dc.date.issued | 2016 | |
| dc.identifier.issn | 1744-2508 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193826 | |
| dc.description.abstractEn | In this paper, we study the infinite-horizon expected discounted continuous-time optimal control problem for Piecewise Deterministic Markov Processes with both impulsive and gradual (also called continuous) controls. The set of admissible control strategies is supposed to be formed by policies possibly randomized and depending on the past-history of the process. We assume that the gradual control acts on the jump intensity and on the transition measure, but not on the flow. The so-called Hamilton–Jacobi–Bellman (HJB) equation associated to this optimization problem is analyzed. We provide sufficient conditions for the existence of a solution to the HJB equation and show that the solution is in fact unique and coincides with the value function of the control problem. Moreover, the existence of an optimal control strategy is proven having the property to be stationary and non-randomized. | |
| dc.description.sponsorship | Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003 | |
| dc.language.iso | en | |
| dc.publisher | Taylor & Francis: STM, Behavioural Science and Public Health Titles | |
| dc.subject.en | Optimal control | |
| dc.subject.en | Piecewise deterministic Markov process | |
| dc.subject.en | Impulsive control | |
| dc.subject.en | Discounted cost | |
| dc.title.en | Optimal impulsive control of piecewise deterministic Markov processes | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| bordeaux.journal | Stochastics: An International Journal of Probability and Stochastic Processes | |
| bordeaux.page | 1073-1098 | |
| bordeaux.volume | 88 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 7 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01420963 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01420963v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Stochastics:%20An%20International%20Journal%20of%20Probability%20and%20Stochastic%20Processes&rft.date=2016&rft.volume=88&rft.issue=7&rft.spage=1073-1098&rft.epage=1073-1098&rft.eissn=1744-2508&rft.issn=1744-2508&rft.au=DUFOUR,%20Fran%C3%A7ois&HORIGUCHI,%20Masayuki&PIUNOVSKIY,%20Alexei&rft.genre=article |
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