Contrôle optimal stochastique des processus de Markov déterministes par morceaux et application à l’optimisation de maintenance

Alizée Geeraert 1
1 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We are interested in a discounted impulse control problem with infinite horizon forpiecewise deterministic Markov processes (PDMPs). In the first part, we model the evolutionof an optronic system by PDMPs. To optimize the maintenance of this equipment, we study animpulse control problem where both maintenance costs and the unavailability cost for the clientare considered. We next apply a numerical method for the approximation of the value function associated with the impulse control problem, which relies on quantization of PDMPs. The influence of the parameters on the numerical results is discussed. In the second part, we extendthe theoretical study of the impulse control problem by explicitly building a family of є-optimalstrategies. This approach is based on the iteration of a single-jump-or-intervention operator associatedto the PDMP and relies on the theory for optimal stopping of a piecewise-deterministic Markov process by U.S. Gugerli. In the present situation, the main difficulty consists in approximating the best position after the interventions, which is done by introducing a new operator.The originality of the proposed approach is the construction of є-optimal strategies that areexplicit, since they do not require preliminary resolutions of complex problems.
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Alizée Geeraert. Contrôle optimal stochastique des processus de Markov déterministes par morceaux et application à l’optimisation de maintenance. Mathématiques générales [math.GM]. Université de Bordeaux, 2017. Français. ⟨NNT : 2017BORD0602⟩. ⟨tel-01557969⟩

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