Convergence of stochastic approximation coupled with perturbation analysis in a class of manufacturing flow control models

Christian van Delft (1) , A. Haurie , Pierre L'Ecuyer (2)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 DIRO - Département d'Informatique et de Recherche Opérationnelle [Montreal]

This paper deals with a class of piecewise determinstic control systems for which the optimal control can be approximated through the use of an optimization-by-simulation approach. The feedback control law is restricted to belong to an a priori fixed class of feedback control laws depending on a (small) finite set of parameters. Under some general conditions developed in this paper, infinitesimal perturbation analysis (IPA) can be used to estimate the gradient of the objective function with respect to these parameters for finite horizon simulation and the consistency of the IPA estimators, as the simulation length goes to infinity, is assured. Also, the parameters can be optimized through a stochastic approximation (SA) algorithm combined with IPA. We prove that in this context, under appropriate conditions, such an approach converges towards the optimum.

Keywords: Discrete event systems; piecewise deterministic control; manufacturing systems; simulation; stochastic approximation; gradient estimation; perturbation analysis

Domains: Humanities and Social Sciences; Business administration; Operations management and information technology

Christian van Delft, A. Haurie, Pierre L'Ecuyer. Convergence of stochastic approximation coupled with perturbation analysis in a class of manufacturing flow control models. Discrete Event Dynamic Systems, 1994, Vol.4,n°1, pp.87-111. ⟨10.1007/BF01516011⟩. ⟨hal-00471357⟩