Limiting average cost control problems in a class of discrete-time stochastic systems

Nadine Hilgert¹ ; Onesimo Hernández-Lerma²

¹ Departamento de Matematicas CINVESTAV-IPN Apartado Postal 14-740 Mexico D.F. 07000, Mexico Permanent address Laboratoire de Biometrie INRA-ENSA.M 2 place Viala 34060 Montpellier Cedex 1, France
² Departamento de Matematicas CINVESTAV-IPN Apartado Postal 14-740 Mexico D.F. 07000, Mexico

Applicationes Mathematicae, Tome 28 (2001) no. 1, pp. 111-123.

Résumé

We consider a class of $ {\Bbb R} ^d$-valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation $x_{t+1}=G_n(x_t,a_t)+\xi _t$ ($t=0,1,\dots $), for each fixed $n=0,1,\dots , $ where the $\xi _t$ are i.i.d. random vectors, and the $G_n$ are given functions converging pointwise to some function $G_{\infty }$ as $n \to \infty $. Under suitable hypotheses, our main results state the existence of stationary control policies that are expected average cost (EAC) optimal and sample path average cost (SPAC) optimal for the limiting control system $x_{t+1}=G_{\infty }(x_t,a_t)+\xi _t$ ($t=0,1,\dots$).

Détail

DOI : 10.4064/am28-1-8

Keywords: consider class bbb d valued stochastic control systems possibly unbounded costs systems evolve according discrete time equation t dots each fixed dots where random vectors given functions converging pointwise function infty infty under suitable hypotheses main results state existence stationary control policies expected average cost eac optimal sample path average cost spac optimal limiting control system infty t dots