Limiting average cost control problems in a class of discrete-time stochastic systems
Volume 28 / 2001
Applicationes Mathematicae 28 (2001), 111-123
MSC: 93E20, 90C40.
DOI: 10.4064/am28-1-8
Abstract
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 $x_{t+1}=G_{\infty }(x_t,a_t)+\xi _t$ ($t=0,1,\dots$).
