Limiting optimal discounted-cost control of a class of time-varying stochastic systems

We consider a class of time-varying R-d-valued control models, and with pos sibly unbounded costs. The processes evolve according to the system equatio n x(n+l) = G(n)(x(n), a(n))+ zeta (n) (n is an element of N), where (zeta ( n)) are i.i.d. random vectors and (G(n)) a sequence of known functions conv erging to some function G(infinity). Under suitable hypotheses, we show the existence of an alpha -discount optimal policy for the limiting system x(n +1) = G(infinity)(x(n), a(n)) + zeta (n). O (C) 2000 Elsevier Science B.V. All rights reserved.