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

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Hilgert N., Hernández-Lerma O.

Applicationes Mathematicae

2001

tom 28

nr 1

111-123

We consider a class of $ℝ^d$-valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation $x_{t+1} = Gₙ(x_t,a_t)+ξ_t$ (t = 0,1,... ), for each fixed n = 0,1,..., where the $ξ_t$ are i.i.d. random vectors, and the Gₙ are given functions converging pointwise to some function $G_{∞}$ as n → ∞. 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 $x_{t+1} = G_{∞}(x_t,a_t)+ξ_t$ (t = 0,1,...).

Ograniczanie wyników

1 Applicationes Mathematicae

1 Hernández-Lerma O.

1 Hilgert N.

1 2001

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