Displaying similar documents to “Optimal replacement under additive damage and self-restoration”

Semi-Markov control models with average costs

Fernando Luque-Vásquez, Onésimo Hernández-Lerma (1999)

Applicationes Mathematicae

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This paper studies semi-Markov control models with Borel state and control spaces, and unbounded cost functions, under the average cost criterion. Conditions are given for (i) the existence of a solution to the average cost optimality equation, and for (ii) the existence of strong optimal control policies. These conditions are illustrated with a semi-Markov replacement model.

Sample path average optimality of Markov control processes with strictly unbounded cost

Oscar Vega-Amaya (1999)

Applicationes Mathematicae

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We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover,...

Adaptive control for discrete-time Markov processes with unbounded costs: Discounted criterion

Evgueni I. Gordienko, J. Adolfo Minjárez-Sosa (1998)

Kybernetika

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We study the adaptive control problem for discrete-time Markov control processes with Borel state and action spaces and possibly unbounded one-stage costs. The processes are given by recurrent equations x t + 1 = F ( x t , a t , ξ t ) , t = 0 , 1 , ... with i.i.d. ℜ k -valued random vectors ξ t whose density ρ is unknown. Assuming observability of ξ t we propose the procedure of statistical estimation of ρ that allows us to prove discounted asymptotic optimality of two types of adaptive policies used early for the processes with bounded...

Average cost Markov control processes with weighted norms: existence of canonical policies

Evgueni Gordienko, Onésimo Hernández-Lerma (1995)

Applicationes Mathematicae

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This paper considers discrete-time Markov control processes on Borel spaces, with possibly unbounded costs, and the long run average cost (AC) criterion. Under appropriate hypotheses on weighted norms for the cost function and the transition law, the existence of solutions to the average cost optimality inequality and the average cost optimality equation are shown, which in turn yield the existence of AC-optimal and AC-canonical policies respectively.

Approximation and estimation in Markov control processes under a discounted criterion

J. Adolfo Minjárez-Sosa (2004)

Kybernetika

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We consider a class of discrete-time Markov control processes with Borel state and action spaces, and ℜ k -valued i.i.d. disturbances with unknown density ρ . Supposing possibly unbounded costs, we combine suitable density estimation methods of ρ with approximation procedures of the optimal cost function, to show the existence of a sequence { f ^ t } of minimizers converging to an optimal stationary policy f ∞ .