Approximation and adaptive control of Markov processes: Average reward criterion
Onésimo Hernández-Lerma (1987)
Kybernetika
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Displaying similar documents to “Optimal control by means switchings”
Approximation and adaptive control of Markov processes: Average reward criterion
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.
Deterministic optimal policies for Markov control processes with pathwise constraints
Armando F. Mendoza-Pérez, Onésimo Hernández-Lerma (2012)
Applicationes Mathematicae
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This paper deals with discrete-time Markov control processes in Borel spaces with unbounded rewards. Under suitable hypotheses, we show that a randomized stationary policy is optimal for a certain expected constrained problem (ECP) if and only if it is optimal for the corresponding pathwise constrained problem (pathwise CP). Moreover, we show that a certain parametric family of unconstrained optimality equations yields convergence properties that lead to an approximation scheme which...
A semimartingale characterization of average optimal stationary policies for Markov decision processes.
Zhu, Quanxin, Guo, Xianping (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Existence of average optimal policies in Markov control processes with strictly unbounded costs
Onésimo Hernández-Lerma (1993)
Kybernetika
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Ergodic control of partially observed Markov processes with equivalent transition probabilities
Łukasz Stettner (1993)
Applicationes Mathematicae
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Optimal control with long run average cost functional of a partially observed Markov process is considered. Under the assumption that the transition probabilities are equivalent, the existence of the solution to the Bellman equation is shown, with the use of which optimal strategies are constructed.
Time-discretization for controlled Markov processes. I. General approximation results
Nico M. van Dijk, Arie Hordijk (1996)
Kybernetika
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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,...