Displaying similar documents to “Discrete-time Markov control processes with recursive discount rates”

Solutions of semi-Markov control models with recursive discount rates and approximation by ϵ -optimal policies

Yofre H. García, Juan González-Hernández (2019)

Kybernetika

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This paper studies a class of discrete-time discounted semi-Markov control model on Borel spaces. We assume possibly unbounded costs and a non-stationary exponential form in the discount factor which depends of on a rate, called the discount rate. Given an initial discount rate the evolution in next steps depends on both the previous discount rate and the sojourn time of the system at the current state. The new results provided here are the existence and the approximation of optimal...

Estimates of stability of Markov control processes with unbounded costs

Evgueni I. Gordienko, Francisco Salem-Silva (2000)

Kybernetika

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For a discrete-time Markov control process with the transition probability p , we compare the total discounted costs V β ( π β ) and V β ( π ˜ β ) , when applying the optimal control policy π β and its approximation π ˜ β . The policy π ˜ β is optimal for an approximating process with the transition probability p ˜ . A cost per stage for considered processes can be unbounded. Under certain ergodicity assumptions we establish the upper bound for the relative stability index [ V β ( π ˜ β ) - V β ( π β ) ] / V β ( π β ) . This bound does not depend...

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...

Modelling and optimal control of networked systems with stochastic communication protocols

Chaoqun Zhu, Bin Yang, Xiang Zhu (2020)

Kybernetika

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This paper is concerned with the finite and infinite horizon optimal control issue for a class of networked control systems with stochastic communication protocols. Due to the limitation of networked bandwidth, only the limited number of sensors and actuators are allowed to get access to network mediums according to stochastic access protocols. A discrete-time Markov chain with a known transition probability matrix is employed to describe the scheduling behaviors of the stochastic access...