873 research outputs found
Average optimality for continuous-time Markov decision processes under weak continuity conditions
This article considers the average optimality for a continuous-time Markov
decision process with Borel state and action spaces and an arbitrarily
unbounded nonnegative cost rate. The existence of a deterministic stationary
optimal policy is proved under a different and general set of conditions as
compared to the previous literature; the controlled process can be explosive,
the transition rates can be arbitrarily unbounded and are weakly continuous,
the multifunction defining the admissible action spaces can be neither
compact-valued nor upper semi-continuous, and the cost rate is not necessarily
inf-compact
Average Continuous Control of Piecewise Deterministic Markov Processes
This paper deals with the long run average continuous control problem of
piecewise deterministic Markov processes (PDMP's) taking values in a general
Borel space and with compact action space depending on the state variable. The
control variable acts on the jump rate and transition measure of the PDMP, and
the running and boundary costs are assumed to be positive but not necessarily
bounded. Our first main result is to obtain an optimality equation for the long
run average cost in terms of a discrete-time optimality equation related to the
embedded Markov chain given by the post-jump location of the PDMP. Our second
main result guarantees the existence of a feedback measurable selector for the
discrete-time optimality equation by establishing a connection between this
equation and an integro-differential equation. Our final main result is to
obtain some sufficient conditions for the existence of a solution for a
discrete-time optimality inequality and an ordinary optimal feedback control
for the long run average cost using the so-called vanishing discount approach.Comment: 34 page
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