Systems & Control Letters
Recurrence conditions for Markov decision processes with Borel state space: a survey
Annals of Operations Research
Discrete-time controlled Markov processes with average cost criterion: a survey
SIAM Journal on Control and Optimization
Stochastic dynamic programming and the control of queueing systems
Stochastic dynamic programming and the control of queueing systems
Stability of Piecewise-Deterministic Markov Processes
SIAM Journal on Control and Optimization
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Stochastic Optimal Control: The Discrete-Time Case
Stochastic Optimal Control: The Discrete-Time Case
A Dynamic Programming Algorithm for the Optimal Control of Piecewise Deterministic Markov Processes
SIAM Journal on Control and Optimization
Continuous Time Discounted Jump Markov Decision Processes: A Discrete-Event Approach
Mathematics of Operations Research
Bias Optimality for Continuous-Time Controlled Markov Chains
SIAM Journal on Control and Optimization
Stability and Ergodicity of Piecewise Deterministic Markov Processes
SIAM Journal on Control and Optimization
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This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) 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 postjump 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. Two examples are presented illustrating the possible applications of the results developed in the paper.