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Piecewise deterministic Markov control processes with feedback controls and unbounded costs. (English) Zbl 1084.49027
Summary: The control of piecewise-deterministic processes is studied where only local boundedness of the data is assumed. Moreover, the discount rate may be zero. The value function is shown to be a solution to the Bellman equation in a weak sense; however, the solution concept is strong enough to generate optimal policies. Continuity and compactness conditions are given for the existence of nonrelaxed optimal feedback controls.

49L20 Dynamic programming in optimal control and differential games
90C40 Markov and semi-Markov decision processes
93E20 Optimal stochastic control
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