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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.

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