Abstract:We study optimal control problems in infinite horizon when the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in [35] to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov's "shaking the coefficients" method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a conv… Show more
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