Optimal control problems of BV trajectories with pointwise state constraints
Résumé
This paper deals with some optimal control problems governed by ordinary differential equations with Radon measures as data and with pointwise state constraints. We study the properties of the value function and obtain its characterization by means of an auxiliary control problem of absolutely continuous trajectories. For this, we use some known techniques of reparametrization and graph completion. We are also interested in the characterization of the value function as the unique constrained viscosity solution of a Hamilton-Jacobi equation with measurable time dependant Hamiltonians.
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