The Mayer and Minimum Time Problems with Stratified State Constraints *

Abstract : This paper studies optimal control problems with state constraints by imposing structural assumptions on the constraint domain coupled with a tangential restriction with the dynamics. These assumptions replace pointing or controllability assumptions that are common in the literature, and provide a framework under which feasible boundary trajectories can be analyzed directly. The value functions associated with the state constrained Mayer and minimal time problems are characterized as solutions to a pair of Hamilton-Jacobi inequalities with appropriate boundary conditions. The novel feature of these inequalities lies in the choice of the Hamiltonian.
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C. Hermosilla, P.R. Wolenski, Hasnaa Zidani. The Mayer and Minimum Time Problems with Stratified State Constraints *. Set-Valued and Variational Analysis, Springer, 2017, ⟨10.1007/s11228-017-0413-z⟩. ⟨hal-01517510⟩

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