The Mayer and Minimum Time Problems with Stratified State Constraints |
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Authors: | C Hermosilla P R Wolenski H Zidani |
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Institution: | 1.Departamento de Matemáticas,Universidad Técnica Federico Santa María,Valparaíso,Chile;2.Department of Mathematics,Louisiana State University,Baton Rouge,USA;3.Unité des Mathématiques Appliquées (UMA), ENSTA ParisTech,Palaiseau,France |
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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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