hal-01517510 https://ensta-paris.hal.science/hal-01517510 https://ensta-paris.hal.science/hal-01517510/document https://ensta-paris.hal.science/hal-01517510/file/VERSIONMar2017.pdf doi:10.1007/s11228-017-0413-z [ENSTA] ENSTA Paris [INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions [OPENAIRE] OpenAIRE [SADCO] Sensitivity Analysis for Deterministic Controller Design (SADCO) [SADCO_FELLOWS] SADCO_fellows [UMA_ENSTA] Unité de Mathématiques Appliquées (UMA) [TDS-MACS] Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes [UNIV-PARIS-SACLAY] Université Paris-Saclay [ENSTA-SACLAY] ENSTA-SACLAY [ANR] ANR The Mayer and Minimum Time Problems with Stratified State Constraints * Hermosilla, C. Wolenski, P.R. Zidani, Hasnaa [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC] [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP] ART minimal time function Hamilton-Jacobi equations State constraints stratified structure Mayer problem 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. 2017 2017-05-03 en Set-Valued and Variational Analysis Springer
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