The Mayer and Minimum Time Problems with Stratified State Constraints

Article

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.

Keywords

State constraints Stratified structure Mayer problem Minimal time function Hamilton-Jacobi equations 

Mathematics Subject Classification (2010)

35B37 49J15 49Lxx 49J53 90C39 

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  3. 3.Unité des Mathématiques Appliquées (UMA), ENSTA ParisTechPalaiseauFrance

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