Set-Valued and Variational Analysis

, Volume 26, Issue 3, pp 643–662 | Cite as

The Mayer and Minimum Time Problems with Stratified State Constraints

  • C. Hermosilla
  • P. R. Wolenski
  • H. Zidani


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.


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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The authors would like to thank the editor and the anonymous referees for their useful comments and suggestions. This work was partially supported by iCODE institue, the European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN Grant agreement number 264735-SADCO and by the ANR project HJNet ANR-12-BS01-0008-01.


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© 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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