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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Acknowledgments

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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Correspondence to H. Zidani.

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Hermosilla, C., Wolenski, P.R. & Zidani, H. The Mayer and Minimum Time Problems with Stratified State Constraints. Set-Valued Var. Anal 26, 643–662 (2018). https://doi.org/10.1007/s11228-017-0413-z

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Keywords

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

Mathematics Subject Classification (2010)

  • 35B37
  • 49J15
  • 49Lxx
  • 49J53
  • 90C39