Stability of Solutions to Hamilton–Jacobi Equations Under State Constraints

  • Hayk Sedrakyan


In the present paper, we investigate stability of solutions of Hamilton–Jacobi–Bellman equations under state constraints by studying stability of value functions of a suitable family of Bolza optimal control problems under state constraints. The stability is guaranteed by the classical assumptions imposed on Hamiltonians and an inward-pointing condition on state constraints.


Hamilton–Jacobi equation Optimal control Bolza problem Viscosity solution State constraints Stability of solutions 

Mathematics Subject Classification

49L25 26E25 34A60 



This study was funded by the European Union under the Seventh Framework Programme ”FP7-PEOPLE-2010-ITN,” grant agreement number 264735-SADCO

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standard

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Additional informed consent was obtained from all individual participants for whom identifying information is included in this article.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.CNRS, IMJ-PRG, UMR 7586Sorbonne Universités, UPMC Univ Paris 06, UniveParis Diderot, Sorbonne Paris CitéParisFrance

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