Stability of Solutions to Hamilton–Jacobi Equations Under State Constraints
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.
KeywordsHamilton–Jacobi equation Optimal control Bolza problem Viscosity solution State constraints Stability of solutions
Mathematics Subject Classification49L25 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.
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional informed consent was obtained from all individual participants for whom identifying information is included in this article.
- 2.Cannarsa, P., Sinestrari, C.: Semiconcave Functions, Hamilton–Jacobi Equations and Optimal Control. Progress in Nonlinear Differential Equations and their Applications, vol. 58. Birkhäuser, Boston (2004)Google Scholar
- 9.Frankowska H., Mazzola M.: On relations of the adjoint state to the value function for optimal control problems with state constraints. NODEA. doi: 10.1007/s00030-012-0183-0
- 11.Frankowska H., Plaskacz S.: Hamilton–Jacobi equations for infinite horizon control problems with state constraints. In: Proceedings of International Conference, Calculus of Variations and Related Topics, Haifa (1999)Google Scholar