Hamilton–Jacobi–Bellman equations for optimal control processes with convex state constraints

Cristopher Hermosilla, Richard Vinter, Hasnaa Zidani

Research output: Contribution to journalArticle

6 Citations (Scopus)


© 2017 Elsevier B.V. This work aims at studying some optimal control problems with convex state constraint sets. It is known that for state constrained problems, and when the state constraint set coincides with the closure of its interior, the value function satisfies a Hamilton–Jacobi equation in the constrained viscosity sense. This notion of solution has been introduced by H.M. Soner (1986) and provides a characterization of the value functions in many situations where an inward pointing condition (IPC) is satisfied. Here, we first identify a class of control problems where the constrained viscosity notion is still suitable to characterize the value function without requiring the IPC. Moreover, we generalize the notion of constrained viscosity solutions to some situations where the state constraint set has an empty interior.
Original languageEnglish
Pages (from-to)30-36
Number of pages7
JournalSystems and Control Letters
Publication statusPublished - 1 Nov 2017

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