On the Hamilton-Jacobi-Bellman equations in Banach spaces

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Abstract

This paper is concerned with a certain class of distributed parameter control problems. The value function of these problems is shown to be the unique viscosity solution of the corresponding Hamiltonian-Jacobi-Bellman equation. The main assumption is the existence of an increasing sequence of compact invariant subsets of the state space. In particular, this assumption is satisfied by a class of controlled delay equations.

Original languageEnglish (US)
Pages (from-to)429-437
Number of pages9
JournalJournal of Optimization Theory and Applications
Volume57
Issue number3
DOIs
StatePublished - Jun 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Keywords

  • controlled delay equations
  • Distributed control problems
  • viscosity solutions

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