Journal of Optimization Theory and Applications

, Volume 57, Issue 3, pp 429–437

On the Hamilton-Jacobi-Bellman equations in Banach spaces

  • H. Mete Soner
Contributed Papers

DOI: 10.1007/BF02346162

Cite this article as:
Mete Soner, H. J Optim Theory Appl (1988) 57: 429. doi:10.1007/BF02346162

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.

Key Words

Distributed control problemsviscosity solutionscontrolled delay equations

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • H. Mete Soner
    • 1
  1. 1.Department of MathematicsCarnegie Mellon UniversityPittsburgh