Contributed Papers

Journal of Optimization Theory and Applications

, Volume 57, Issue 3, pp 429-437

First online:

On the Hamilton-Jacobi-Bellman equations in Banach spaces

  • H. Mete SonerAffiliated withDepartment of Mathematics, Carnegie Mellon University

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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.

Key Words

Distributed control problems viscosity solutions controlled delay equations