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.
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
- controlled delay equations
- Distributed control problems
- viscosity solutions