We investigate the optimal value of a deterministic control problem with state space constraint. We show that the optimal value function is the only viscosity subsolution, on the open domain, and the viscosity supersolution, on the closed domain, of the corresponding Bellman equation. Finally, the uniform continuity of the optimal value function is obtained under an assumption on the vector field.
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics