A Viscosity Approach To Infinite Dimensional Hamilton Jacobi Equations Arising In Optimal Control With State Constraints

Mathematics Research Report MRR95-072

A Viscosity Approach To Infinite Dimensional Hamilton Jacobi Equations Arising In Optimal Control With State Constraints

Maciej Kocan and Pierpaolo Soravia

Abstract: We consider nonlinear optimal control problems with state constraints and nonnegative cost in infinite dimensions, where the constraint is a closed set possibly with empty interior, for a class of systems with certain stability properties of the set of trajectories that allow the value function to be lower semicontinuous. We prove that the value function is a viscosity solution of the Bellman equation and is in fact the minimal nonnegative supersolution.

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