Optimal control of a one-dimensional storage process
The author considers the discounted and ergodic control problems related to a one-dimensional storage process. He used feedback strategies and shows that, under mild conditions, the value function is differentiable and satisfies an integro-differential equation with boundary condition (Bellman equation). Moreover an optimal strategy \(\pi^*\) is derived by measurable selection and the origin is reachable under \(\pi^*\). The ergodic control is related to the limit of discounted control, as the discount factor tends to 0.
scientific article; zbMATH DE number 3914035