Semigroup approach for the approximation of a control problem with unbounded dynamics

In this paper, we approximate a control problem in an infinite-dimensional Hilbert space by means of a sequence of discrete problems. In the differential equation which describes the dynamics, a Lipschitz perturbation of an unbounded linear operator appears. We prove a convergence result of the approximation value functions to the value function of the original problem.This research was supported by Ministero dell'Università e della Ricerca Scientifica e Technologica and by Consiglio Nazionale delle Ricerche, Rome, Italy.