Approximation of optimal control problem with state constraints: estimates and applications

We present some a priori estimates for the rate of convergence of two approximation schemes related to the deterministic infinite horizon problem with state constraints. A first order and a second order scheme are studied in detail and some hints on the construction of higher order methods are given. We prove that the schemes converge to the constrained viscosity solution of the related \hjb equation and we show that they can also be used to produce approximate optimal trajectories. The above results are applied to the numerical solution of a Vidale-Wolfe advertising model with state constraint.