An a Priori Estimate for Discrete Approximations in Nonlinear Optimal Control

We examine the convergence of an approximate discretization applied to the first-order optimality conditions for a nonlinear optimal control problem with convex control constraints. Under an assumption of the coercivity type we prove the existence of an optimal control for the original problem such that its L^∞ distance from the approximating sequence is proportional to the error. In a corollary we give conditions for Riemann integrability of the optimal control.