Convergence of approximations vs. regularity of solutions for convex,control-constrained optimal-control problems

A method of estimating the rate of convergence of approximation to convex, control-constrained optimal-control problems is proposed. In the method, conditions of optimality involving projections on the set of admissible control are exploited. General results are illustrated by examples of Galerkin-type approximations to optimal-control problems for parabolic systems.