Error estimates for linear-quadratic control problems with control constraints

An abstract linear-quadratic optimal control problem with pointwise control constraints is investigated. This article is concerned with the discretization of the control by piecewise linear functions. Under the assumption that the optimal control and the optimal adjoint state are Lipschitz continuous and piecewise of class C(2), an approximation of order h(3/2), is proved for the solution of the control discretized problem with respect to the solution of the continuous one. The theoretical results are illustrated by numerical tests.