In this article, we propose and analyse a sparse grid collocation method to
solve an optimal control problem involving an elliptic partial differential equation with
random coefficients and forcing terms. The input data are assumed to be dependent on a finite number of random variables. We prove that an optimal solution exists, and derive
an optimality system. A Galerkin approximation in physical space and a sparse grid
collocation in the probability space is used. Error estimates for a fully discrete solution
using an appropriate norm are provided, and we analyse the computational efficiency.
Computational evidence complements the present theory, to show the effectiveness of
our stochastic collocation method.