In this paper some of the relationships between optimal control and statistics are examined. We produce generalized, smoothing splines by solving an optimal control problem for linear control systems, minimizing the L-2-norm of the control signal, while driving the scalar output of the control system close to given, prespecified interpolation points. We then prove a convergence result for the smoothing splines, using results from the theory of numerical quadrature. Finally, we show, in simulations, that our approach works in practice as well as in theory.