In this paper it is shown that the generalized smoothing spline obtained by solving an optimal control problem for a linear control system converges to a deterministic curve even when the data points are perturbed by random noise. We furthermore show that such a spline acts as a filter for white noise. Examples are constructed that support the practical usefulness of the method as well as gives some hints as to the speed of convergence.

Classification: 93-xx

Keywords: optimal control, smoothing splines, linear systems, interpolation

@article{COCV_2003__9__553_0, author = {Egerstedt, Magnus and Martin, Clyde}, title = {Statistical estimates for generalized splines}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {9}, year = {2003}, pages = {553-562}, doi = {10.1051/cocv:2003026}, zbl = {1070.41003}, mrnumber = {1998714}, language = {en}, url = {http://www.numdam.org/item/COCV_2003__9__553_0} }

Egerstedt, Magnus; Martin, Clyde. Statistical estimates for generalized splines. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003) , pp. 553-562. doi : 10.1051/cocv:2003026. http://www.numdam.org/item/COCV_2003__9__553_0/

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