Displaying similar documents to “Generalized splines in ℝ n and optimal control.”

Statistical estimates for generalized splines

Magnus Egerstedt, Clyde Martin (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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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.

Statistical Estimates for Generalized Splines

Magnus Egerstedt, Clyde Martin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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.