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Statistical estimates for generalized splines

Magnus EgerstedtClyde Martin — 2003

ESAIM: Control, Optimisation and Calculus of Variations

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 EgerstedtClyde Martin — 2010

ESAIM: Control, Optimisation and Calculus of Variations

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.

Optimal impulsive control of delay systems

Florent DelmotteErik I. VerriestMagnus Egerstedt — 2008

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we solve an optimal control problem using the calculus of variation. The system under consideration is a switched autonomous delay system that undergoes jumps at the switching times. The control variables are the instants when the switches occur, and a set of scalars which determine the jump amplitudes. Optimality conditions involving analytic expressions for the partial derivatives of a given cost function with respect to the control variables are derived using the calculus of variation....

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