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.
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.
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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