Control theoretic smoothing splines

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/sup 2/-norm of the control signal, while driving the scalar output of the control system close t...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2000-12, Vol.45 (12), p.2271-2279
Main Authors: Sun, S., Egerstedt, M.B., Martin, C.F.
Format: Article
Language:English
Subjects:
Control systems
Convergence
Convergence of numerical methods
Interpolation
Linear control
Linear systems
Optimal control
Polynomials
Smoothing
Smoothing methods
Splines
Statistics
Sun
Trajectory
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Summary: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/sup 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.895563