Brief paper: Periodic smoothing splines

Authors:
Hiroyuki Kano;Magnus Egerstedt;Hiroyuki Fujioka;Satoru Takahashi;Clyde Martin
Affiliations:
Department of Information Sciences, Tokyo Denki University, Hatoyama, Hiki-gun, Saitama 350-0394, Japan;School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;Department of Information Sciences, Tokyo Denki University, Hatoyama, Hiki-gun, Saitama 350-0394, Japan;Department of Intelligent Mechanical Systems Engineering, Kagawa University, 2217-20, Hayashi-Cho, Takamatsu-City, 761-0396, Japan;Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

Periodic smoothing splines appear for example as generators of closed, planar curves, and in this paper they are constructed using a controlled two point boundary value problem in order to generate the desired spline function. The procedure is based on minimum norm problems in Hilbert spaces and a suitable Hilbert space is defined together with a corresponding linear affine variety that captures the constraints. The optimization is then reduced to the computationally stable problem of finding the point in the constraint variety closest to the data points.