Multi-Level Smoothing Splines by Discrete-Time Control Systems

Hiroyuki Kano; Hiroyuki Fujioka; Keiichi Inoue

doi:10.11511/jacc.48.0.67.0

48th Proceedings of the Japan Joint Automatic Control Conference

Session ID : D2-24

DOI https://doi.org/10.11511/jacc.48.0.67.0

Conference information

Host: The Society of Instrument and Control Engineers, The Institute of Systems, Control and Information Engineers, The Japan Society of Mechanical Engineers, The Society of Chemical Engineers, Japan, The Japan Society for Precision Engineering, The Japan Society for Aeronautical and Space Sciences

Co-host: Technically Cosponsored by 43 Socies and Institutes

Multi-Level Smoothing Splines by Discrete-Time Control Systems

Hiroyuki Kano, Hiroyuki Fujioka, *Keiichi Inoue

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Keywords: multi-level smoothing splines, linear control systems, Hermite interpolation

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Abstract

We consider a problem of designing optimal smoothing spline curves by employing an approach based on linear control systems. In particular, we establish a design method of multi-level smoothing splines, a smoothing counterpart of Hermite interpolations, assuming that not only function values but also its derivatives are available as the data. The problem is formulated as an optimal control problem, and a necessary and sufficient condition for the existence of unique optimal solution is derived. The computational algorithm is simple as well as feasible numerically, and its effectiveness is verified by numerical examples.

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