Communications in Information and Systems

Volume 10 (2010)

Number 3

Periodic and Recursive Control Theoretic Smoothing Splines

Pages: 137 – 154



Xiaoming Hu

Maja Karasalo

Clyde F. Martin


In this paper, a recursive control theoretic smoothing spline approach is proposed for reconstructing a closed contour. Periodic splines are generated by minimizing a cost function subject to constraints imposed by a linear control system. The optimal control problem is shown to be proper, and sufficient optimality conditions are derived for a special case of the problem using Hamilton-Jacobi-Bellman theory.

The filtering effect of the smoothing splines allows for usage of noisy sensor data. An important feature of the method is that several data sets for the same closed contour can be processed recursively so that the accuracy is improved stepwise as new data becomes available.


Smoothing splines; optimal control; Hamilton-Jacobi-Bellman theory; periodic solutions

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