  In this article, we consider control theoretic splines with L1 optimization
for rejecting outliers in data. Control theoretic splines are either
interpolating or smoothing splines, depending on a cost function with a
constraint defined by linear differential equations. Control theoretic splines
are effective for Gaussian noise in data since the estimation is based on L2
optimization. However, in practice, there may be outliers in data, which may
occur with vanishingly small probability under the Gaussian assumption of
noise, to which L2-optimized spline regression may be very sensitive. To
achieve robustness against outliers, we propose to use L1 optimality, which is
also used in support vector regression. A numerical example shows the
effectiveness of the proposed method.
