Maja Karasalo, KTH
E-mail: karasalo at math.kth.se
The focus of the talk will be on papers C, D and E, in which we investigate theoretical properties and applications for control theoretic smoothing splines.
Paper C, we consider the problem of estimating a closed curve in the plane based
on noise contaminated samples. A recursive control theoretic smoothing spline
approach is proposed, that yields an initial estimate of the
curve and subsequently computes refinements of the estimate iteratively. 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.
Paper D continues the study of recursive control theoretic smoothing splines. A discretization of the problem is derived, yielding an unconstrained quadratic programming problem. A proof of convexity for the discretized problem is provided, and the recursive algorithm is evaluated in simulations and experiments using a SICK laser scanner mounted on a PowerBot from ActivMedia Robotics.
Finally, in Paper E we explore the issue of optimal smoothing for control theoretic smoothing splines. The output of the control theoretic smoothing spline problem is essentially a tradeoff between faithfulness to measurement data and smoothness. This tradeoff is regulated by the so-called smoothing parameter. In Paper E, a method is developed for estimating the optimal value of this smoothing parameter. The procedure is based on general cross validation and requires no a priori information about the underlying curve or level of noise in the measurements.