DOI: 10.5176/2251-3388_1.1.15
Authors: Clyde F. Martin and Rochana Meegaskumbura
Abstract:
Over the recent years constrained smoothing splines have drawn much attention and significant amount of research is being done in this area. In this paper producing control theoretic smoothing splines with constraints on the derivative is discussed.Producing monotone control theoretic splines for general linear systems have been solved by formulating the problem as asemidefinite quadratic programming problem. The main focus of this paper will be on producing convex control theoretic splines.The linear system considered is two dimensional and therefore would give rise to a convex cubic control theoretic spline. A new basis functions are defined and a discretization technique based on fast discretization was adopted. Then the problem is reduced to a finite dimensional quadratic programming and can be solved easily by numerical computation. The construction of the optimal smooth convex curve is based on minimization of a quadratic cost functional using sequential quadratic programming.
Keywords: Controls; Convex Splines; Smoothing Spline
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