Title :
Control theoretic smoothing splines
Author :
Sun, Shan ; Egerstedt, Magnus B. ; Martin, Clyde F.
Author_Institution :
Dept. of Math. & Stat., Texas Tech. Univ., Lubbock, TX, USA
fDate :
12/1/2000 12:00:00 AM
Abstract :
Some of the relationships between optimal control and statistics are examined. We produce generalized, smoothing splines by solving an optimal control problem for linear control systems, minimizing the L2-norm of the control signal, while driving the scalar output of the control system close to given, prespecified interpolation points. We then prove a convergence result for the smoothing splines, using results from the theory of numerical quadrature. Finally, we show, in simulations, that our approach works in practice as well as in theory
Keywords :
convergence of numerical methods; integration; interpolation; linear systems; optimal control; splines (mathematics); statistics; L2-norm; control theoretic smoothing splines; generalized smoothing splines; linear control systems; numerical quadrature; prespecified interpolation points; scalar output; Control systems; Convergence of numerical methods; Interpolation; Linear systems; Optimal control; Polynomials; Smoothing methods; Statistics; Sun; Trajectory;
Journal_Title :
Automatic Control, IEEE Transactions on
