Generalized splines in R^n and optimal control
摘要
We have found an inconsistency in our previous version of the paper "Generalized splines in R^n and optimal control". We give a new-time-dependent definition of spline curves in R^n which results from solving a non-autonomous linear quadratic optimal control problem (P) where the matrix B(t) is assumed to be rectangular with maximum rank. Nevertheless, our results are only valid if B(t) is a square (nonsingular) matrix. This was pointed out to us by Andrey Sarychev. We have proceeded with the necessary corrections. %%%%%%%%%%%%%%%%%% We give a new time-dependent definition of spline curves in R^n, which extends a recent definition of vector-valued splines introduced by Rodrigues and Silva Leite for the time-independent case. Previous results are based on a variational approach, with lengthy arguments, which do not cover the non-autonomous situation. We show that the previous results are a consequence of the Pontryagin maximum principle, and are easily generalized using the methods of optimal control. Main result asserts that vector-valued splines are related to the Pontryagin extremals of a non-autonomous linear-quadratic optimal control problem.
关键词
引用
@article{arxiv.math/0405200,
title = {Generalized splines in R^n and optimal control},
author = {Rui C. Rodrigues and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:math/0405200},
year = {2007}
}
备注
This research was partially presented, as an oral communication, at the Second Junior European Meeting on "Control Theory and Stabilization", Dipartimento di Matematica del Politecnico di Torino, Torino, Italy, 3-5 December 2003. To appear on Rend. Sem. Mat. Univ. Pol. Torino, Vol. 64 (2006) No.1