Generalized splines in R^n and optimal control
| dc.creator | Rodrigues, Rui C. | |
| dc.creator | Torres, Delfim F. M. | |
| dc.date | 2004-05-11 | |
| dc.date | 2005-06-14 | |
| dc.date.accessioned | 2026-07-07T06:26:11Z | |
| dc.date.available | 2026-07-07T06:26:11Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/0405200 | |
| dc.identifier | http://arxiv.org/abs/math/0405200 | |
| dc.identifier | Rend. Sem. Mat. Univ. Pol. Torino, Vol. 64 (2006) No.1, pp. 63--78 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97035 | |
| dc.subject | Optimization and Control | |
| dc.subject | 49K15; 49N10; 41A15; 34H05 | |
| dc.title | Generalized splines in R^n and optimal control | |
| dc.type | text |