B-splines and control theory

Applied Mathematics and Computation

Volumn 145, Issue 2-3, 2003, Pages 263-288

  Kano, Hiroyuki ^a   Egerstedt, Magnus ^b   Nakata, Hiroaki ^a   Martin, Clyde F ^c  

^a TOKYO DENKI UNIVERSITY   (Japan)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c TEXAS TECH UNIVERSITY   (United States)

Author keywords

Approximation; B splines; Control theory; Dynamic splines; Interpolation

Indexed keywords

APPROXIMATION THEORY; CONTROL THEORY; INTERPOLATION; PROBLEM SOLVING; SPLINES;

DYNAMIC SPLINES;

LINEAR CONTROL SYSTEMS;

EID: 0042522633     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00486-1     Document Type: Article

References (10)

1. de Boor C. On uniform approximation by splines. J. Approx. Theory. 1:1968;219-235.
2. de Boor C. A Practical Guide to Splines. 1978;Springer-Verlag, New York.
3. Crouch P., Jackson J. Dynamic interpolation and application to flight control. J. Guidance, Control and Dynamics. 14:1991;814-822.
4. Shoenberg I. Spline functions, convex curves, and mechanical quadrature. Bull Amer. Math. Soc. 64:1958;352-357.
5. Shoenberg I., Whitney A. On the Poyla frequency function III. The positivity of translation determinants with an application to the interpolation problem for spline curves. Trans. Amer. Math. Soc. 74:1953;246-259.
6. Sun S., Egerstedt M., Martin C. Control theoretic smoothing splines. IEEE Trans. Automat. Control. 45:2000;2271-2279.
7. Martin C., Sun S., Egerstedt M. Optimal control, statistics and path planning. Math. Comput. Modelling. 33:2001;237-253.
8. Zhou Y., Martin C., Egerstedt M. Optimal approximation of functions. Comm. Inform. Systems. 1:2001.
9. Takayama K., Kano H. A new approach to synthesizing free motions of robotic manipulators based on the concept of unit motion. IEEE Trans. Systems Man Cybernet. 25:1995;453-463.
10. Luenberger D. Optimization by Vector Space Methods. 1969;John Wiley, New York.