The Perfect B-Splines and a Time-Optimal Control Problem.

Abstract

Let x sub nu = cos ((pi)(nu)/n) (nu = 0, 1, ..., n). It is shown that the B-spline M(x) = M(x; x sub 0, x sub 1, ..., x sub n) is such that (M sub n, sup (n)) (x) has a constant absolute value (=(2 to the power (n-2)) (n-1) factorial in (-1,1). Its integral f sub 0 (x) = the integral from -1 to x M(t)dt is shown to have an optimal property that allows to solve explicitly a certain time-optimal control problem. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1971
Accession Number
AD0725094

Entities

People

  • Isaac Jacob Schoenberg

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Integrals

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Regression Analysis.