Accession Number : AD0725094

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

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Schoenberg.,I. J.

Report Date : MAR 1971

Pagination or Media Count : 25

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)

Descriptors :   (*APPROXIMATION(MATHEMATICS), FUNCTIONS(MATHEMATICS)), (*INTERPOLATION, FUNCTIONS(MATHEMATICS)), ADAPTIVE CONTROL SYSTEMS, MATHEMATICAL MODELS, EQUATIONS OF MOTION, OPTIMIZATION, POLYNOMIALS, THEOREMS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE