# 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):

# Report Date:

## 1971-03-01

# Pagination or Media Count:

## 25.0

# Abstract:

Let x sub nu cos pinun nu 0, 1, ..., n. It is shown that the B-spline Mx Mx 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 Mtdt is shown to have an optimal property that allows to solve explicitly a certain time-optimal control problem. Author

# Descriptors:

# Subject Categories:

- Numerical Mathematics