The perfectB-splines and a time-optimal control problem |
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| Authors: | I J Schoenberg |
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| Institution: | (1) Mathematics Research Center, The University of Wisconsin, USA |
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| Abstract: | Letx
v
=cos (πν/n) (v=0, 1, …,n). It is shown that theB-splineM(x)=M(x; x
0
,x
1
,…, x
n
) is such thatM
n
(n)
(x) has a constant absolute value (=2
n−2 (n−1)!) in −1, 1]. Its integralf
0(x)=∫
−1
x
M(t)dt is shown to have an optimal property that allows to solveexplicitly a certain time-optimal control problem. |
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| Keywords: | |
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