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A Generalization of the Bang-Bang Principle of Linear Control Theory*

Published online by Cambridge University Press:  20 November 2018

Richard Datko
Richard Datko*
Affiliation:
McGill University
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Extract

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In a paper by LaSalle [l] on linear time optimal control the following lemma is proved:

Let Ω be the set of all r-dimensional vector functions U(τ) measurable on [ 0, t] with |ui(τ)≦1. Let Ωo be the subset of functions uo(τ) with |uo i(τ) = 1. Let Y(τ) be any (n × r ) matrix function in L1([ 0, t]).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 783 - 789
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. LaSalle, J. P., The Time Optimal Control Problem. Annals of Math. Studies, No. 45, pp. 1-24.Google Scholar
2. Blackwell, D., The Range of Certain Vector Integrals. Proc. Amer. Math. Soc. 2 (1951), 390-395.Google Scholar
3. Neustadt, L. W., The Existence of Optimal Controls in the Absence of Convexity Conditions. J. Math. Anal. Appl. 7, (1963), 110-117.Google Scholar