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A Generalization of the Bang-Bang Principle of Linear Control Theory*
Published online by Cambridge University Press: 20 November 2018
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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 |uoi(τ) = 1. Let Y(τ) be any (n × r ) matrix function in L1([ 0, t]).
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- 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
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