Abstract
We consider those functionsu∈L ∞(a, b) which satisfyX′=Ax+Bu, whereX satisfies certain prescribed interpolatory constraints. We show that there is au with smallest sup norm and that suchu are uniquely determined on a certain subset of [a, b]; more restrictions allow us to conclude thatX is uniquely determined on this set. An extension is given to certain linear control systems on the real line.
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Fisher, S. D., andJerome, J. W.,Minimum Norm Extremals in Function Spaces, Lecture Notes in Mathematics, Vol. 479, Springer-Verlag, Berlin, Germany, 1975.
McClure, D. E., Perfect Spline Solutions ofL ∞ Extremal Problems by Control Methods, Journal of Approximation Theory, Vol. 15, pp. 226–242, 1975.
Hermes, H., andLaSalle, J. P.,Functional Analysis and Time Optimal Control, Academic Press, New York, New York, 1969.
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Communicated by G. Leitmann
Research supported in part by National Science Foundation Grant Nos. GP-43955 and MCS 75-05591.
Research supported in part by National Science Foundation Grant Nos. GP-43955 and MPS 74-02292-A01.
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Fisher, S.D., Jerome, J.W. Uniqueness of optimal controls inL ∞ . J Optim Theory Appl 21, 469–476 (1977). https://doi.org/10.1007/BF00933091
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DOI: https://doi.org/10.1007/BF00933091