Abstract
Lower closure theorems are proved for optimal control problems governed by ordinary differential equations for which the interval of definition may be unbounded. One theorem assumes that Cesari's property (Q) holds. Two theorems are proved which do not require property (Q), but assume either a generalized Lipschitz condition or a bound on the controls in an appropriateL p-space. An example shows that these hypotheses can hold without property (Q) holding.
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References
Berkovitz, L. D.,Optimal Control Theory, Springer-Verlag, New York, New York, 1974.
Baum, R. F.,Existence Theorems for Lagrange Control Problems with Unbounded Time Domain,Journal of Optimization Theory and Applications, Vol. 19, pp. 89–115, 1976.
Hille, E., andPhillips, R. S.,Functional Analysis and Semigroups, Revised Edition, American Mathematical Society, Providence, Rhode Island, 1957.
McShane, E. J., andWarfield, R. B.,On Filippov's Implicit Functions Lemma,Proceedings of the American Mathematical Society, Vol. 18, pp. 41–47, 1967.
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Communicated by L. D. Berkovitz
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Bates, G.R. Lower closure and existence theorems for optimal control problems with infinite horizon. J Optim Theory Appl 24, 639–649 (1978). https://doi.org/10.1007/BF00935304
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DOI: https://doi.org/10.1007/BF00935304