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Published in:
2013 | OriginalPaper | Chapter
7. Nonoccurrence of the Lavrentiev Phenomenon in Optimal Control
Author : Alexander J. Zaslavski
Published in: Nonconvex Optimal Control and Variational Problems
Publisher: Springer New York
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Abstract
In this chapter we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonconvex optimal control problems which is identified with the corresponding complete metric space of integrands \(\mathcal{M}\) which satisfy a growth condition common in the literature and are Lipschitzian on bounded sets. We establish that for most elements of \(\mathcal{M}\) (in the sense of Baire category) the infimum on the full admissible class of trajectory-control pairs is equal to the infimum on a subclass of trajectory-control pairs whose controls are bounded by a certain constant.