Nonoccurrence of the Lavrentiev Phenomenon in Optimal Control

Alexander J. Zaslavski
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Alexander J. Zaslavski: Technion - Israel Institute of Technology

Chapter Chapter 7 in Nonconvex Optimal Control and Variational Problems, 2013, pp 197-231 from Springer

Abstract: 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.

Keywords: Lavrentiev Phenomenon; Trajectory-control Pair; Nonconvex Optimal Control Problems; Baire Category; Integrand (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-7378-7_7

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DOI: 10.1007/978-1-4614-7378-7_7

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