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2013 | OriginalPaper | Buchkapitel

2. Well-posedness of Optimal Control Problems Without Convexity Assumptions

verfasst von : Alexander J. Zaslavski

Erschienen in: Nonconvex Optimal Control and Variational Problems

Verlag: Springer New York

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Abstract

In this chapter we prove generic existence results for classes of optimal control problems in which constraint maps are also subject to variations as well as the cost functions. These results were obtained in [87, 90]. More precisely, we establish generic existence results for classes of optimal control problems (with the same system of differential equations, the same boundary conditions and without convexity assumptions) which are identified with the corresponding complete metric spaces of pairs (f, U) (where f is an integrand satisfying a certain growth condition and U is a constraint map) endowed with some natural topology. We will show that for a generic pair (f, U) the corresponding optimal control problem has a unique solution.

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Metadaten
Titel
Well-posedness of Optimal Control Problems Without Convexity Assumptions
verfasst von
Alexander J. Zaslavski
Copyright-Jahr
2013
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-7378-7_2