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Published in:
2013 | OriginalPaper | Chapter
2. Well-posedness of Optimal Control Problems Without Convexity Assumptions
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 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.