Abstract
This chapter starts with an example of a simple control problem without an optimal solution showing a need for existence results. A proof of the classic Filippov theorem on existence is also presented.
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   Theorem 13.1 is due to A.F. Filippov [39]. In its proof we followed. W.H. Fleming and R.W. Rishel [37]. The proof contains essential ingredients—in a simple form—of stronger existence results which can be found in the book by I. Cesari [15] or in the paper by C. Olech [72].
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Zabczyk, J. (2020). The existence of optimal strategies. In: Mathematical Control Theory. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-44778-6_13
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DOI: https://doi.org/10.1007/978-3-030-44778-6_13
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-44776-2
Online ISBN: 978-3-030-44778-6
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