Abstract
This chapter is devoted to the proof of the maximum principle, Theorem V.3.1. We shall actually prove a theorem that is more general than the maximum principle and shall obtain the maximum principle as a special case of this theorem. An essential property of an optimal trajectory is used to motivate the introduction of a concept called ℱ-N extremality. A necessary condition for ℱ-N extremality is then stated (Theorem 3.1 of this chapter), and it is shown how this implies Theorem V.3.1.
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© 1974 Springer Science+Business Media New York
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Berkovitz, L.D. (1974). Proof of the Maximum Principle. In: Optimal Control Theory. Applied Mathematical Sciences, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6097-2_6
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DOI: https://doi.org/10.1007/978-1-4757-6097-2_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2804-7
Online ISBN: 978-1-4757-6097-2
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