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arXiv · 1806.10418

Generalized maximum principle in optimal control

Evgeny Avakov·Georgii Magaril-Il'yaev
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Abstract

For an optimal control problem, the concept of a strong local infimum is introduce, for which necessary conditions consisting of some family of "maximum principles" are formulated. If a function delivers a strong local minimum in this problem (and therefore, a~strong local infimum), then this family contains the classical Pontryagin maximum principle. As a corollary, we derive generalized necessary conditions for a strong local minimum for a problem of the calculus of variations. Examples are given to show that the necessary conditions obtained in the present paper generalize and strengthen classical results.

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Evgeny Avakov, Georgii Magaril-Il'yaev. 2018-06-27. Generalized maximum principle in optimal control. https://arxiv.org/abs/1806.10418

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