2018•Doklady MathematicsRequires access

Generalized Maximum Principle in Optimal Control

Evgeny Rachievich Avakov, Georgii Georgievich Magaril-Il'yaev

Abstract

The concept of a local infimum for an optimal control problem is introduced, and necessary conditions for it are formulated in the form of a family of “maximum principles.” If the infimum coincides with a strong minimum, then this family contains the classical Pontryagin maximum principle. Examples are given to show that the obtained necessary conditions strengthen and generalize previously known results.

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Key concepts: Maximum principle, Infimum and supremum, Pontryagin's minimum principle, Mathematics, Optimal control, Control (management), Applied mathematics, Mathematical optimization