Generalized Maximum Principle in Optimal Control

E. R. Avakov^a^,^b^,* and G. G. Magaril-Il’yaev^b^,^c
Translated by I. Ruzanova

^aTrapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia

^bFaculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia

^cKharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127994 Russia

Correspondence to: *e-mail: eramag@mail.ru

Received 19 June, 2018

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.

DOI: 10.1134/S1064562418070116