Article 3220

Title of the article

INVESTIGATION OF CONDITIONS FOR NORMALITY IN CONTROL PROBLEMS WITH EQUALITY AND INEQUALITY STATE CONSTRAINTS 

Authors

Karamzin Dmitriy Yur'evich, doctor of physical and mathematical sciences, leading researcher, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (42/2 Vavilova street, Moscow, Russia), E-mail: dmitry_karamzin@mail.ru
Pereira Fernando Lobo, Ph.D in mathematics, Director of SYSTEC/FEUP, University of Porto (Porto, Portugal), E-mail: flp@fe.up.pt 

Index UDK

517.51 

DOI

10.21685/2307-4205-2020-2-3 

Abstract

This work aims to investigate conditions for normality of the maximum principle for general stateconstrained optimal control problems in which the state constraints are given by equalities and inequalities. Normality is proved under a regularity condition formulated in terms of the limiting normal cone to the feasible control set. The regularity condition implies normality of the maximum principle if one of the end-points is free. In this case, the case of a closed control set is considered. An estimate is given of the Lagrange multipliers responsible for state constraints of the type of equalities, which is closely related to the regularity property of the trajectory with respect to state constraints of this type. We also note that optimal control problems with state constraints play an important role in modeling various technical processes and systems. 

Key words

optimal control, maximum principle, state constraints 

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Дата создания: 17.07.2020 11:10
Дата обновления: 17.07.2020 11:40