On the maximum principle when the endpoints of the optimal trajectory lie on the state boundary

Andrei V. Dmitruk; Nikolai P. Osmolovskii

doi:10.2478/candc-2024-0005

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On the maximum principle when the endpoints of the optimal trajectory lie on the state boundary

Control and Cybernetics

Volume 53 (2024): Issue 1 (March 2024)

By: Andrei V. Dmitruk and Nikolai P. Osmolovskii

Open Access

|Jan 2025

Abstract

We consider an optimal control problem in the Mayer form with an autonomous control system, a bounded control set U, endpoint equality constraints, and one pointwise state inequality constraint. We analyze the case when the starting point of the optimal trajectory belongs to the state boundary. A nontrivial maximum principle was obtained for this case by A.Ya. Dubovitskii and V.A. Dubovitskii about 40 years ago, but the proof was written in an extremely condensed form. Here we offer a new proof of their result.

References

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Articles in this issue

DOI: https://doi.org/10.2478/candc-2024-0005 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569

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Language: English

Page range: 77 - 107

Submitted on: May 1, 2024

Accepted on: Jun 1, 2024

Published on: Jan 17, 2025

Published by: Systems Research Institute Polish Academy of Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Lebesgue–Stieltjes measure,

singular measure,

costate equation

Related subjects:

Computer sciences,

Computer sciences, other,

Engineering,

Electrical engineering,

Fundamentals of electrical engineering,

Mechanical engineering,

Fundamentals of mechanical engineering,

Mathematics,

General mathematics

© 2025 Andrei V. Dmitruk, Nikolai P. Osmolovskii, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 53 (2024): Issue 1 (March 2024)