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LIPSCHITZ CONTINUITY OF THE MEASURE LAGRANGE MULTIPLIER FROM THE MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS OF EQUALITY AND INEQUALITY TYPE

Annotation

Properties of regular extremals in optimal control problems with equality and inequality state constraints are studied. It is proved that, under the regularity conditions, the strengthened Legendre condition implies Lipschitz continuity of the measure Lagrange multiplier from the maximum principle.

Keywords

optimal control; maximum principle; state constraints; Legendre condition

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DOI

10.20310/1810-0198-2017-22-3-508-516

UDC

517.977.52

Pages

508-516

References

1. Gorbacheva A.V., Karamzin D.Yu. Utochnenie uslovij optimal’nosti v zadachah upravleniya s fazovymi ogranicheniyami tipa ravenstv i neravenstv // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences. Tambov, 2016. V. 21. Iss. 1. P. 40–55. 2. Gorbacheva A.V. Nepreryvnost’ mery-mnozhitelya Lagranzha iz principa maksimuma dlya zadachi optimal’nogo upravleniya s fazovymi ogranicheniyami tipa ravenstv i neravenstv v usloviyah slaboj regulyarnosti ehkstremal’nogo processa // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences. Tambov, 2016. V. 21. Iss. 1. P. 28–39. 3. Arutyunov A.V., Karamzin D.Yu. On some continuity properties of the measure Lagrange multiplier from the maximum principle for state constrained problems // SIAM J. Control Optim. 2015. V. 53. № 4. P. 2514–2540. 4. Dubovickij A.YA., Milyutin A.A. Neobhodimye usloviya slabogo ehkstremuma v zadachah optimal’nogo upravleniya so smeshannymi ogranicheniyami tipa neravenstv // Zhurnal vychislitel’noj matematiki i matematicheskoj fiziki. 1968. T. 8. № 4. S. 725–779. 5. Natanson I.P. Teoriya funkcij veshchestvennoj peremennoj. M.: Nauka, 1974. 6. Alekseev V.M., Tihomirov V.M., Fomin S.V. Optimal’noe upravlenie. M.: Nauka, 1979.

Received

2017-06-03

Section of issue

Functional-differential equations and inclusions and their applications to mathematical modeling

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