Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/properties-of-the-lagrange-multipliers-in-the-pontryagin-maximum-3Cw0yAeE02
References (14)
-
A. Arutyunov, D. Karamzin, F. Pereira (2011)
R.V. Gamkrelidze’s maximum principle for optimal control problems with bounded phase coordinates and its relation to other optimality conditionsDoklady Mathematics, 83
-
I.P. Natanson (1974)
Teoriya funktsii veshchestvennoi peremennoi -
A. Arutyunov, D. Karamzin, F. Pereira (2011)
The Maximum Principle for Optimal Control Problems with State Constraints by R.V. Gamkrelidze: RevisitedJournal of Optimization Theory and Applications, 149
-
A.V. Arutyunov, D.Yu. Karamzin, F. Pereira (2011)
Gamkrelidze’s Maximum Principle for Optimal Control Problems with Bounded State Coordinates and Its Relation to Other Optimality ConditionsDokl. Akad. Nauk, 436
-
(2006)
Printsip maksimuma Pontryagina. Dokazatel’stva i prilozheniya (Pontryagin Maximum Principle -
P. Lax, H. Grossman, G. Avila (1959)
Theory of functions of a real variable -
(1997)
Usloviya ekstremuma. Anormal’nye i vyrozhdennye zadachi (Extremum Conditions -
(1990)
Neobkhodimoe uslovie v optimal’nom upravlenii (A Necessary Condition in Optimal Control) -
A.V. Arutyunov, D.A. Zhukov (2010)
Analysis of a Linear Optimal Control Problem with State ConstraintsVladikavkaz. Mat. Zh., 12
-
R. Hartl, S. Sethi, R. Vickson (1995)
A Survey of the Maximum Principles for Optimal Control Problems with State ConstraintsOPER: Continuous (Topic)
-
(1997)
Anormal'nye i vyrozhdennye zadachi (Extremum Conditions. Abnormal and Degenerate Problems) -
A.P. Afanas’ev, V.V. Dikusar, A.A. Milyutin, S.A. Chukanov (1990)
Neobkhodimoe uslovie v optimal’nom upravlenii -
(1983)
Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes) -
L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko (1983)
Matematicheskaya teoriya optimal’nykh protsessov
- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266112120051
- Publisher site
- See Article on Publisher Site
Abstract
We study the Pontryagin maximum principle for an optimal control problem with state constraints. We analyze the continuity of a vector function µ (which is one of the Lagrange multipliers corresponding to an extremal by virtue of the maximum principle) at the points where the extremal trajectory meets the boundary of the set given by the state constraints. We obtain sufficient conditions for the continuity of µ in terms of the smoothness of the extremal trajectory.
Journal
Differential Equations – Springer Journals
Published: Jan 23, 2013