Generalized Needles and Second-Order Conditions in Optimal Control
Informatics and Automation, Optimal control and differential equations, Tome 304 (2019), pp. 15-31.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using generalized needle variations, we derive second-order necessary optimality conditions for a strong minimum in an optimal control problem with endpoint constraints of general form.
@article{TRSPY_2019_304_a1,
     author = {E. R. Avakov and G. G. Magaril-Il'yaev},
     title = {Generalized {Needles} and {Second-Order} {Conditions} in {Optimal} {Control}},
     journal = {Informatics and Automation},
     pages = {15--31},
     publisher = {mathdoc},
     volume = {304},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a1/}
}
TY  - JOUR
AU  - E. R. Avakov
AU  - G. G. Magaril-Il'yaev
TI  - Generalized Needles and Second-Order Conditions in Optimal Control
JO  - Informatics and Automation
PY  - 2019
SP  - 15
EP  - 31
VL  - 304
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a1/
LA  - ru
ID  - TRSPY_2019_304_a1
ER  - 
%0 Journal Article
%A E. R. Avakov
%A G. G. Magaril-Il'yaev
%T Generalized Needles and Second-Order Conditions in Optimal Control
%J Informatics and Automation
%D 2019
%P 15-31
%V 304
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a1/
%G ru
%F TRSPY_2019_304_a1
E. R. Avakov; G. G. Magaril-Il'yaev. Generalized Needles and Second-Order Conditions in Optimal Control. Informatics and Automation, Optimal control and differential equations, Tome 304 (2019), pp. 15-31. http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a1/

[1] V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control, Consultants Bureau, New York, 1987 | MR | MR | Zbl

[2] A. V. Arutyunov, “Smooth abnormal problems in extremum theory and analysis”, Russ. Math. Surv., 67:3 (2012), 403–457 | DOI | DOI | MR | Zbl

[3] A. V. Arutyunov and N. T. Tynyanskii, “On necessary conditions for a local minimum in optimal control theory”, Sov. Math., Dokl., 29 (1984), 176–179 | MR | Zbl

[4] E. R. Avakov and G. G. Magaril-Il'yaev, “Controllability and second-order necessary conditions for optimality”, Sb. Math., 210:1 (2019), 1–23 | DOI | DOI | MR

[5] E. S. Levitin, A. A. Milyutin, and N. P. Osmolovskii, “Conditions of high order for a local minimum in problems with constraints”, Russ. Math. Surv., 33:6 (1978), 97–168 | DOI | MR | Zbl

[6] G. G. Magaril-Il'yaev, “The Pontryagin maximum principle. Ab ovo usque ad mala”, Proc. Steklov Inst. Math., 291 (2015), 203–218 | DOI | MR | Zbl

[7] Osmolovskii N.P., “Necessary quadratic conditions of extremum for discontinuous controls in optimal control problems with mixed constraints”, J. Math. Sci., 183:4 (2012), 435–576 | DOI | MR | Zbl

[8] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Pergamon, Oxford, 1964 | MR | MR | Zbl

[9] V. A. Zorich, Mathematical Analysis II, Springer, Berlin, 2016 | MR | Zbl