Geodesic
Symplectic geometry and conditions necessary conditions for optimality
Sbornik. Mathematics, Tome 72 (1992) no. 1, pp. 29-45 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

With the help of a symplectic technique the concept of a field of extremals in the classical calculus of variations is generalized to optimal control problems. This enables us to get new optimality conditions that are equally suitable for regular, bang-bang, and singular extremals. Special attention is given to systems of the form $\dot x=f_0(x)+uf_1(x)$ with a scalar control. New pointwise conditions for optimality and sufficient conditions for local controllability are obtained as a consequence of the general theory. 
@article{SM_1992_72_1_a1,
     author = {A. A. Agrachev and R. V. Gamkrelidze},
     title = {Symplectic geometry and conditions necessary conditions for optimality},
     journal = {Sbornik. Mathematics},
     pages = {29--45},
     year = {1992},
     volume = {72},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_72_1_a1/}
}
TY  - JOUR
AU  - A. A. Agrachev
AU  - R. V. Gamkrelidze
TI  - Symplectic geometry and conditions necessary conditions for optimality
JO  - Sbornik. Mathematics
PY  - 1992
SP  - 29
EP  - 45
VL  - 72
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1992_72_1_a1/
LA  - en
ID  - SM_1992_72_1_a1
ER  - 
%0 Journal Article
%A A. A. Agrachev
%A R. V. Gamkrelidze
%T Symplectic geometry and conditions necessary conditions for optimality
%J Sbornik. Mathematics
%D 1992
%P 29-45
%V 72
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1992_72_1_a1/
%G en
%F SM_1992_72_1_a1
A. A. Agrachev; R. V. Gamkrelidze. Symplectic geometry and conditions necessary conditions for optimality. Sbornik. Mathematics, Tome 72 (1992) no. 1, pp. 29-45. http://geodesic.mathdoc.fr/item/SM_1992_72_1_a1/

[1] Agrachev A. A., “Kvadratichnye otobrazheniya v geometricheskoi teorii upravleniya”, Probl. geometrii, Itogi nauki i tekhn., VINITI, M., 1988, 111–205 | MR

[2] Agrachev A. A., Gamkrelidze R. V., “Indeks ekstremalnosti i kvaziekstremalnye upravleniya”, DAN SSSR, 284 (1985), 777–781 | MR | Zbl

[3] Agrachev A. A., Gamkrelidze R. V., “Indeksy Morsa i Maslova dlya gladkikh upravlyayuschikh sistem”, DAN SSSR, 284:3 (1986) | MR

[4] Agrachev A. A., Gamkrelidze R. V., “Kvaziekstremalnost dlya upravlyaemykh sistem”, Sovrem. probl. matem. Noveishie dostizheniya, Itogi nauki i tekhn., VINITI, M., 1989, 109–134 | MR

[5] Guillemin V., Sternberg S., Geometric Asymptolics, Math. Surveys, 14, AMS, Providence R. I., 1977 | MR | Zbl