Geodesic
The index of the second variation of a~control system
Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 383-401

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

The constancy of sign of the second variation of a nonlinear control system is investigated. Sufficient conditions for controllability of second order and also sufficient conditions for optimality with respect to fast action of the extremals of this system analogous to the Legendre–Jacobi conditions of the classical calculus of variation are obtained. Bibliography: 6 titles. 
@article{SM_1982_41_3_a3,
     author = {A. V. Sarychev},
     title = {The index of the second variation of a~control system},
     journal = {Sbornik. Mathematics},
     pages = {383--401},
     publisher = {mathdoc},
     volume = {41},
     number = {3},
     year = {1982},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_41_3_a3/}
}
TY  - JOUR
AU  - A. V. Sarychev
TI  - The index of the second variation of a~control system
JO  - Sbornik. Mathematics
PY  - 1982
SP  - 383
EP  - 401
VL  - 41
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1982_41_3_a3/
LA  - en
ID  - SM_1982_41_3_a3
ER  - 
%0 Journal Article
%A A. V. Sarychev
%T The index of the second variation of a~control system
%J Sbornik. Mathematics
%D 1982
%P 383-401
%V 41
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1982_41_3_a3/
%G en
%F SM_1982_41_3_a3
A. V. Sarychev. The index of the second variation of a~control system. Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 383-401. http://geodesic.mathdoc.fr/item/SM_1982_41_3_a3/