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

[1] M. R. Hestenes, “On Quadratic Control Problems”, Calculus of Variations and Control Theory (Proc. Symp. Madison, Wis., 1975), New York, e. a., 1976, 289–304 | MR | Zbl

[2] A. V. Dmitruk, “Ob uravnenii Eilera–Yakobi v variatsionnom ischislenii”, Matem. zametki, 20:6 (1976), 847–858 | MR | Zbl

[3] A. A. Agrachev, R. V. Gamkrelidze, “Eksponentsialnoe predstavlenie potokov i khronologicheskoe ischislenie”, Matem. sb., 107(149) (1978), 468–532 | MR

[4] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, izd-vo “Nauka”, Moskva, 1972

[5] M. Spivak, Matematicheskii analiz na mnogoobraziyakh, izd-vo “Mir”, Moskva, 1968 | MR

[6] R. V. Gamkrelidze, Osnovy optimalnogo upravleniya, izd-vo Tbil. un-ta, Tbilisi, 1977 | MR | Zbl