Geodesic
A second order optimality principle for a time-optimal problem
Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 547-576 
A. A. Agrachev; R. V. Gamkrelidze. A second order optimality principle for a time-optimal problem. Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 547-576. http://geodesic.mathdoc.fr/item/SM_1976_29_4_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a general necessary optimality condition of second order is proved for a time-optimal problem. Necessary optimality conditions of second order are applied, in general, in studying singular optimal regimes which can not be found with the aid of the first-order necessary condition for optimality, i.e. with the aid of the Pontryagin maximum principle. Bibliography: 4 titles.

[1] H. J. Kelley, R. E. Kopp, H. G. Moyer, “Singular extremals”, Topics in Optimization, Acad. Press, New York, 1967 | MR

[2] R. Gabasov, F. M. Kirillova, Osobye optimalnye upravleniya, izd-vo «Nauka», Moskva, 1973 | MR

[3] A. Krener, The high order maximal principle for singular extremals, preprint, Univ. of California, Davis, 1973

[4] A. Krener, The high order maximal principle and its application to singular extremals, preprint, Univ. of California, Davis, 1975 | MR