A. A. Agrachev, R. V. Gamkrelidze, “A second order optimality principle for a time-optimal problem”, Mat. Sb. (N.S.), 100(142):4(8) (1976), 610–643
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 Pontrjagin maximum principle.