This article is cited in 26 papers

The index of the second variation of a control system

A. V. Sarychev


Abstract: 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.

UDC: 519.3

MSC: 49B10, 93B05

Received: 05.03.1980

 English version: Mathematics of the USSR-Sbornik, 1982, 41:3, 383–401

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