GENERIC LOCAL TIME-OPTIMAL STABILIZING CONTROLS IN DIMENSION 3.

This paper studies the control system dx(t)/dt equals X(x(t)) plus Y(x(t))u(t), X(p//0) equals 0, vertical u(t) vertical less than equivalent to 1, where X and Y are C** infinity vector fields on a 3-dimensional manifold M. Under generic assumptions on X, Y, the structure of the time-optimal stabilizing controls is completely determined in a neighborhood of p//0. The proofs rely on a systematic use of a local asymptotic approximation of X and Y by means of vector fields which generate a nilpotent Lie algebra.