Geometric local controllability: second-order conditions

Abstract

In a geometric point of view, a nonlinear control system, affine in the controls, is thought of as an affine subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from this point of view, one should describe those properties of the affine subbundle that either ensure or prohibit local controllability. In this paper, second-order conditions of this nature are provided. The techniques involve a fusion of well-established analytical methods with differential geometric ideas.