Controllability of nonlinear control systems

Controllability properties of analytic affine control systems ?? with an arbitrary number of controls and no a priori bounds are studied, without any restriction on the dimension of the Lie algebra T´ generated by the input vector fields. Sufficient conditions for local controllability at a point are presented, involving the Lie brackets at that point, and global controllability results for codimension one systems are derived from the geometric properties of the set where a necessary condition is verified. A sufficient condition for local controllability along a reference trajectory of scalar input systems is also presented.