Controllability Along a Trajectory: a Variational Approach

This paper unifies and improves most sufficient conditions of local controllability both along a trajectory and at a point. This is accomplished by defining high-order variations that can be continuously summed. The peculiar property of these variations is that they may be generated by thin conditions as relations in the Lie algebra associated with a control system. This property leads to a variational interpretation of Sussmann-type sufficient conditions of local controllability (neutralization of obstructions), and it allows the use of different weights for neutralization.