Gradient techniques for systems with no drift: a classical idea revisited

This paper proposes a technique for the control of analytic systems with no drift. It is based on the generation of “nonsingular loops” which allow linearized controllability. Once such loops are available, it is possible to employ standard Newton or steepest descent methods. The theoretical justification of the approach relies on results on genericity of nonsingular controls as well as a simple convergence lemma