Control of systems without drift via generic loops

Abstract

This paper proposes a simple numerical tech- nique for the steering of arbitrary analytic systems with no drift. It is based on the generation of \nonsingular loops" which allow linearized controllability along suitable trajeto- ries. Once such loops are available, it is possible to employ standard Newton or steepest descent methods, as classically done in numerical control. The theoretical justication of the approach relies on recent results establishing the gener- icity of nonsingular controls, as well as a simple convergence lemma.