Local feedback structures and nilpotent approximations

A precise definition of when two control systems have equivalent local time-optimal feedback structures (LTOFS) is given. As expected, feedback equivalence implies equivalent LTOFS, but the latter is definitely a weaker equivalence. The resulting equivalence classes for low-dimensional affine systems are studied, and canonical representatives are given for systems of dimensions two and three. Results and questions concerning the LTOFS equivalence of an affine system and a nilpotent approximation of the system are included