Summary: We consider local feedback equivalence of control-affine systems in the plane. We present a general normal form for such systems with scalar control. In this form a polynomial of one variable appears, with coefficients which are functions of another variable. We show that these coefficients (called functional parameters) are invariants. This gives a complete feedback classification of planar systems. The classification results are stated separately for nonequilibrium and equilibrium points. The functional invariants which appear in the normal form have a direct interpretation in terms of singular, time-extremal trajectories of the systems. We show that, roughly, the singular extremals determine the functional invariants of the system and vice versa.
For the entire collection see [Zbl 0773.00014].