Jet bundles and algebro-geometric characterisations for controllability of affine systems

A geometric setting for studying control-affine systems is presented and a feedback-invariant approach to studying local controllability is introduced. The principal geometric object in this construction is a system-independent linear map which, when restricted to system-dependent data, describes a class of variations for the system. The resulting conditions for controllability take the form of algebraic equations on the jets of sections of certain vector bundles.