Part I. Motivation and problem formulation

In the usual formulation of nonlinear control theory, one has a drift vector
field, representing the uncontrolled dynamics, and control vector fields,
representing that part of the dynamics that one can control. The choice of
drift vector field and control vector fields is not unique, and therefore a
formulation is developed that is independent of these choices. Very little
work has been done on this purely geometric formulation of control theory.
To give some idea of the sorts of problems that arise, we formulate some
novel definitions of controllability.

Part II. Controllability theorems

Carrying on from part I of the talk, some results describing controllability
are developed. ``Zeroth-order'' and ``first-order'' results from the
literature are given in the geometric formulation. Finally, new second-order
controllability results are stated.

No online version avaliable.