Presheaves and Sheaves of Sets of Vector Fields

We choose to phrase our notion of control in the language of sheaf theory which we believe has the following benefits: it permits natural formulations of problems lacking a natural formulation in “ordinary” control theory; sheaves are the proper framework for constructing germs of control systems which are often important in the study of local system structure; and sheaf theory provides a natural class of mappings between systems of which we take advantage.