We define an extension of the classical notion of a control system which we call a control structure. This is a geometric structure which can be defined on manifolds whose underlying topology is more complicated than that of a domain in $ℝ^n$. Every control structure turns out to be locally representable as a classical control system, but our extension has the advantage that it has various naturality properties which the (classical) coordinate formulation does not, including the existence of so-called universal objects and classifying maps. This more general viewpoint simplifies the study of the invariants of even classical control systems. Its main technical advantage is that tools like the method of equivalence can be directly and easily applied to the study of control structures.
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