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Blog - categories in control (part 4)

Categories in Control (Part 4): Behavioural controllability

Now we view a system as a set of trajectories. But control theory is about controlling systems. What does it mean to have control of a system? One definition, proposed by the great Dutch control theorist Jan Willems, is that a system is controllable if

  1. given some current trajectory cc and some present time tt
  2. you pick any other trajectory dd
  3. you can find a trajectory ww that is the same as cc until time tt, and after some finite time later tt', is the same as dd.

This says that

But what are the axioms for turning cospans into spans? Bonchi, Sobocinski, and Zanasi proved that they are