Control in a behavioral setting

One of the main features of the behavioral approach as a foundation framework for the theory of dynamical systems is that it does not take the input/output structure as the starting point for describing systems in interaction with their environment. Instead, a mathematical model is simply viewed as any relation among variables. In the dynamic case this relation constrains the time-evolution which a set of variables can take. The collection of time trajectories in which the model declares possible is called the behaviour of the dynamical system. This behaviour, hence a set of time functions, can be specified in many different ways. In this note we explain our new view of control, and address some issues that come up in developing a theory of control in a behavioral setting. We also give a few examples of control problems in behavioral setting