Supervisory control of differentially flat systems based on abstraction

The limiting factor in most implementations of safety enforcing controllers is the model's complexity, and a common work-around includes the abstraction of the physical model, based on differential equations, to a finite symbolic model. We exploit the specific structure of a class of systems (the differentially flat systems) to perform the abstraction. The objective is to construct a supervisor enforcing a set of safety rules, while imposing as little constraints as possible on the system's functionality. An example - a collision avoidance algorithm for a fleet of vehicles converging to an intersection - is presented. Our approach improves on previous results by providing a deterministic symbolic model irrespective of the stability properties of a system, and by addressing explicitly the problem of enforcing safety.