Supervisory control for collision avoidance in vehicular networks with imperfect measurements

We consider the problem of collision avoidance at road intersections in vehicular networks in the presence of uncontrolled vehicles, a disturbance, and measurement uncertainty. Our goal is to construct a supervisor of the continuous time system that is safe (i.e., avoids collisions), non-blocking (i.e., all vehicles eventually cross the intersection), and maximally permissive with respect to the discretization, despite the presence of a disturbance and of measurement uncertainty. We proceed in four steps: defining a discrete event system (DES) abstraction of the continuous time system, using uncontrollable events to model the uncontrolled vehicles and the disturbance; translating safety and non-blocking requirements to the DES level; solving at the DES level; and translating the resulting supervisor back from the DES level to the continuous level. We give sufficient conditions for this procedure to maintain the safety, non-blocking and maximal permissive properties as the supervisor is translated back from the DES level to the continuous level. Prior work on this problem based on similar abstractions assumes perfect measurement of position. Our method for handling measurement uncertainty is to introduce measurement events into the DES abstraction and then to compute the observer of the DES abstraction and the supremal controllable solution of the DES supervisory control problem.