Optimal and least restrictive supervisory control: Safety verification methods for human-driven vehicles at traffic intersections

We consider a cooperative conflict resolution problem at traffic intersections. Our goal is to design a least restrictive supervisor able to identify the optimal corrections to a human-decided input with respect to a given performance index, while keeping the system safe. Here, safety is formulated in terms of a maximal safe controlled invariant set. Leveraging results from scheduling theory, we characterize the preorder of the optimal solution set and propose an efficient optimization algorithm providing Pareto optimal solutions. We illustrate the application of the proposed algorithm through simulations in which vehicles crossing an intersection are optimally overridden by the supervisor only when necessary to maintain safety.