Real-time discrete control law synthesis for hybrid systems using MILP: application to congested airspace

We use mathematical model based on hybrid automata theory to describe air traffic flow in arrival regions near airports. We show that the problem of scheduling the arrival flow subject to airspace and airport metering constraints may be formulated as a mixed integer linear program (MILP). We demonstrate an implementation of this program, which accepts air traffic control (ATC) data, performs the scheduling, and generates a set of ATC commands directly executable by the aircraft. Simulations indicate an empirical upper bound on the number of aircraft the program can treat while still resolving the problem in real time.