Air traffic management with target windows: An approach using reachability

We present the applications of reachability methods and computational tools based on game theory to a problem in air traffic management. The use of such methods in air traffic has been proposed several times in the past. It has, however, been hampered by the fact that most of the concepts of operation proposed for restructuring the current air traffic management system either impose too many constraints on the aircraft or too few; in the former case the reachability problem is typically trivial, in the latter infeasible. In the CATS project a novel concept of operations is being developed based on the so called Target Windows. Target Windows are 4D constraints imposed on the flight to increase its predictability. We show how such constraints can be coded in the reachability framework. Through a series of approximations we are able to use computational tools to quantify the freedom that TW constraints leave to an aircraft. Our results suggest that Target Windows provide a promising balance between predictability and maneuverability.