Tactical re-planning within the 4D contracts ATC concept

Continuously growing air traffic density, mainly over Europe and the U.S., introduces a need for new concepts in air-traffic control. One of such new concepts involves air-traffic management using four dimensional (4D) contracts. According to this approach, all the air traffic is pre-planned and optimized in advance in four dimensions: 3D location and time. Before take-off each aircraft is given a flyable confiict-free 4D flight plan, called 4D contract. The aircraft is committed to comply with its contract during the entire flight. Whenever the aircraft can not respect its prescribed 4D contract, a new 4D contract should be re-computed for it. New contract computation is performed when the aircraft is airborne and therefore should be completed in a matter of minutes. The paper introduces an algorithm for re-planning of the 4D contracts with the mentioned time limitations. The update task is treated as an optimization problem minimizing the influence of the contract change on the surrounding traffic. To increase the efficiency of the algorithm, only the neighboring traffic is considered during the replanning process. The paper concludes with two numerical examples used to demonstrate the performance of the proposed algorithm.