Tactical replanning algorithms for four-dimensional contracts in air traffic control

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 trafficmanagement using four-dimensional contracts. According to this approach, all the air traffic is preplanned and optimized in advance in four dimensions: three-dimensional location and time. Before takeoff, each aircraft is given a flyable conflict-free four-dimensional flight plan, called a fourdimensional contract. The aircraft is committed to complywith its contract during the entire flight. Whenever an aircraft cannot respect its prescribed four-dimensional contract, a new one should be recomputed for it. New contract computation is performed when the aircraft are airborne and, therefore, should be completed in a matter ofminutes. The paper introduces an algorithm for replanning of four-dimensional contracts within the mentioned time limitation. 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. Numerical examples are presented to demonstrate the capabilities and performance of the proposed algorithm.