A SDP relaxation approach to air traffic control under free flight

Under "free flight", each individual aircraft will have the first responsibility to resolve its own conflicts. Therefore, a centralized air traffic controller (ATC) will issue a resolution command only when a physical conflict would be unavoidable if the ATC did not do so. Regarding the operation of an ATC under "free flight", hence, determining when the ATC should issue a resolution command would be one of the most important problems. This paper presents a systematic and efficient algorithm as a solution to this problem. This algorithm is based on the well-known semi-definite program (SDP) relaxation method.