Optimal conflict resolution method based on inner-point restriction

In the condition of free flight, in order to ensure the distance of two aircrafts could not less than a given safety distance, the Pontryagin minimum principle(PMP) of optimal control theory and inner-point restriction condition were introduced to study the conflict resolution problem of free flight aircrafts, in which control vectors were restricted. Two different schemes were designed, one only changed flying velocity magnitude, the other only changed flying velocity angle. Different schemes had different control vectors, different control vectors had different restricted ranges. The optimal control variable was gained according to the PMP, the start time, end time and switch time of conflict resolution were obtained by inner-point restriction condition. An example shows that the method is feasible, the wasting cost of one aircraft resolution is tenfold of the wasting cast of two aircrafts resolution in changing velocity method, the wasting cost of one aircraft resolution is one third of the wasting cast of two aircrafts resolution in changing angle method when the intersectant angle of two aircrafts is smaller.