Solution of an emergency air traffic control problem by differential dynamic programming†

Abstract
An Air Traffic Control (ATC) problem in a case of emergency, when some of the airports become unoperational, is considered. The problem is first stated as a fully cooperative Non-zero-Sum Differential Game (NZDG) with perfect information. It is immediately reformulated as an optimal control problem. A computer programme, solving this problem numerically, has been developed. The programme is based on the Differential Dynamic Programming (DDP) algorithm. A numerical example is solved on the CDC CYBER-73 computer. The results are presented in a form understandable by laymen unfamiliar with the mathematical methods utilized in the solution.

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