Probabilistic aircraft conflict resolution: A stochastic optimal control approach

This paper is focused on the aircraft midair conflict resolution problem which is a key function to enable the automated and decentralized air traffic control in the Next Generation Air Transportation System (NextGen). In most previous research, conflict resolution is to generate conflict-free trajectories for aircraft to follow. However, in real applications, aircraft subject to various disturbances could not exactly follow the predesigned trajectories. If the cross-track error is too big, going back to the predesigned trajectories may not necessarily be optimal. In this paper, the problem is solved by using a stochastic optimal control approach which generates an optimal conflict-free feedback control law rather than trajectories. If the aircraft always uses the optimal feedback control law, the resulted nondeterministic trajectories are optimal and conflict-free. This stochastic optimal control problem is solved numerically by a Markov chain approximation approach.