Stochastic optimal control for aircraft conflict resolution under wind uncertainty

In this paper, a stochastic optimal control method is developed for determining three-dimensional conflict-free aircraft trajectories under wind uncertainty. First, a spatially correlated wind model is used to describe the wind uncertainty, and a probabilistic conflict detection algorithm using the generalized polynomial chaos method is proposed. The generalized polynomial chaos algorithm can quantify uncertainties in complex nonlinear dynamical systems with high computational efficiency. In addition, a numerical algorithm that incorporates the generalized polynomial chaos method into the pseudospectral method is proposed to solve the conflict resolution problem as the stochastic optimal control problem. The stochastic optimal control method is combined with the proposed conflict detection algorithm to solve the conflict resolution problem under the wind uncertainty. Through illustrative three-dimensional aircraft conflict detection and resolution examples with multiple heterogeneous aircraft, the performance and effectiveness of the proposed conflict detection and resolution algorithms are evaluated and demonstrated.