Nonlinear model predictive control for optimal aircraft sequencing

A real-time, bi-level feedback control algorithm for assigning arrival times is presented, which are optimal with regard to the cumulated fuel consumption of inbound aircraft. The bi-level structure implements the solution of optimal control problems for each individual aircraft to determine the minimum fuel consumption for the assigned arrival time. Additional constraints are included in the upper level to assure safe time separations at the merge point. After obtaining the solution of the original problem at the initial time point, the bi-level problem is approximated by a blended quadratic program. This program provides a prediction and correction of the optimal arrival times for the next time point and the respective change in initial states of all aircraft. Furthermore, exact solutions for the lower level optimal control problems are calculated for the updated arrival times. The algorithm is successfully validated for a example of nine aircraft and a frequency of six updates per minute for the arrival time assignment.