Abstract

In this paper we study the en-route strategic flight planning of a commercial aircraft constrained to pass through a set of waypoints whose sequence is not predefined. This problem has been solved as an hybrid optimal control problem in which, given the dynamic model of the aircraft, the initial and final states, the path constraints constituting the envelope of flight, and a set of waypoints in the European air space, one has to find the control inputs, the switching times, the optimal sequence of waypoints and the corresponding trajectory of the aircraft that minimize the direct operating cost during the flight. The complete layout of waypoints in the European airspace is reduced and waypoints are gathered into a small number of clusters. The aircraft is constrained to pass through one waypoint inside every cluster of waypoints. The presence of multi point constraints makes the optimal control problem particularly difficult to solve. The hybrid optimal control problem is converted into a mixed integer non linear programming problem first making the unknown switching times part of the state, then introducing binary variable to enforce the constraint of passing through one waypoint inside every cluster, and finally applying a direct collocation method. The resulting mixed integer non linear programming problem has been solved using a branch and bound algorithm. The cases studied and the numerical results show the effectiveness, efficiency and applicability of this method for enroute strategic flight plans definition.