Optimization of Multiphase Aircraft Trajectories Using Hybrid Optimal Control

Abstract

An approach to optimize multiphase trajectories of commercial transport aircraft is presented. The approach is based on the theory of hybrid optimal control, and it is applied to the case of minimum-fuel trajectories. The multiphase trajectories are composed of three types of phases, climb, cruise, and descent, in a given sequence. In each phase, the optimal control is scalar and of the bang–singular–bang type, and the optimal path is formed by a singular arc and two minimum/maximum-control arcs joining the singular arc with the initial and final switching points. An indirect numerical method is developed, which takes into account the structure of the solution directly in the algorithm and exploits the singular character of the problem. In the analysis, the effects of horizontal winds are taken into account; general along-track wind and crosswind profiles are considered, dependent both on altitude and along-track position. The optimal trajectories are computed for a model of a Boeing 767-300ER performing a climb–cruise–descent trajectory with a one-step cruise climb, and for different wind profiles. The influence of the wind profiles on the optimal results is analyzed and shown to be important.