Commercial Aircraft Trajectory Planning based on Multiphase Mixed-Integer Optimal Control

Abstract

The main goal of this dissertation is to develop optimal control techniques for aircraft trajectory planning looking at reduction of fuel consumption, emissions and overfly charges in flight plans. The calculation of a flight plan involves the consideration of multiple factors. They can be classified as either continuous or discrete, and include nonlinear aircraft performance, atmospheric conditions, wind conditions, airspace structure, amount of departure fuel, and operational constraints. Moreover, multiple differently characterized flight phases must be considered in flight planning, which typically also involves decision-making processes. The flight planning problem can be regarded as a trajectory optimization problem. The most natural way to address a trajectory optimization problem is using optimal control techniques. One of the main advantages of using optimal control is that it allows the aircraft continuous non-linear dynamics to be considered. The solution to the problem provides the optimal amount of departure fuel, the optimal four dimensional trajectory (horizontal route and the vertical profile over time), speed, consumption and attitude profiles over time, and the corresponding optimal control inputs of the aircraft. The multiphase nature of the problem, the non-linear dynamics of the aircraft, and the introduction of integer variables to model decision-making processes lead to the formulation of a multiphase mixed-integer optimal control problem. The duration of the phases is optimized including the switching times as unknowns of the problem, which is modeled using a direct numerical approach. In particular, a collocation method is employed to transcribe the infinite dimensional optimal control problem into a finite dimensional optimization one, which is solved using a mixed integer nonlinear programming solver. It is shown that the flight planning problem can be effectively tackled using mixedinteger optimal control, considering multiple phases and including decision-making processes. Results show that the efficiency of current flight plans could be substantially improved and that the techniques studied in this thesis have a strong potentiality to be employed in the definition of more efficient flight plans under future operational concepts in air traffic management.