Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization

Abstract

In this paper, an approach to aircraft trajectory optimization is presented in which integer and continuous variables are considered. Integer variables model decision-making processes, and continuous variables describe the state of the aircraft, which evolves according to differential-algebraic equations. The problem is formulated as a multiphase mixed-integer optimal control problem. It is transcribed into a mixed-integer nonlinear programming problem by applying a fifth degree Gauss-Lobatto direct collocation method and is then solved using a nonlinear-programming-based branch-and-bound algorithm. The approach is applied to the following en route flight planning problem: Given an aircraft point mass model, a wind forecast, an airspace structure, and the relevant flying information regions with their associated overflying costs, find the control inputs that steer the aircraft from the initial fix to the final fix, following a route of waypoints while minimizing the fuel consumption and overflying costs during the flight. The decision-making process arises in determining the optimal sequence of waypoints. The optimal times at which the waypoints are to be overflown are also to be determined. Numerical results are presented and discussed, showing the effectiveness of the approach.

A Comparison of Optimal Control Methods for Minimum Fuel Cruise at Constant Altitude and Course with Fixed Arrival Time

“…For instance, Hermite-Legendre-Gauss-Lobatto collocation methods have been used to solve commercial aircraft trajectory planning problems [8,9,10,11]. Also, recent advances have been made in pseudospectral collocation methods [12,13].…”

Analytic Approach to Optimal Routing for Commercial Formation Flight

“…This, along with a case study, shows significant fuelsaving potential even with heuristically chosen routes. These prior works adopt numerical trajectory optimization techniques [25][26][27] to calculate high-fidelity solutions to the routing problem. Once the routing problem is solved, evaluating the cost for each potential formation, the subsequent assignment problem is readily solved by a discrete optimization [20].…”

Lateral Reference Trajectory Algorithm Using Ant Colony Optimization

“…The set of altitudes and speeds that compose a flight is called the vertical reference trajectory. Algorithms optimizing the vertical reference trajectory have been developed by using Optimal control [15][16][17][18][19], Mixed-Integer Linear Programming [20,21], and Dynamic Programming [22,23]. Most of these techniques use the point-mass equations of motion and the BADA database provided by Eurocontrol to compute the aircraft fuel burn.…”