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.Publicad

This work is partially supported by the Spanish Government through the Ministerio de Ciencia e Innovación, the Comunidad de Madrid, and the project i-Math Ingenio Mathematica. This work has been carried out within the framework of the Atlantida project, partially funded by the Spanish Centro para el Desarrollo Tecnológico e Industrial, in which the Universidad Rey Juan Carlos is collaborating with GVM Aerospace and Defence.Publicad

The calculation of a flight plan involves the consideration of multiple elements. They can be classified as either continuous or discrete, and they can include nonlinear aircraft performance, atmospheric conditions, wind forecasts, airspace structure, amount of departure fuel, and operational constraints. Moreover, multiple differently characterized flight phases must be considered in flight planning. The flight-planning problem can be regarded as a trajectory optimization problem. A natural way to address a trajectory optimization problem is using optimal control techniques. The multiphase nature of the problem and the nonlinear dynamics of the aircraft lead to the formulation of a multiphase optimal control problem. A Hermite–Simpson collocation method is employed to transcribe the infinite-dimensional optimal control problem into a finite-dimensional optimization one, which is solved using a nonlinear programming solver. An application to the optimal takeoff weight, minimum fuel consumption trajectory ...

This work is partially supported by the Spanish Government through the Ministerio de Ciencia e Innovación, the Comunidad de Madrid, the project i-Math Ingenio Mathematica, and the project Optimización en Computación en Paralelo de Planificación bajo Incertidumbre under grant no. MTM2009-14087-C04-01. This work has been carried out within the framework of the Atlantida project, partially funded by the Spanish Centro para el Desarrollo Tecnológico e Industrial, in which the Universidad Rey Juan Carlos collaborated with GMVAerospace and Defence S.A.Publicad

This article proposes a recursive Gaussian process regression with a joint optimization-based iterative learning control algorithm to estimate and predict disturbances and model uncertainties affecting a flight. The algorithm proactively compensates for the predicted disturbances, improving precision in aircraft trajectory tracking. Higher precision in trajectory tracking implies an improvement of the aircraft trajectory predictability and, therefore, of the air traffic management system efficiency. Airlines can also benefit from this higher predictability by reducing the number of alterations when following their designed trajectories, which entails a reduction of costs and emissions. The iterative learning control algorithm is divided into two steps: first, a recursive Gaussian process regression estimates and predicts perturbations and model errors with no need for prior knowledge about their dynamics and with low computational cost, and second, this information is used to update the control inputs so that the subsequent aircraft intending to fly the same planned trajectory will follow it with greater precision than the previous ones. This method is tested on a simulated commercial aircraft performing a continuous climb operation and compared to an iterative learning algorithm using a Kalman filter estimator in a similar scenario. The results show that the proposed approach provides 62 and 42% precision improvement in tracking the desired trajectory, as compared to the Kalman filter approach, in two experiments, where no prior knowledge of the unmodeled dynamics was available, also achieving it in less iterations.