Collocation Methods to Minimum-Fuel Trajectory Problems with Required Time of Arrival in ATM

Abstract

In the future air traffic management system, the trajectory becomes the fundamental element of a new set of operating procedures collectively referred to as trajectory-based operations. Trajectory-based operations require the air traffic management to introduce profound innovations to enable the envisioned changes. Some of these include collaborative decision-making processes, better data and information management, and advanced decision support tools to aid human operators. In particular, fast and accurate computation of optimal trajectories could certainly contribute to enhance trajectory management within the future air traffic management. The trajectory optimization problem can be solved using optimal control methods. In this paper, the existing methods for solving optimal control problems focusing on direct collocation are discussed. In particular, pseudospectral collocation methods have shown to be numerically more accurate and computationally much faster than other direct methods. A very relevant p...