Abstract

This report provides an insight into the mathematical methods developed to model the speed regulation problem in Air Traffic Flow Management. The speed regulation problem aims at optimizing aircraft speeds along their flights in order to smooth the air traffic flow. We chose to develop a linear framework for the speed regulation problem therefore most of the techniques presented aim at providing a linear formulation of the model.

Abstract

To accommodate the growing air traffic demand, flights will need to be planned and navigated with a much higher level of precision than today's aircraft flight path. The Next Generation Air Transportation System (NextGen) stands to benefit significantly in safety and efficiency from such movement of aircraft along precisely defined paths. Air Traffic Operations (ATO) relying on such precision--the Precision Air Traffic Operations or PATO--are the foundation of high throughput capacity envisioned for the future airports. In PATO, the preferred method is to manage the air traffic by assigning a speed profile to each aircraft in a given fleet in a given airspace (in practice known as ("italic"speed control"/italic"). In this research, an algorithm has been developed, set in the context of a Hybrid Control System (HCS) model, that determines whether a speed control solution exists for a given fleet of aircraft in a given airspace and if so, computes this solution as a collective speed profile that assures separation if executed without deviation. Uncertainties such as weather are not considered but the algorithm can be modified to include uncertainties. The algorithm first computes all feasible sequences (i.e., all sequences that allow the given fleet of aircraft to reach destinations without violating the FAA's separation requirement) by looking at all pairs of aircraft. Then, the most likely sequence is determined and the speed control solution is constructed by a backward trajectory generation, starting with the aircraft last out and proceeds to the first out. This computation can be done for different sequences in parallel which helps to reduce the computation time. If such a solution does not exist, then the algorithm calculates a minimal path modification (known as "italic"path control"/italic") that will allow separation-compliance speed control. We will also prove that the algorithm will modify the path without creating a new separation violation. The new path will be generated by adding new waypoints in the airspace. As a byproduct, instead of minimal path modification, one can use the aircraft arrival time schedule to generate the sequence in which the aircraft reach their destinations.