# Optimal air traffic control for collision avoidance

The explosive growth of the world population has produced problems never yet encountered before. These problems that need to be solved also include some that involve computer science and control theory. In my thesis I deal with a special branch of these problems, which is air traffic management and control. Increased traffic is an especially important and critical problem near airports, where the airspace is so congested that it causes traffic jams on the airports. Current traffic management systems (e.g. TCAS) have their limitations. For instance, they usually prefer adjusting trajectories by changing altitudes in order to avoid collision and critical situations. Nevertheless, these systems are still somewhat in their infancy. We can expect traffic to increase ever further, making it inevitable to use trajectory adjustments also within the horizontal plain, despite this solution being somewhat less passenger friendly.

As part of preparing my thesis I used an article (John C. Clements, 1999) dealing with optimal air traffic control as the basis for my calculations and solutions. This article describes the optimal control of a multi-agent system, albeit with relatively strict conditions. Accordingly, each airplane has its own constant airspeed and maximum turning capabilities. The solution provided is a non-reciprocal collision avoidance trajectory, that is, only one of the planes changes its course. It also assumes the other plane to maintain a constant heading throughout the conflict. The goal of my thesis was to expand the applicability of the solutions in the article. I first derived the mathematical/optimization solution in the event the heading of the plane being avoided is variable. Combining the solutions so obtained with the A* algorithm, I attempted to solve the collision avoidance problem for more than two planes, demonstrating this with a Matlab simulation. Finally I do mention a few ways to continue the study of this particular method and introduce some of the simulations results.