Weighted time-optimal control for air traffic management applications

Air traffic management system is responsible for a safe and orderly flow of air traffic, thus preventing collisions between aircraft both in the air and on the ground. This paper shows that an air traffic management problem can be transferred into a weighted time-optimal problem for hybrid system. In particular, it is shown that the problem can be transformed into a constrained optimization problem whose constraints are a set of inequalities with quantifiers. Quantifier elimination (QE) techniques are employed in order to derive quantifier free inequalities. The optimal cost is obtained using linear programming