Linear matrix inequalities for free flight conflict problems

Under the concept of free flight, aircraft will be allowed much greater flexibility in trajectory planning than ever before. The ability to anticipate and resolve conflicts provides one of the greatest challenges to this proposed environment. In this paper, the following problem is addressed: given two aircraft, their intended trajectories and uncertainty about their behavior, what is their worst-case miss distance over a given time horizon? This question is answered using linear matrix inequalities and positive semi-definite programming. The proposed approach provides guaranteed lower bounds on minimum miss distances in polynomial time. Several increasingly complex examples are given that illustrate the efficiency of the proposed method