Distributed Control and Stochastic Analysis of Hybrid Systems Supporting Safety Critical Real-Time Systems Design WP3: Reachability analysis for probabilistic hybrid systems Probabilistic Aircraft Conflict Detection

In this deliverable we study algorithms for mid-term aircraft conflict detection. A twoaircraft conflict occurs when some prescribed separation distance between two aircraft is violated. In a mid-term time scale, the contribution of the different sources of uncertainty affecting the aircraft motion cannot be neglected when predicting the aircraft future positions. Based on this consideration, we address mid-term aircraft conflict detection according to a probabilistic viewpoint. We consider, in particular, the probability of conflict as criticality measure. Computing the probability of conflict is generally a difficult task. A possible solution to this issue is the simulation-based approach, characterized by repeated simulations of the aircraft trajectories according to the model describing their motion: the fraction of trajectories that generate a conflict is an unbiased estimate of the probability of conflict. This approach has the advantage of being applicable to general models and general contexts. Obviously, the more complex the model, the more time-consuming is generating simulations according to it. Given the time constraints of our specific application context, we look into solutions to speed-up the simulation-based method. These solutions are inspired by the multi-level approach to rare-event probability estimation and the sequential Monte Carlo approach. ∗Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy, [email protected] †Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, U.K., [email protected].