Showing papers by "Maria Prandini published in 2010"

A probabilistic measure of air traffic complexity in 3‐D airspace

Abstract: In this paper, we propose a new method to evaluate air traffic complexity in 3-D airspace through a probabilistic measure of the airspace occupancy. The key novelty of the approach is that uncertainty in the future aircraft positions is explicitly accounted for when evaluating complexity. Analytic—though approximate—expressions of the complexity measure are derived. Prospective applications for the proposed complexity metric include the timely identification of those multi-aircraft conflict situations that would be difficult to solve because of limited maneuverability space, and the design of trajectories so as to avoid congested regions that would require many tactical maneuvers to pass them through. Numerical examples are provided to illustrate the approach. Copyright © 2010 John Wiley & Sons, Ltd.

Randomized sampling for large zero-sum games

Abstract: This paper addresses the solution of large zero-sum matrix games using randomized methods. We provide a procedure by which a player can compute mixed policies that, with high probability, are security policies against an adversary that is also using randomized methods to solve the game. The computational savings result from solving subgames that are much smaller than the original game and we provide bounds on how large these subgames should be to guarantee the desired high probability. We propose two methodologies to solve this problem. The first provides a game-independent bound on the size of the subgames that can be computed a-priori. The second procedure is useful when computation limitations prevent a player from satisfying the first a-priori bound and provides a high-probability a-posteriori bound on how much the outcome of the game can violate the precomputed security level. All our probabilistic bounds are independent of the size of the original game and could, in fact, apply to games with continuous action spaces. To demonstrate the usefulness of these results, we apply them to solve a hide-and-seek game that exhibits exponential complexity.

A probabilistic measure of air tra-c complexity in three-dimensional airspace

Abstract: SUMMARY In this paper, we propose a new method to evaluate air tra‐c complexity in 3-D airspace through a probabilistic measure of the airspace occupancy. The key novelty of the approach is that uncertainty in the future aircraft positions is explicitly accounted for when evaluating complexity. Analytic {though approximate{ expressions of the complexity measure are derived. Prospective applications for the proposed complexity metric include the timely identiflcation of those multi-aircraft con∞ict situations that would be di‐cult to solve because of limited maneuverability space, and the design of trajectories so as to avoid congested regions that would require many tactical maneuvers to pass them through. Numerical examples are provided to illustrate the approach. Copyright c ∞ 2010 John Wiley & Sons, Ltd.

A geometric approach to air traffic complexity evaluation for strategic trajectory management

Abstract: In the prospective next generation Air Traffic Management systems, aircraft will be endowed with part of the responsibility for separation maintenance, and traffic complexity reduction functions will play an important role in avoiding to overload the on-board conflict resolution system. In this work, a method for assessing air traffic complexity in the long term is presented, that may be used to detect critical situations with limited aircraft manoeuvrability in the time/space coordinates, and provide support to the flow/strategic trajectory management functions. The method is based on the concept of ‘influence zone’ of an aircraft, which accounts for both the direction and velocity of the aircraft, and can be regarded as the set of possible locations reachable by an aircraft through local deviations from its intended trajectory. Complexity is then related to the presence and magnitude of intersections between influence zones of different aircraft. The influence zones (as well as other regions of the airspace to be avoided) can be approximated with polyhedra, and their interaction analyzed using efficient tools borrowed from computational geometry.

Air traffic complexity in advanced automated Air Traffic Management systems

Abstract: In this paper we study the issue of characterizing the complexity of air traffic to support Air Traffic Management (ATM) operations. We discuss, in particular, the relevant features of a complexity metric in advanced automated ATM systems where part of the responsibility for separation maintenance is delegated to the aircrews, and trajectory management functions are further automated and distributed. A probabilistic complexity metric is described and analyzed in some detail. Possible applications to conflict detection and resolution and trajectory management operations are presented through numerical examples.

Constrained control design via a simulation-based scenario approach

Abstract: This paper deals with constrained control design for linear systems affected by stochastic disturbances. The goal is to optimize the control performance while guaranteeing that the constraints are satisfied for most of the disturbance realizations, that is with probability 1 − . In mathematical terms, this amounts to solve a “chance-constrained” optimization program and we introduce here a randomized approach to this problem that builds on certain recent results in robust convex optimization.