Computer-Aided Eulerian Air Traffic Flow Modeling and Predictive Control

Abstract

Eulerian models are used to represent the air traffic environment as traffic flows between interconnected control volumes representing the airspace system. While these models can be manually derived for simple air traffic patterns, computer-based approaches are essential for modeling realistic airspaces involving multiple traffic streams. A computeraided methodology for deriving large-dimensional Eulerian models of air traffic flow is described here. Starting from the specification of a few airspace parameters, and traffic data, the modeling technique can automatically construct Eulerian models of the airspace. The synthesis of air traffic flow control algorithms using the model predictive control technique in conjunction with these models is given. It is shown that the flow control logic synthesis can be cast as a linear programming problem. The flow control methodology is illustrated using air traffic data over two regions in U.S. airspace.

Network Congestion Control of Airport Surface Operations

“…[4][5][6][7] Since surface operations are highly heterogenous in terms of taxi speeds, routes and pilot behavior, Eulerian models 8,9 of traffic flow are not applicable here. Most traditional solution approaches involve the use of optimal scheduling algorithms 6,7 or queuing theory, [3][4][5] both of which have certain drawbacks.…”

Feedback Control of the National Airspace System

“…The control strategies they propose rely on linear systems theory, and do not account for crucial state and control constraints present in the system. A refined model is presented in a later paper by the same authors, 25 and a model predictive control strategy is proposed to handle these constraints. Similar models are used by Sridhar et al, 40 and by Sun and Bayen.…”

“…Menon et al previously proposed to use MPC to control a deterministic Eulerian model of the NAS. 25 We also use MPC for the weather scenario considered in Section IV. To obtain a feedback control law via MPC for the general problem (8)- (12), we proceed as follows.…”

A linear programming approach to routing control in networks of constrained nonlinear positive systems with concave flow rates

“…where A r (η r (t k )) is defined as in (10), B r is defined as in (11), and the fixed scalar value η i (k) is chosen such that…”

“…Previous work in this area [1,9,10,12,13] has focused primarily on the use of linear models to describe the outflow of each compartment, or section, of the network. Such models describe the outflow rate of a section as depending linearly on the amount of material in that section.…”