Efficient algorithms for optimal arrival scheduling and air traffic flow management

The research presented in this dissertation is motivated by the need for new, efficient algorithms for the solution of two important problems currently faced by the air-traffic control community: (i) optimal scheduling of aircraft arrivals at congested airports, and (ii) optimal National Airspace System (NAS) wide traffic flow management.; In the first part of this dissertation, we present an optimal airport arrival scheduling algorithm, which works within a hierarchical scheduling structure. This structure consists of schedulers at multiple points along the arrival-route. Schedulers are linked through acceptance-rate constraints, which are passed up from downstream metering-points. The innovation in this scheduling algorithm is that these constraints are computed by using an Eulerian model-based optimization scheme. This rate computation removes inefficiencies introduced in the schedule through ad hoc acceptance-rate computations. The scheduling process at every metering-point uses its optimal acceptance-rate as a constraint and computes optimal arrival sequences by using a combinatorial search-algorithm. We test this algorithm in a dynamic air-traffic environment, which can be customized to emulate different arrival scenarios.; In the second part of this dissertation, we introduce a novel two-level control system for optimal traffic-flow management. The outer-level control module of this two-level control system generates an Eulerian-model of the NAS by aggregating aircraft into interconnected control-volumes. Using this Eulerian model of the airspace, control strategies like Model Predictive Control are applied to find the optimal inflow and outflow commands for each control-volume so that efficient flows are achieved in the NAS. Each control-volume has its separate inner-level control-module. The inner-level control-module takes in the optimal inflow and outflow commands generated by the outer control-module as reference inputs and uses hybrid aircraft models to search for optimal trajectories to be flown by each aircraft so that the flows commanded by the outer control-module are achieved. The two-level control system is tested in a dynamic simulation.; Furthermore, as a component of the Eulerian part of this two-level system, we present a method for deriving an aggregate airspace-model in real-time, without depending on online integration of aircraft trajectories. This method uses a baseline Eulerian airspace-model, which is derived offline using historical track-data. In real-time, parameters of this model are adapted depending on the differences between the baseline-model and the real-world. This book-keeping based model-derivation indirectly retains some trajectory information. Hence, it serves as an excellent trade-off between Eulerian and trajectory-based modeling approaches. Most importantly, as a vital improvement over previous approaches, we take into consideration the control-dependent nature of the Eulerian-model while computing optimal flow-control decisions. As a proof of concept, we derive a baseline model for the Fort-Worth center and adapt it to predict sector-counts for another set of air traffic data. We also demonstrate the use of this model in a simulation-based optimization scheme for regulating the arrival flow at the Dallas Fort-Worth airport. An application to optimal re-routing strategy computation is also presented.