Control design techniques for constrained positive compartmental systems with applications to air traffic flow management

The current air traffic management system has been pushed to its limit and will not be able to keep up with the predicted increase in air traffic over the coming years. Recent research in air traffic management is concerned with increasing the capacity and throughput of the National Airspace System in order to accommodate this growing demand. Many approaches presented in the literature are systematic and performance based. In the work presented here, two particular problems are addressed: delay scheduling in the presence of uncertain flow rate constraints, and traffic flow routing under time varying airspace capacity constraints. Aggregate models are used to describe the flow of traffic in the region of airspace of interest. The solution methods presented are based on sliding mode control theory and linear programming theory. Contributions of this work are methods which: (a) react in real time to changing flow rate constraints, and (b) use routing parameters to satisfy time varying capacity constraints for linear, uncertain linear, and nonlinear models describing the flow of traffic through the region of interest. Unlike most methods described in the literature, solution method (a) does not make use of a constraint forecast. Simulation results show a reduction of flow rate constraint violation over the baseline schedule. Routing control is rarely used in the literature. The proposed approach (b) makes use of routing parameters as the primary control input. Linear constraints are derived to find time varying routing parameters which satisfy time varying capacity constraints.