Abstract
Model Predictive Control (MPC) is a model-based control method based on a receding horizon approach and online optimization. A key advantage of MPC is that it can accommodate constraints on the inputs and outputs. This paper proposes a max-plus general modeling framework adapted to the robust optimal control of air traffic flow in the airspace. It is shown that the problem can be posed as the control of queues with safety separation-dependent service rate. We extend MPC to a class of discrete-event system that can be described by models that are linear in the max-plus algebra with noise or modeling errors. Regarding the single aircraft as a batch, the relationships between input variables, state variables and output variable are established. We discuss some key properties of the system model and indicate how these properties can be used to analyze the behavior of air traffic flow. The model predictive control design problems are defined for this type of discrete event system to help prepare the airspace for various robust regulation needs and we give some extensions of the air traffic max-plus linear systems.
Highlights
Air traffic flow is characterized by ever tighter time specifications, increasing airspace capacity and decreasing air traffic controller workloads
Assuming that the air traffic controllers don’t change the expected departure time of all the aircrafts which are involved in the conflict, their flight speed in the jet route should be changed
This paper presented a max-plus model that can be used to develop robust optimal control policies for the air traffic flow and the reason for using model predictive control approach for max-plus system is the same as for conventional linear systems
Summary
Air traffic flow is characterized by ever tighter time specifications, increasing airspace capacity and decreasing air traffic controller workloads. Unlike some conflict-resolution models mentioned above, hybrid system model was formulated to synthesize provably safe conflict resolution maneuvers (Tomlin et al, 1998, 2000, 2001) All these tasks are currently conducted manually by air traffic controllers, and contribute significantly to their workload. The internal linear properties of max-plus models that describe air traffic flow make control policies for the airspace very attractive. Attempts like this have been made to manufacturing systems, telecommunication networks, railway networks and parallel computing (Goverde et al, 1999; Olsder, 1989; Olsder, 1993). We end with planned further works to enhance the approach
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