An optimal control approach to terminal area air traffic control

Abstract

In this investigation, the problem addressed is the specification of the curved approach paths and landing sequence for a group of aircraft desiring to land in a terminal area such that the terminalarea system performance is maximized. The multiple-aircraft problem includes the aspect of competition or cooperation between the vehicles by formulating the problem as a set of disconnected optimal trajectories. The flight paths are governed by kinematic equations of motion while in-flight and terminal-time separation inequality constraints between trajectories are imposed. The performance criterion for the system is the sum of the flight durations plus the integrated weighted accelerations of the aircraft. The solution approach employs penalty functions for the treatment of the inequality constraints and is based on the steepest descent algorithm. A num'ber of examples are presented which involve interactions between two and three aircraft. Parametric results are also included for some single-aircraft examples. The basic approach assumes the initial conditions are known for all aircraft before the solution process begins. In addition, a sequential solution algorithm is also demonstrated which allows the initial conditions to be made known to the system only a short time before arrival into the terminal area. A comparison between the two algorithms is presented.