Optimal horizontal guidance law for aircraft in the terminal area

The automation of many of the functions currently performed by the controllers and pilots is essential for a safe and efficient air traffic control (ATC) system. A major aspect of the overall ATC system is the guidance and flight control of aircraft. This paper deals with the horizontal guidance of aircraft in and near the terminal area. The problem of guiding an aircraft in minimum time from an arbitrary point to the outer marker is formulated as a nonlinear optimal control problem, and the control law solution is obtained by the application of the maximum principle. It is found that for some initial states the problem is singular. Furthermore, the extremal controls for this problem are not unique. Consequently, the optimal controls must be obtained on the basis of the value of the performance index. The control law is implemented in the form of a digital computer program which computes the optimal trajectory for arbitrary initial conditions.