Abstract
This paper is concerned with the horizontal guidance of an aircraft in and near the terminal area when no flying is permitted in a half plane of the space. The problem of guiding an aircraft in minimum time from arbitrary initial position and heading to fixed terminal position and heading is considered, under the condition of constant speed and with the constraint on bank angle. It is found that an optimal path cannot have a boundary segment on the boundary of the constrained space, more than one junction point and more than three switching times, while if the flight path remains interior then the maximum number of the switching times is two. Furthermore, in view of these results it is found that there are at most twelve extremal controls and their control regions are not disjoint. The optimal control is chosen to minimize the performance index among extremal controls.
