Control and trajectory optimization of an aircraft’s alignment with the desired track

Abstract

The synthesis of the control with the optimal trajectory length is constructed for the problem of aligning an aircraft with the desired track with the ground speed vector direction along the desired track. The solution is based on the maximum principle and involves the use of numerical methods for solving the boundary value problem and analytical investigations for determining the set of possible extremals and comparing the lengths of the trajectories when selecting the optimal one. As a result of these investigations, the switching and separation lines are determined that bound the regions in the phase space which correspond to different values of the optimal relay control.