Range optimal trajectories for an aircraft flying in the vertical plane

Range optimal trajectories for an aircraft flying in the vertical plane are obtained from P on try agin's minimum principle. Control variables are the load factor, which appears nonlinearly in the equations of motion, and the throttle setting, which appears only linearly. Both controls are subject to fixed bounds. Additionally, a dynamic pressure limit is imposed, which represents a first-order state-inequality constraint. For fixed flight time, initial coordinates, and final coordinates of the trajectory, the effect of the load factor limit on the resulting optimal switching structure is studied. All trajectories involve singular control along arcs with active dynamic pressure limit. For large flight times the optimal switching structures have not yet been found.