Minimum-time three-dimensional turn to a point of supersonic aircraft

The objective of this paper is to present real-time, on-line, minimum-time three-dimensional turn to a point of supersonic aircraft/The analytic aspect of the theory of optimal trajectories is emphasized. This includes the general properties of optimal trajectories consisting of the integrals of motion and the characteristic features in engine and aerodynamic controls. By using the integrals of motion the totality of the optimal trajectories can be obtained as a family of curves depending on a certain number of arbitrary constants. The optimal control is obtained by geometrical method through the domain of maneuverability. This makes explicit the switching characteristics of the optimal control, in particular when singular or chattering control is involved. The optimality of singular thrust control and the optimal junction of different subarcs are analyzed. The computation of the optimal trajectories is carried out using the aerodynamic and engine characteristics of a lightweight, high thrust-to-weight ratio supersonic fighter. By using normalized control variables, i.e., the thrust-to-weight ratio, the bank angle, and the load factor, results can be applied to any supersonic aircraft.