Lyapunov Guidance Law for Bank-to-Turn Aircraft Singularity Control

Conventional Bank-to-Turn (BTT) aircraft guidance commands are obtained based on a polar converting logic (PCL), however, a mathematical singularity is introduced when the magnitude of the guidance command becomes zero, the formation principle of control singularity of BTT-90 logic was analyzed with the method of partial derivative. Based on the Lyapunov stability theorem, a BTT aircraft guidance law that directly computes the pitch acceleration and roll angle commands is presented in this paper. A new form zero effort miss-distance (ZEM) with impact angle constraint and target maneuver compensation is introduced. BTT aircraft Lyapunov guidance and control system is realized with Extended Kalman Filter. When the Lyapunov BTT guidance law is applied to BTT aircraft guidance, the acceleration command will keep above the zero and completely eliminate the trigonometric polar conversion singularity as the roll command is computed. Various simulation results from two kinds of representative engagement scenarios demonstrate the highly effectiveness and reasonability of the proposed guidance law.