Nonlinear Optimal Impact - Time-Control Guidance Against Maneuvering Targets

Aiming to cope with the challenge of impact-time control (ITC) for engaging maneuvering targets, a nonlinear optimal guidance method is proposed in this paper. Utilizing the classical differential geometric curve theory and the relative virtual frame, the ITC is accomplished by the combination of the relative trajectory-length control (RTLC) and the relative speed prediction. The characteristics of the ideal proportional navigation (IPN) guidance law is fully leveraged in this paper: 1) with the series solution of the relative trajectory length-to-go under IPN, the guidance law for RTLC is formulated using the optimal error dynamic method; 2) to provide the real-time and stable estimation of the future relative speed profile, the implementation framework of ITC is developed based on IPN. Besides, the linear solutions of the relative lead angle and the relative guidance curvature are derived, which are compared with the exact numerical solutions to explore the properties of the proposed law. Finally, numerical simulations are carried out to validate the effectiveness of method and the accuracy of relevant theoretical results.