Abstract: This paper develops a guidance law for the interceptors against highly maneuverable targets, such as tactical ballistic missiles (TBM) and cruise missiles with intelligent control systems, by using a nonlinear differential game formulation with bounded controls. It also analyzes the admissible initial flight-path errors of perfect intercept. Since the kinematics of the relative motion between the target and the interceptor is actually nonlinear, guidance laws traditionally based on linearization cause errors in the interception. In this paper, the guidance law is proposed by using nonlinear kinematics, taking the flight-path error of the intercept missile as the performance function and utilizing the feedback linearization and optimal control theory. The admissible initial flight-path errors of perfect intercept are studied in three intercept cases: head-on intercept, tail-chase intercept, and head-pursuit intercept. The results show that a smaller closing velocity and a greater maneuver acceleration of the intercept missile lead to a bigger admissible initial flight-path error. If the intercept missile possesses the advantage of velocity, a bigger admissible initial flight-path error can also be tolerated when the lead-angle of the target approximates 90°, or when the tail-chase mode of intercept is adopted.

Key words: intercept missile, differential game, nonlinear model, guidance, admissible flight-path error