Differential Game Guidance Law with Intercept Angle Considering Aerodynamic Drag

A differential-game interception guidance law considering aerodynamic drag and terminal intercept-angle constraints is proposed. The proposed law is designed to achieve precise interception of high-speed maneuvering targets. Unlike existing guidance-law studies, which commonly assume constant speeds for both the interceptor and the target, this work establishes a refined dynamic model to better represent realistic engagement scenarios. Based on this model, the terminal projection theorem is used to reduce the order of the two-player optimal control problem. This reduction decreases the dimensionality of the costate variables and enables their analytical expressions to be derived. This process avoids the need to solve high-dimensional two-point boundary value problems, greatly enhancing computational efficiency and theoretical interpretability. Using Pontryagin’s maximum principle, an analytical closed-loop form of the linear quadratic differential game guidance law considering aerodynamic drag (LQDGA) is derived. The LQDGA incorporates two adaptive gains that can be dynamically adjusted in real time in response to changes in the interception state. The boundedness of the guidance gains is verified through analytical analysis and numerical simulations under various selections of weight coefficients, thereby ensuring the stability and robustness of the guidance law. Simulation results, including comparative and Monte Carlo tests, demonstrate that LQDGA achieves accurate interception, satisfies terminal intercept-angle constraints, and maintains robustness under bounded uncertainties.