KAN-based analytic expression inversion for three-dimensional impact angle and time control guidance

This paper addresses the problem of missile intercepting a stationary target in three-dimensional space with desired impact time and angle constraints. A novel guidance law based on the Kolmogorov-Arnold network (KAN) is proposed. First, a variable-speed nonlinear guidance model incorporating aerodynamic effects is established according to the relative motion dynamics between the missile and target, eliminating the need for the constant velocity assumption. Second, the guidance command is decomposed into pitch and yaw channels. Bias term commands for each channel are designed based on the biased proportional navigation guidance law, thereby simplifying the guidance law design. Subsequently, KAN is employed to perform supervised learning on flight data, innovatively deriving the analytical expressions of the guidance law in a data-driven manner. Finally, a generative adversarial imitation learning (GAIL)-based method is used to fine-tune the unknown parameters within the derived analytical expressions. This approach eliminates the need for manual reward function design and avoids the sparse reward problem inherent in traditional reinforcement learning. Additionally, the interpretability of the KAN-derived analytical guidance law expressions is analyzed and validated through relevant simulations. Numerical simulation results demonstrate that the proposed guidance law not only simultaneously satisfies the time and angle constraints but also maintains high guidance accuracy in untrained scenarios.