Nonlinear Optimal Impact Angle Control Guidance With Acceleration Constraints

This article presents the development of a nonlinear optimal guidance to control the impact angle for an acceleration-constrained and speed-varying interceptor against a stationary target. The interceptor's velocity varies due to aerodynamic forces and gravity, while the constraints of maximal admissible acceleration and zero terminal acceleration are considered. The zero terminal acceleration imposes a terminal control constraint for the corresponding optimal control problem. To address this, a regularization term is incorporated to the cost function to ensure compliance with the zero terminal acceleration condition. A saturation function is then utilized to enforce the maximal admissible acceleration constraint, preserving the smoothness of the optimal control and providing a safety margin. To enable real-time implementation, a parameterized system is established to generate optimal trajectories for training a neural network. Furthermore, a combined guidance strategy is employed, integrating the nonlinear nature of the neural network-based approach with the convergence performance of a linear feedback guidance. Consequently, the proposed approach generates optimal guidance commands that achieve interceptions with minimal terminal accelerations, as verified by numerical simulations.