Generalized-Newton-Iteration-Based MPSP Method for Terminal Constrained Guidance

This article presents a generalized-Newton-iteration-based model-predictive static programming (MPSP) algorithm for the terminal constrained guidance problems. In the proposed approach, the Chebyshev polynomial is used to approximate the dynamics and constraint equations, by which the continuous-time guidance problem is transcribed into a discrete root-finding problem, and then, it is solved by the Newton method. A significant improvement to the previous methods lies in the fact that both the state and control are treated as the variables to be determined and simultaneously iteratively solved on the principle of the Newton method, which greatly reduces the computational complexity as well as improves the convergence robustness. The simulation case with a scenario of intercepting a high-speed target with both impact-angle and impact-time constraint in the midcourse phase was conducted to illustrate the effectiveness of the proposed method. The results show that the proposed guidance is superior to MPSP and other state-of-the-art Newton-type methods in terms of computational efficiency and convergence robustness.