Parallel-Structured Newton-Type Guidance by Using Modified Chebyshev–Picard Iteration

Abstract

This paper presents a parallel-structured Newton-type guidance law for the missile guidance problems. In the proposed approach, the modified Chebyshev–Picard iteration is used to approximate the dynamic equations, by which the continuous-time guidance problem is transcribed into a sequence of discrete-time subproblems, and both serial and parallel computing can be supported. The subproblems can then be iteratively solved by the Newton-type methods. Numerical demonstrations in a 3-D air-to-surface missile guidance problem with both impact-time and impact-angle constraints are provided to illustrate the effectiveness of the proposed guidance law. The simulation results show that the proposed guidance is superior to the state-of-the-art adaptive damped Newton-type guidance and quasi-spectral model predictive static programming in both computational efficiency and accuracy, even before parallel implementation.