Pseudospectral Convex Optimization Based Model Predictive Static Programming for Constrained Guidance

Abstract

This paper presents a pseudospectral convex optimization-based model predictive static programming (PCMPSP) for the constrained guidance problem. First, the sensitivity relation between the state increment and control correction is reformulated using Legendre-Gauss (LG) and Legendre-Gauss-Radau (LGR) pseudospectral transcriptions. Second, the convex optimal control problem associated with the trajectory optimization is defined by introducing the quadratic performance index. Third, modifications to the initial guess solution and reference trajectory update are introduced to enhance the accuracy and robustness of the algorithm. Finally, a model predictive guidance law is designed based on the proposed PCMPSP algorithm for the air-to-surface missile guidance with impact angle constraint. The simulation results show that the PCMPSP has lower sensitivity to the initial guess trajectory, higher accuracy, as well as faster convergence speed than existing convex programming methods. Moreover, the robustness of the proposed guidance law to uncertainties is demonstrated through the Monte Carlo campaign.