Non-Gaussian Distribution Steering in Nonlinear Dynamics with Conjugate Unscented Transformation

Abstract: In highly nonlinear systems such as the ones commonly found in astrodynamics, Gaussian distributions generally evolve into non-Gaussian distributions. This paper introduces a method for effectively controlling non-Gaussian distributions in nonlinear environments using optimized linear feedback control. This paper utilizes Conjugate Unscented Transformation to quantify the higher-order statistical moments of non-Gaussian distributions. The formulation focuses on controlling and constraining the sigma points associated with the uncertainty quantification, which would thereby reflect the control of the entire distribution and constraints on the moments themselves. This paper develops an algorithm to solve this problem with sequential convex programming, and it is demonstrated through a two-body and three-body example. The examples show that individual moments can be directly controlled, and the moments are accurately approximated for non-Gaussian distributions throughout the controller's time horizon in nonlinear dynamics.