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

2025/10/14 by Daniel C. Qi, Qi, Daniel C., Kenshiro Oguri +5 · 2 citations
Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2510.12946

openalex publication_date 2025/10/14 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

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.

Citations

• Robust Cislunar Low-Thrust Trajectory Optimization under Uncertainties via Sequential Covariance Steering
• Unscented Trajectory Optimization
• Chance-Constrained Gaussian Mixture Steering to a Terminal Gaussian Distribution
• Chance-Constrained Control for Safe Spacecraft Autonomy: Convex Programming Approach
• Probabilistic Trajectory Design Via Approximate Gaussian Mixture Steering
• Distribution Steering for Discrete-Time Linear Systems with General Disturbances using Characteristic Functions
• Optimal Covariance Control for Stochastic Systems Under Chance Constraints

Cited by

• Convex Bound of Nonlinear Dynamical Errors for Stochastic Optimal Control
• Chance-Constrained Nonlinear Covariance Control via Robust Linearization Remainder Bounds

Related

• Approximate Relative Entropy Constraints for Nonlinear Covariance Steering Under Distribution Ambiguity
• Nonlinear Uncertainty Control with Iterative Covariance Steering
• Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform
• Nonlinear Covariance Steering using Variational Gaussian Process Predictive Models
• Density Steering by Power Moments