发表机构
School of Aeronautics and Astronautics, Purdue University（普渡大学航空航天学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对确定性非线性系统中的非高斯分布引导问题，提出基于容积的统计矩引导方法，结合序贯凸优化求解，并以二维振荡器数值示例验证。
AI 中文摘要
本文研究确定性非线性系统中离散时间非高斯分布引导问题。分布引导是一种在轨迹分布上设计控制策略而非优化单一轨迹的问题。非线性系统的挑战在于，即使是初始高斯分布也会演化为非高斯分布，这常常使得概率密度的闭式表示不可行。一种称为统计矩引导的方法采用基于容积的方法来近似非高斯分布，从而为该问题提供近似解。本文提供了理论支持，并详细说明了如何通过序贯凸优化来求解。文中给出了一个描述二维振荡器的耦合非线性二阶常微分方程作为数值示例。
英文摘要
This paper addresses discrete-time non-Gaussian distribution steering in deterministic nonlinear systems. Distribution steering is a problem in which a control policy is designed over a distribution of trajectories rather than optimizing a single trajectory. The challenge with nonlinear systems is that even initially Gaussian distributions evolve into non-Gaussian distributions, often precluding a closed-form representation of the probability density. A method called statistical moment steering applies a cubature-based method to approximate non-Gaussian distributions for an approximate solution to this problem. This paper provides theoretical support and details how it can be solved with sequential convex optimization. A coupled, nonlinear, second-order ordinary differential equation describing a two-dimensional oscillator is provided as a numerical example.
