分布模糊下非线性协方差控制的近似相对熵约束
Approximate Relative Entropy Constraints for Nonlinear Covariance Steering Under Distribution Ambiguity
- University of Colorado Boulder（科罗拉多大学博尔德分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究针对非线性协方差控制中高斯替代与真实分布差异导致风险敏感量估计不准的问题，基于相对熵开发分布鲁棒框架，推导相关上界并纳入算法，用于设计随机制导策略，在航天器转移实例中得到验证。
AI中文摘要：
协方差控制为设计线性随机反馈策略提供了有效框架，但其向非线性系统的扩展依赖通过局部线性化得到的高斯替代。由于该替代可能与真实非线性状态分布有很大差异，诸如碰撞概率和均方误差等风险敏感量可能估计不准确。本文基于相对熵（又称库尔贝克-莱布勒散度，KLD）开发了一个分布鲁棒协方差控制框架，以考虑传播概率密度函数中的模糊性。利用指数积分的变分表示，我们在KLD模糊集上推导了风险敏感量的可计算上界。然后我们制定了真实非线性分布与高斯参考替代之间KLD变化率的上界。在一些假设下，该界由协方差控制公式中的决策变量控制。所得约束被纳入顺序凸规划算法，以设计随机制导策略，使真实分布接近其高斯替代，同时对风险敏感性能指标进行约束。所提方法在两个近直线晕轨道间具有挑战性的非线性航天器转移上得到了验证。
英文摘要：
Covariance steering provides an efficient framework for designing linear stochastic feedback policies, but its extension to nonlinear systems relies on a Gaussian surrogate obtained through local linearization. Because this surrogate may differ substantially from the true nonlinear state distribution, risk-sensitive quantities such as collision probability and mean-squared error may be inaccurately estimated. This work develops a distributionally robust covariance-steering framework based on the relative entropy, also known as the Kullback-Leibler divergence (KLD), to account for ambiguity in the propagated probability density function. Using a variational representation of exponential integrals, we derive computable upper bounds on risk-sensitive quantities over a KLD ambiguity set. We then formulate an upper bound on the time rate of change of the KLD between the true nonlinear distribution and a Gaussian reference surrogate. Under some assumptions, this bound is controlled by decision variables within a covariance-steering formulation. The resulting constraints are incorporated into a sequential convex programming algorithm to design stochastic guidance policies that keep the true distribution close to its Gaussian surrogate while enforcing bounds on risk-sensitive performance measures. The proposed approach is demonstrated on a challenging nonlinear spacecraft transfer between two near-rectilinear halo orbits.
