发表机构
Smead Department of Aerospace Engineering Sciences, University of Colorado Boulder（苏尔兹德部航空航天工程科学系，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 中文总结
研究非线性系统中分布模糊下随机控制的风险概率定义，利用指数积分变分表达式界定预期风险值，给出确定相对熵距离的方法，为处理非线性协方差转向问题中的分布模糊提供框架并通过航天器制导示例展示成果。
AI 中文摘要
我们考虑在分布模糊下的随机控制问题中定义风险概率。当前机会约束控制方法通常假设真实状态分布已知且为高斯分布。但在许多实际工程应用中，系统动力学是非线性且仅近似建模，这些假设并不适用。在这项工作中，我们定义了一个分布模糊集，并利用指数积分的变分表达式，在位于名义高斯参考分布相对熵距离内的未知分布下，界定预期风险值。我们的界在零散度极限下恢复参考风险值。提出了一种确定定义模糊集的相对熵距离的方法，它是参考协方差演化和二阶动力学截断误差的函数。所得成果为处理非线性协方差转向问题中的分布模糊提供了一个框架。通过一个随机航天器制导示例展示了我们的成果。
英文摘要
We consider defining risk probability in stochastic control problems under distribution ambiguity. Current approaches for chance-constrained control typically assume that the true state distribution is known and Gaussian distributed. These assumptions are not amenable to many real-world engineering applications where system dynamics are nonlinear and only approximately modeled. In this work, we define a distribution ambiguity set and, with a variational expression for exponential integrals, bound the expected risk value under an unknown distribution that resides within a relative entropy distance of a nominal Gaussian reference distribution. Our bound recovers the reference risk value in the zero-divergence limit. A method is presented to determine the relative entropy distance defining the ambiguity set that is a function of the reference covariance evolution and second-order dynamical truncation errors. The resulting contributions provide a framework for handling distributional ambiguity in nonlinear covariance steering problems. A stochastic spacecraft guidance example is presented to demonstrate our contributions.
CommentsEuropean Control Conference (ECC) 2026
