针对非线性系统在分布不确定下的鲁棒规划问题，提出基于相对熵约束的随机约束方法。
Relative Entropy-Bounded Ambiguous Chance Constraints for Robust Planning in Nonlinear Systems
- 用相对熵定义分布模糊集，结合变分法控制未知分布的风险
- 在零偏差时恢复参考风险值，且模糊范围与系统协方差和二阶误差相关
- 适用于非线性系统中仅近似建模的工程场景，如航天器随机制导
本文研究在分布模糊性下的随机控制问题中的风险概率定义。现有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，这不适用于系统动力学非线性且仅近似建模的许多实际工程场景。本文定义了一个分布模糊集，并利用指数积分的变分表达式，对位于名义高斯参考分布相对熵距离内的未知分布下的期望风险值进行上界估计。该边界在相对熵为零时恢复参考风险值。本文提出一种确定模糊集相对熵距离的方法，其依赖于参考协方差演化和二阶动力学截断误差。所提方法为处理非线性协方差引导问题中的分布不确定性提供了框架。通过一个随机航天器制导示例验证了方法的有效性。
原文摘要 · Abstract (English)
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.
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