论文标题
关于随机控制的统计线性化的可访问性和可控性：代数等级及其通用性
On the Accessibility and Controllability of Statistical Linearization for Stochastic Control: Algebraic Rank Conditions and their Genericity
论文作者
论文摘要
统计线性化最近将特殊的兴趣激增视为一种数值便宜的方法，用于稳健地控制随机微分方程。尽管它已经成功地用于控制复杂的随机系统，但尚未研究统计线性化的可访问性和可控性能，这是使可靠控制问题充分解决的关键。在本文中，我们通过为统计线性化的可访问性和可控性提供足够的条件来弥合这一差距。具体而言，我们为统计线性化的可访问性和可控性建立了简单的足够代数条件，涉及仅漂移产生的LIE代数的等级。此外，我们通过反例本质上表明这些后一个代数条件基本上是鲜明的，并且它们相对于漂移和初始条件是一般性的。
Statistical linearization has recently seen a particular surge of interest as a numerically cheap method for robust control of stochastic differential equations. Although it has already been successfully applied to control complex stochastic systems, accessibility and controllability properties of statistical linearization, which are key to make the robust control problem well-posed, have not been investigated yet. In this paper, we bridge this gap by providing sufficient conditions for the accessibility and controllability of statistical linearization. Specifically, we establish simple sufficient algebraic conditions for the accessibility and controllability of statistical linearization, which involve the rank of the Lie algebra generated by the drift only. In addition, we show these latter algebraic conditions are essentially sharp, by means of a counterexample, and that they are generic with respect to the drift and the initial condition.
