# On the Accessibility and Controllability of Statistical Linearization for Stochastic Control: Algebraic Rank Conditions and their Genericity

arXiv: https://arxiv.org/abs/2207.10944 · HTML: https://mlsanity.com/paper/2207.10944/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2022.

## Built on by (most cited first, 2 of 2)

- [Automatic Solver Generator for Systems of Laurent Polynomial Equations](https://mlsanity.com/paper/2307.00320/) (2023)
- [A Hybrid Registration and Fusion Method for Hyperspectral Super-resolution](https://mlsanity.com/paper/2407.05279/) (2024)

## Abstract (arXiv)

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.