# Data-driven stabilization of nonlinear polynomial systems with noisy data

arXiv: https://arxiv.org/abs/2011.07833 · HTML: https://mlsanity.com/paper/2011.07833/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Safely Learning Dynamical Systems](https://mlsanity.com/paper/2305.12284/) (2023)
- [Symplectic Inductive Bias for Data-Driven Target Reachability in Hamiltonian Systems](https://mlsanity.com/paper/2604.17213/) (2026)
- [k-Inductive Neural Barrier Certificates for Unknown Nonlinear Dynamics](https://mlsanity.com/paper/2605.20108/) (2026)

## Abstract (arXiv)

In a recent paper we have shown how to learn controllers for unknown linear systems using finite-sized noisy data by solving linear matrix inequalities. In this note we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system.