# Learning control for polynomial systems using sum of squares relaxations

arXiv: https://arxiv.org/abs/2004.00850 · HTML: https://mlsanity.com/paper/2004.00850/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2020.

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

- [Joint Differentiable Optimization and Verification for Certified Reinforcement Learning](https://mlsanity.com/paper/2201.12243/) (2022)
- [Imitation Learning of Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2109.10854/) (2021)

## Abstract (arXiv)

This paper considers the problem of learning control laws for nonlinear polynomial systems directly from the data, which are input-output measurements collected in an experiment over a finite time period. Without explicitly identifying the system dynamics, stabilizing laws are directly designed for nonlinear polynomial systems using experimental data alone. By using data-based sum of square programming, the stabilizing state-dependent control gains can be constructed.