# Continuous Abstraction of Nonlinear Systems using Sum-of-Squares Programming

arXiv: https://arxiv.org/abs/1909.06468 · HTML: https://mlsanity.com/paper/1909.06468/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2019.

## Built on by (most cited first, 1 of 1)

- [Transfer Learning for Control Systems via Neural Simulation Relations](https://mlsanity.com/paper/2412.01783/) (2024)

## Abstract (arXiv)

We present a control design procedure for nonlinear control systems in which we represent a potentially high dimensional system with a low dimensional continuous-state abstraction. The abstraction generates a reference which the original system follows with a low level controller. We propose sum-of-squares programming as a tool to design this controller and to provide an upper bound on the relative error between the system and its abstraction. We compute the low level controller simultaneously with a simulation function that gives the boundedness guarantee for the relative error.