# Data-driven design of safe control for polynomial systems

arXiv: https://arxiv.org/abs/2112.12664 · HTML: https://mlsanity.com/paper/2112.12664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2021.

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

- [Safely Learning Dynamical Systems](https://mlsanity.com/paper/2305.12284/) (2023)

## Abstract (arXiv)

We consider the problem of designing an invariant set using only a finite set of input-state data collected from an unknown polynomial system in continuous time. We consider noisy data, i.e., corrupted by an unknown-but-bounded disturbance. We derive a data-dependent sum-of-squares program that enforces invariance of a set and also optimizes the size of the invariant set while keeping it within a set of user-defined safety constraints; the solution of this program directly provides a polynomial invariant set and a state-feedback controller. We numerically test the design on a system of two platooning cars.