# Symbolic Abstractions for Nonlinear Control Systems via Feedback Refinement Relation

arXiv: https://arxiv.org/abs/2011.12824 · HTML: https://mlsanity.com/paper/2011.12824/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

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

- [GenCtrl -- A Formal Controllability Toolkit for Generative Models](https://mlsanity.com/paper/2601.05637/) (2026)

## Abstract (arXiv)

This paper studies the construction of symbolic abstractions for nonlinear control systems via feedback refinement relation. Both the delay-free and time-delay cases are addressed. For the delay-free case, to reduce the computational complexity, we propose a new approximation approach for the state and input sets based on a static quantizer, and then a novel symbolic model is constructed such that the original system and the symbolic model satisfy the feedback refinement relation. For the time-delay case, both static and dynamic quantizers are combined to approximate the state and input sets. This leads to a novel dynamic symbolic model for time-delay control systems, and a feedback refinement relation is established between the original system and the symbolic model. Finally, a numerical example is presented to illustrate the obtained results.