# Hybrid Zonotope-Based Backward Reachability Analysis for Neural Feedback Systems With Nonlinear Plant Models

arXiv: https://arxiv.org/abs/2310.06921 · HTML: https://mlsanity.com/paper/2310.06921/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2023.

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

- [PREMAP: A Unifying PREiMage APproximation Framework for Neural Networks](https://mlsanity.com/paper/2408.09262/) (2024)
- [Provably-Safe Neural Network Training Using Hybrid Zonotope Reachability Analysis](https://mlsanity.com/paper/2501.13023/) (2025)
- [Efficient Reachability Analysis for Convolutional Neural Networks Using Hybrid Zonotopes](https://mlsanity.com/paper/2503.10840/) (2025)

## Abstract (arXiv)

The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing hybrid zonotopes to compute the over-approximation of backward reachable sets for neural feedback systems with nonlinear plant models and general activation functions. Closed-form expressions as hybrid zonotopes are provided for the over-approximated backward reachable sets, and a refinement procedure is proposed to alleviate the potential conservatism of the approximation. Two numerical examples are provided to illustrate the effectiveness of the proposed approach.