# Hybrid zonotopes: a new set representation for reachability analysis of mixed logical dynamical systems

arXiv: https://arxiv.org/abs/2106.14831 · HTML: https://mlsanity.com/paper/2106.14831/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2021.

## Built on by (most cited first, 7 of 7)

- [Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imagination](https://mlsanity.com/paper/2405.00846/) (2024)
- [Neural Network Verification with PyRAT](https://mlsanity.com/paper/2410.23903/) (2024)
- [Hybrid Zonotopes Exactly Represent ReLU Neural Networks](https://mlsanity.com/paper/2304.02755/) (2023)
- [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)
- [Hybrid Probabilistic Zonotopes for Identifiable and Refinable Predictive Uncertainty](https://mlsanity.com/paper/2608.05454/) (2026)
- [Towards Safe Reinforcement Learning with Reduced Conservativeness: A Case Study on Drone Flight Control](https://mlsanity.com/paper/2608.26852/) (2026)

## Abstract (arXiv)

This article presents a new set representation named the hybrid zonotope that is equivalent to the union of 2N constrained zonotopes -- convex polytopes -- through the addition of N binary zonotope factors. The major contribution of this manuscript is a closed-form solution for exact forward reachable sets of discrete-time, linear hybrid systems modeled as mixed logical dynamical systems. The proposed approach captures the worst-case exponential growth in the number of convex sets required to represent the nonconvex reachable set while exhibiting only linear growth in the complexity of the hybrid zonotope set representation. Redundancy removal techniques are provided that leverage binary trees to store the combinations of binary factors of the hybrid zonotope that map to nonempty convex subsets. Numerical examples show the hybrid zonotope's ability to compactly represent nonconvex reachable sets with an exponential number of features. Furthermore, the hybrid zonotope is shown to be closed under linear mappings, Minkowski sums, generalized intersections, and halfspace intersections.