# Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysis

## TL;DR

This paper introduces sparse polynomial zonotopes, a new set representation that efficiently handles non-convex sets and nonlinear system reachability, reducing computational complexity and wrapping effects.

## Contribution

The paper presents sparse polynomial zonotopes as a novel set representation that generalizes existing models and improves efficiency in reachability analysis of nonlinear systems.

## Key findings

- Reduces wrapping effect in nonlinear reachability analysis
- Decreases computation time compared to zonotopes
- Handles non-convex sets effectively

## Abstract

We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models. Operations like Minkowski sum, quadratic mapping, and reduction of the representation size can be computed with polynomial complexity w.r.t. the dimension of the system. In particular, for reachability analysis of nonlinear systems, the wrapping effect is substantially reduced using sparse polynomial zonotopes, as demonstrated by numerical examples. In addition, we can significantly reduce the computation time compared to zonotopes when dealing with nonlinear dynamics.