Successor Sets of Discrete-time Nonlinear Systems Using Hybrid Zonotopes

TL;DR

This paper introduces a method using hybrid zonotopes to efficiently compute over-approximations of successor sets in discrete-time nonlinear systems, extending previous linear techniques to nonlinear dynamics.

Contribution

It extends the state-update set construct to nonlinear systems using hybrid zonotopes, enabling efficient forward reachability analysis with set operations.

Findings

Provides a computationally-efficient method for over-approximating nonlinear system successor sets.

Demonstrates tight over-approximations in a numerical example with a piecewise-affine control law.

Extends linear hybrid system techniques to nonlinear systems using hybrid zonotopes.

Abstract

This paper presents identities for calculating over-approximated successor sets of discrete-time nonlinear systems using hybrid zonotopes. The proposed technique extends the state-update set construct, previously developed for linear hybrid systems, to nonlinear systems. Forward reachability of nonlinear systems can then be performed using only projection, intersection, and Cartesian product set operations with the state-update set. It is shown that use of an over-approximation of the state-update set yields over-approximations of successor sets. A technique to over-approximate a nonlinear function using a special ordered set approximation, equivalently represented as a hybrid zonotope, is then presented. A numerical example of a nonlinear system controlled by a piecewise-affine control law demonstrates that the approach provides a computationally-efficient and tight over-approximation of the closed-loop reachable set.