Reachability of weakly nonlinear systems using Carleman linearization

TL;DR

This paper presents a novel method for analyzing the reachability of weakly nonlinear systems by embedding them into a linear framework using Carleman linearization, enabling set-based propagation with high-dimensional linear solvers.

Contribution

It introduces a new approach that combines Carleman linearization with support function-based reachability analysis for nonlinear systems.

Findings

Effective set-based reachability analysis for weakly nonlinear systems.

Utilizes high-dimensional linear solvers for nonlinear system behavior.

Provides a global error bound for the Carleman linearization abstraction.

Abstract

In this article we introduce a solution method for a special class of nonlinear initial-value problems using set-based propagation techniques. The novelty of the approach is that we employ a particular embedding (Carleman linearization) to leverage recent advances of high-dimensional reachability solvers for linear ordinary differential equations based on the support function. Using a global error bound for the Carleman linearization abstraction, we are able to describe the full set of behaviors of the system for sets of initial conditions and in dense time.