Certification of Linear Inclusions for Nonlinear Systems

TL;DR

This paper introduces a new optimization-based method to certify linear inclusions for nonlinear systems, providing a binary Yes/No certificate and enabling less conservative system enclosures.

Contribution

It presents a novel approach to verify linear difference inclusions for nonlinear systems using an optimization formulation, which is a new contribution.

Findings

Provides a binary certification method for linear inclusions

Enables less conservative linear enclosures for nonlinear systems

Demonstrates practical usefulness of the certification approach

Abstract

In this work, we propose novel method for certifying if a given set of vertex linear systems constitute a linear difference inclusion for a nonlinear system. The method relies on formulating the verification of the inclusion as an optimization problem in a novel manner. The result is a Yes/No certificate. We illustrate how the method can be useful in obtaining less conservative linear enclosures for nonlinear systems.