Polynomial Constraints for Robustness Analysis of Nonlinear Systems

TL;DR

This paper introduces a polynomial constraint framework to analyze the robustness of nonlinear systems, broadening the applicability of polynomial-based tools like sum-of-squares programming.

Contribution

It proposes a numerical method for constructing polynomial constraints and explores their relationship with IQCs, enhancing nonlinear system analysis.

Findings

Validated polynomial constraints for nonlinearities using numerical examples.

Enabled computation of inner estimates of the region of attraction.

Linked polynomial constraints with existing IQCs for better analysis.

Abstract

This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming, to a broader class of non-polynomial systems. A numerical method for constructing these constraints is proposed. The relationship between polynomial constraints and existing integral quadratic constraints (IQCs) is investigated, providing transformations of IQCs into polynomial constraints. The effectiveness of polynomial constraints in characterizing nonlinearities is validated via numerical examples to compute inner estimates of the region of attraction for two systems.