Sequential sum-of-squares programming for analysis of nonlinear systems

TL;DR

This paper introduces a sequential sum-of-squares programming method that linearizes nonlinear systems locally to efficiently solve polynomial optimization problems, with proven convergence and practical application to aircraft models.

Contribution

It presents a novel sequential approach for sum-of-squares problems that improves computational tractability and convergence analysis for nonlinear systems.

Findings

Effective estimation of the region of attraction for a polynomial aircraft model.

Proven local convergence under strong regularity assumptions.

Enhanced efficiency in solving nonconvex polynomial optimization problems.

Abstract

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local linearizations leading to tractable, convex sum-of-squares problems. Local convergence is proven under the assumption of strong regularity and the new approach is applied to estimate the region of attraction of a polynomial aircraft model.