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

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.

Submitted to 2023 American Control Conference

References in corpus (1)

• Low-Rank Univariate Sum of Squares Has No Spurious Local Minima

Cited by in corpus (2)

• Learning Barrier-Certified Polynomial Dynamical Systems for Obstacle Avoidance with Robots
• CaΣoS: A nonlinear sum-of-squares optimization suite