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

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. We prove local convergence under the assumption of strong regularity, a common condition in variational analysis. The new approach is applied to estimate the region of attraction of a polynomial aircraft model, where it outperforms previous methods for nonconvex sum-of-squares problems.