Approximating regions of attraction of a sparse polynomial differential system *

2019/11/21 by Didier Henrion, Henrion, Didier, Matteo Tacchi +5
Decision Sciences · Engineering · Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Power System Optimization and Stability #Probabilistic and Robust Engineering Design #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1911.09500

openalex publication_date 2019/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by stability analysis of large scale power systems, we describe how the Lasserre (moment-sums of squares, SOS) hierarchy can be used to generate outer approximations of the region of attraction (ROA) of sparse polynomial differential systems, at the price of solving linear matrix inequalities (LMI) of increasing size. We identify specific sparsity structures for which we can provide numerically certified outer approximations of the region of attraction in high dimension. For this purpose, we combine previous results on non-sparse ROA approximations with sparse semi-algebraic set volume computation.

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