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arXiv · 2409.11196

Towards Optimal Spatio-Temporal Decomposition of Control-Related Sum-of-Squares Programs

Vít Cibulka·Milan Korda·Tomáš Haniš
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Abstract

This paper presents a method for calculating the Region of Attraction (ROA) of nonlinear dynamical systems, both with and without control. The ROA is determined by solving a hierarchy of semidefinite programs (SDPs) defined on a splitting of the time and state space. Previous works demonstrated that this splitting could significantly enhance approximation accuracy, although the improvement was highly dependent on the ad-hoc selection of split locations. In this work, we eliminate the need for this ad-hoc selection by introducing an optimization-based method that performs the splits through conic differentiation of the underlying semidefinite programming problem. We provide the differentiability conditions for the split ROA problem, prove the absence of a duality gap, and demonstrate the effectiveness of our method through numerical examples.

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Vít Cibulka, Milan Korda, Tomáš Haniš. 2024-09-17. Towards Optimal Spatio-Temporal Decomposition of Control-Related Sum-of-Squares Programs. https://arxiv.org/abs/2409.11196

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