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arXiv · 2103.03531

Spatio-Temporal Decomposition of Sum-of-Squares Programs for the Region of Attraction and Reachability

Vít Cibulka·Milan Korda·Tomáš Haniš
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Abstract

This paper presents a method for calculating Region of Attraction of a target set (not necessarily an equilibrium) for controlled polynomial dynamical systems, using a hierarchy of semidefinite programming problems (SDPs). Our approach builds on previous work and addresses its main issue, the fast-growing memory demands for solving large-scale SDPs. The main idea in this work is in dissecting the original resource-demanding problem into multiple smaller, interconnected, and easier to solve problems. This is achieved by spatio-temporal splitting akin to methods based on partial differential equations. We show that the splitting procedure retains the convergence and outer-approximation guarantees of the previous work, while achieving higher precision in less time and with smaller memory footprint.

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Vít Cibulka, Milan Korda, Tomáš Haniš. 2021-03-05. Spatio-Temporal Decomposition of Sum-of-Squares Programs for the Region of Attraction and Reachability. https://arxiv.org/abs/2103.03531

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