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Article Dans Une Revue IEEE Control Systems Letters Année : 2021

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

Vit Cibulka
Milan Korda
Tomas Hanis

Résumé

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 pro- gramming 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.

Dates et versions

hal-03441655 , version 1 (22-11-2021)

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Vit Cibulka, Milan Korda, Tomas Hanis. Spatio-Temporal Decomposition of Sum-of-Squares Programs for the Region of Attraction and Reachability. IEEE Control Systems Letters, 2021, 6, pp.812-817. ⟨10.1109/LCSYS.2021.3086585⟩. ⟨hal-03441655⟩
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