Towards Optimal Spatio-Temporal Decomposition of Control-Related Sum-of-Squares Programs
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.
Keywords
Cite
@article{arxiv.2409.11196,
title = {Towards Optimal Spatio-Temporal Decomposition of Control-Related Sum-of-Squares Programs},
author = {Vít Cibulka and Milan Korda and Tomáš Haniš},
journal= {arXiv preprint arXiv:2409.11196},
year = {2024}
}