2021/03/05 by Vít Cibulka, Milan Korda, Cibulka, Vít +3 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #Dynamical Systems (math.DS) #FOS: Mathematics #Machine Learning and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2103.03531
openalex publication_date 2021/03/05 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
This paper presents a method for calculating Region of Attraction of a target\nset (not necessarily an equilibrium) for controlled polynomial dynamical\nsystems, using a hierarchy of semidefinite programming problems (SDPs). Our\napproach builds on previous work and addresses its main issue, the fast-growing\nmemory demands for solving large-scale SDPs. The main idea in this work is in\ndissecting the original resource-demanding problem into multiple smaller,\ninterconnected, and easier to solve problems. This is achieved by\nspatio-temporal splitting akin to methods based on partial differential\nequations. We show that the splitting procedure retains the convergence and\nouter-approximation guarantees of the previous work, while achieving higher\nprecision in less time and with smaller memory footprint.\n