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Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions
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SYSNO ASEP 0351298 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions Author(s) Ratschan, Stefan (UIVT-O) SAI, RID, ORCID
She, Z. (CN)Source Title SIAM Journal on Control and Optimization. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0363-0129
Roč. 48, č. 7 (2010), s. 4377-4394Number of pages 18 s. Language eng - English Country US - United States Keywords basin of attraction ; stability ; constraint solving ; interval computation ; algorithms Subject RIV IN - Informatics, Computer Science R&D Projects GC201/08/J020 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000281673500009 EID SCOPUS 77958536851 DOI 10.1137/090749955 Annotation In this paper, we present a method for computing a basin of attraction to a target region for polynomial ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly. It iteratively refines these relaxations in order to ensure that, whenever a nondegenerate solution exists, it will eventually be found by the algorithm. Application of an implementation to a range of benchmark problems shows the usefulness of the approach. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2011
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