Converging outer approximations to global attractors using semidefinite programming

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355970" target="_blank" >RIV/68407700:21230/21:00355970 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.automatica.2021.109900" target="_blank" >https://doi.org/10.1016/j.automatica.2021.109900</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.automatica.2021.109900" target="_blank" >10.1016/j.automatica.2021.109900</a>

Result language
angličtina
Original language name
Converging outer approximations to global attractors using semidefinite programming
Original language description
This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of increasing size with guaranteed convergence to the global attractor. The approach taken follows an established line of reasoning, where we first characterize the global attractor via an infinite dimensional linear programming problem (LP) in the space of Borel measures. The dual to this LP is in the space of continuous functions and its feasible solutions provide guaranteed outer approximations to the global attractor. For systems with polynomial dynamics, a hierarchy of finite-dimensional sum-of-squares tightenings of the dual LP provides a sequence of outer approximations to the global attractor with guaranteed convergence in the sense of volume discrep-ancy tending to zero. The method is very simple to use and based purely on convex optimization. Numerical examples with the code available online demonstrate the method. (C) 2021 Published by Elsevier Ltd.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20205 - Automation and control systems

Project
<a href="/en/project/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koopman operator framework for control of complex nonlinear dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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