Computational Schemes for Optimizing Domains of Attraction in Dynamical Systems

Castillo López, Angela and Zufiria Zatarain, Pedro Jose (2011). Computational Schemes for Optimizing Domains of Attraction in Dynamical Systems. In: "Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2011 ", 28/08/2011 - 31/08/2011, Washington, DC, USA. pp. 637-646. https://doi.org/10.1115/DECT2011-48158.

Description

Title: Computational Schemes for Optimizing Domains of Attraction in Dynamical Systems
Author/s:
  • Castillo López, Angela
  • Zufiria Zatarain, Pedro Jose
Item Type: Presentation at Congress or Conference (Article)
Event Title: Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2011
Event Dates: 28/08/2011 - 31/08/2011
Event Location: Washington, DC, USA
Title of Book: Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
Date: 2011
Subjects:
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In this paper, several computational schemes are presented for the optimal tuning of the global behavior of nonlinear dynamical sys- tems. Specifically, the maximization of the size of domains of attraction associated with invariants in parametrized dynamical sys- tems is addressed. Cell Mapping (CM) tech- niques are used to estimate the size of the domains, and such size is then maximized via different optimization tools. First, a ge- netic algorithm is tested whose performance shows to be good for determining global maxima at the expense of high computa- tional cost. Secondly, an iterative scheme based on a Stochastic Approximation proce- dure (the Kiefer-Wolfowitz algorithm) is eval- uated showing acceptable performance at low cost. Finally, several schemes combining neu- ral network based estimations and optimiza- tion procedures are addressed with promising results. The performance of the methods is illus- trated with two applications: first on the well-known van der Pol equation with stan- dard parametrization, and second the tuning of a controller for saturated systems.

More information

Item ID: 12644
DC Identifier: http://oa.upm.es/12644/
OAI Identifier: oai:oa.upm.es:12644
DOI: 10.1115/DECT2011-48158
Deposited by: Memoria Investigacion
Deposited on: 27 Feb 2013 08:44
Last Modified: 21 Apr 2016 11:55
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