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Computing a Basin of Attraction to a Target Region by Solving Bilinear Semi-Definite Problems

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Computer Algebra in Scientific Computing (CASC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6885))

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Abstract

In this paper, we present a sum of squares programming based method for computing a basin of attraction to a target region as large as possible by iteratively searching for Lyapunov-like functions. We start with the basic mathematical notions and show how attraction to a target region can be ensured by Lyapunov-like functions. Then, we present an initial framework for getting an increasing sequence of basins of attraction by iteratively computing Lyapunov-like functions. This framework can be realized by solving bilinear semi-definite problems based on sums of squares decomposition. We implement our algorithm and test it on some interesting examples. The computation results show the usefulness of our method.

This work was partly supported by NSFC-61003021, Beijing Nova Program and SKLSDE-2011ZX-16.

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Authors and Affiliations

  1. SKLSDE, LMIB and School of Mathematics and Systems Science, Beihang University, China

    Zhikun She & Bai Xue

Authors
  1. Zhikun She
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  2. Bai Xue
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Evgenii V. Vorozhtsov

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© 2011 Springer-Verlag Berlin Heidelberg

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She, Z., Xue, B. (2011). Computing a Basin of Attraction to a Target Region by Solving Bilinear Semi-Definite Problems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2011. Lecture Notes in Computer Science, vol 6885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23568-9_26

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  • DOI: https://doi.org/10.1007/978-3-642-23568-9_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23567-2

  • Online ISBN: 978-3-642-23568-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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