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A regularization of Zubov’s equation for robust domains of attraction

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Nonlinear control in the Year 2000

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 258))

Abstract

We derive a method for the computation of robust domains of attraction based on a recent generalization of Zubov’s theorem on representing robust domains of attraction for perturbed systems via the viscosity solution of a suitable partial differential equation. While a direct discretization of the equation leads to numerical difficulties due to a singularity at the stable equilibrium, a suitable regularization enables us to apply a standard discretization technique for Hamilton-Jacobi-Bellman equations. We present the resulting fully discrete scheme and show a numerical example.

Research supported by the TMR Networks “Nonlinear Control Network” and “Viscosity Solutions and their applications”, and the DFG Priority Research Program “Ergodentheorie, Analysis und effiziente Simulation dynamischer Systeme”

This paper was written while Fabian Wirth was a guest at the Centre Automatique et Systèmes, Ecole des Mines de Paris, Fontainebleau, France. The hospitality of all the members of the centre is gratefully acknowledged.

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Author information

Authors and Affiliations

  1. Dip. di Energetica, Fac. di Ingegneria, Università de l’Aquila, 67040, Roio Poggio (AQ), Italy

    Fabio Camilli

  2. Fachbereich Mathematik, J.W. Goethe-Universität, Postfach 11 19 32, 60054, Frankfurt a.M., Germany

    Lars Grüne

  3. Center for Technomathematics, University of Bremen, 28334, Bremen, Germany

    Fabian Wirth

Authors
  1. Fabio Camilli
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  2. Lars Grüne
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  3. Fabian Wirth
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Editor information

Alberto Isidori (Professor)Françoise Lamnabhi-Lagarrigue (Docteur D’état)Witold Respondek (Professor)

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© 2001 Springer-Verlag London Limited

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Camilli, F., Grüne, L., Wirth, F. (2001). A regularization of Zubov’s equation for robust domains of attraction. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the Year 2000. Lecture Notes in Control and Information Sciences, vol 258. Springer, London. https://doi.org/10.1007/BFb0110220

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  • DOI: https://doi.org/10.1007/BFb0110220

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-363-8

  • Online ISBN: 978-1-84628-568-4

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