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

Titelangaben

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
A regularization of Zubov's equation for robust domains of attraction.
In: Isidori, Alberto ; Lamnabhi-Lagarrigue, Françoise ; Respondek, Witold (Hrsg.): Nonlinear control in the Year 2000. Volume 1. - Berlin : Springer , 2001 . - S. 277-290 . - (Lecture Notes in Control and Information Sciences ; 258 )
ISBN 978-1-85233-363-8
DOI: https://doi.org/10.1007/BFb0110220

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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 (available here). 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.