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

F. Camilli, L. Grüne, F. Wirth: A regularization of Zubov's equation for robust domains of attraction
in: Nonlinear Control in the Year 2000 Volume 1 (NCN), A. Isidori, F. Lamnabhi-Lagarrigue, W. Respondek (eds.)
Lecture Notes in Control and Information Sciences 258, Springer Verlag, London, 2000, 277 - 290

DOI: 10.1007/BFb0110202
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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.

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