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.