Fabio Camilli, Lars Grüne, Fabian Wirth
A regularization of Zubov's equation for robust domains of attraction
The paper is published: in Nonlinear Control in the Year 2000, A. Isidori et al., eds., Lecture Notes in Control and Information Sciences, Vol. 258, Springer-Verlag, London, 2000, pp. 277 - 290.
MSC:
34D10 Perturbations
49L25 Viscosity solutions
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.

Keywords: robust domain of attraction, Zubov's method, viscosity solutions

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Home Fabian Wirth's publication page Research Group "Regelungssysteme"
Zentrum für Technomathematik (German)
Institute for Dynamical Systems
The Maths Department
The University of Bremen

Notes:
submitted