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.

A regularization of Zubov's equation for robust domains of attraction / Camilli, Fabio; Lars, Gruene; Fabian, Wirth. - STAMPA. - 258:(2002), pp. 277-290. ((Intervento presentato al convegno 2nd Workshop of the Nonlinear Control Network tenutosi a Paris nel JUN 05-09, 2000.

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

CAMILLI, FABIO;
2002

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.
2nd Workshop of the Nonlinear Control Network
Zubov method; stability; domain of attraction
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
A regularization of Zubov's equation for robust domains of attraction / Camilli, Fabio; Lars, Gruene; Fabian, Wirth. - STAMPA. - 258:(2002), pp. 277-290. ((Intervento presentato al convegno 2nd Workshop of the Nonlinear Control Network tenutosi a Paris nel JUN 05-09, 2000.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/405777
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