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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
