Stabilization of controlled diffusions via Zubov's method

L. Grüne, F. Camilli, A. Cesaroni, F. Wirth: Stabilization of controlled diffusions via Zubov's method
Stochastics & Dynamics 6, 373 - 394, 2006

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Abstract:

We consider a controlled stochastic system which is exponentially stabilizable in probability near an attractor. Our aim is to characterize the set of points which can be driven by a suitable control to the attractor with either positive probability or with probability one. This will be done by associating to the stochastic system a suitable control problem and the corresponding Zubov equation. We then show that this approach can be used as a basis for numerical computations of these sets.

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