Stabilization of controlled diffusions and Zubov's method

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Camilli, Fabio ; Cesaroni, Annalisa ; Grüne, Lars ; Wirth, Fabian:
Stabilization of controlled diffusions and Zubov's method.
Bayreuth , 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.