Characterizing controllability probabilities of stochastic control systems via Zubov’s method

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

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