Zubov's method for controlled diffusions with state constraints

Titelangaben

Grüne, Lars ; Picarelli, Athena:
Zubov's method for controlled diffusions with state constraints.
In: Nonlinear Differential Equations and Applications NoDEA. Bd. 22 (2015) Heft 6 . - S. 1765-1799.
ISSN 1021-9722
DOI: https://doi.org/10.1007/s00030-015-0343-0

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Abstract

We consider a controlled stochastic system in presence of state-constraints. Under the assumption of exponential stabilizability of the system near a target set, we aim to characterize the set of points which can be asymptotically driven by an admissible control to the target with positive probability. We show that this set can be characterized as a level set of the optimal value function of a suitable unconstrained optimal control problem which in turn is the unique viscosity solution of a second order PDE which can thus be interpreted as a generalized Zubov equation.