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Zubov's method for controlled diffusions with state constraints

Title data

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

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Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: controllability for diffusion systems; Hamilton-Jacobi-Bellman equations; viscosity solutions; stochastic optimal control
Subject classification: Mathematics Subject Classification Code: 93B05 (93E20 49L25)
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 28 Oct 2015 09:44
Last Modified: 28 Oct 2015 09:44
URI: https://eref.uni-bayreuth.de/id/eprint/20842

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