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Zubov's equation for state-constrained perturbed nonlinear systems

URN to cite this document: urn:nbn:de:bvb:703-epub-1906-4

Title data

Grüne, Lars ; Zidani, Hasnaa:
Zubov's equation for state-constrained perturbed nonlinear systems.
Department of Mathematics, University of Bayreuth
Bayreuth , 2015 . - 19 S.

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Project information

Project title:
Project's official title
Project's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)
264735-SADCO
Project financing: Andere
European Union "FP7-People-ITN" programme

Abstract

The paper gives a characterization of the uniform robust domain of attraction for a finite non-linear controlled system subject to perturbations and state constraints. We extend the Zubov approach to characterize this domain by means of the value function of a suitable infinite horizon state-constrained control problem which at the same time is a Lyapunov function for the system. We provide associated Hamilton-Jacobi-Bellman equations and prove existence and uniqueness of the solutions of these generalized Zubov equations.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen in:
Mathematical Control and Related Fields. Bd. 5 (März 2015) Heft 1 . - S. 55-71.
DOI: https://doi.org/10.3934/mcrf.2015.5.55
Keywords: domain of attraction; state-constrained nonlinear systems; Zubov's approach; Hamilton-Jacobi equations; viscosity solution
Subject classification: Mathematics Subject Classification Code: 93D09 (35F21 49L25)
DDC Subjects: 500 Science > 510 Mathematics
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
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-1906-4
Date Deposited: 13 Mar 2015 09:40
Last Modified: 01 Jun 2021 05:23
URI: https://epub.uni-bayreuth.de/id/eprint/1906
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