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Zubov's equation for state-constrained perturbed nonlinear systems

Title data

Grüne, Lars ; Zidani, Hasnaa:
Zubov's equation for state-constrained perturbed nonlinear systems.
Department of Mathematics, University of Bayreuth
In: Mathematical Control and Related Fields. Vol. 5 (March 2015) Issue 1 . - pp. 55-71.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2015.5.55

This is the latest version of this item.

Project information

Project title:
Project's official titleProject's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO

Project financing: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union

Abstract in another language

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: Article in a journal
Refereed: Yes
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)
Institutions of the University: 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 > Advanced Fields > Nonlinear Dynamics
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)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 19 Mar 2015 10:22
Last Modified: 23 Mar 2015 12:21
URI: https://eref.uni-bayreuth.de/id/eprint/8412

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