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A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions

Title data

Baier, Robert ; Farkhi, Elza:
A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions.
Mathematisches Institut, Universität Bayreuth; School of Mathematical Sciences, Tel Aviv University
Bayreuth ; Tel Aviv , 2023 . - 31 p.
DOI: https://doi.org/10.15495/EPub_UBT_00007160

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Official URL: Volltext

Project information

Project financing: Andere
Bayerische Forschungsallianz „BayFor“
Mathematical Institute at Tel Aviv “MINT”, Tel Aviv University, Israel

Abstract in another language

We consider differential inclusions with strengthened one-sided Lipschitz (SOSL) right-hand sides. The class of SOSL multivalued maps is wider than the class of Lipschitz ones and a subclass of the class of one-sided Lipschitz maps.

We prove a Filippov stability theorem for the solutions of such differential inclusions with perturbations in the right-hand side, both of the set of the velocities (outer perturbations) and of the state (inner perturbations). The obtained estimate extends the known Filippov estimate for Lipschitz maps to SOSL ones and improves the order of approximation with respect to the inner perturbation known for one-sided Lipschitz (OSL) right-hand sides from 1/2 to 1.

Further data

Item Type: Preprint, postprint
Additional notes: accepted for publication in a special issue in the journal “Computational Optimization and Applications” in memory of Asen Dontchev

Contents:
1. Introduction
2. Preliminaries and examples
2.1 Notation
2.2 Inner and outer perturbations
2.3 Examples for SOSL/OSL set-valued maps
3. Filippov-type theorems for SOSL maps
3.1 Existence and boundednes of solutions
3.2 Filippov approximation theorem for the SOSL case
3.3 Stability and approximation results
4 Examples of differential inclusions with SOSL right-hand side
Conclusions
Keywords: differential inclusions; Filippov theorem; (strengthened) one-sided Lipschitz condition; monotonicity; set-valued Euler method; reachable sets
Subject classification: Mathematics Subject Classification Code: 47H05, 47H06, 54C60 (26E25, 34A60, 34A36, 49M25)
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)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS
Research Institutions
Research Institutions > Central research institutes
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 05 Aug 2023 21:00
Last Modified: 16 Oct 2023 05:53
URI: https://eref.uni-bayreuth.de/id/eprint/86520

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