URN to cite this document: urn:nbn:de:bvb:703epub71606
Title data
Baier, Robert ; Farkhi, Elza:
A Filippov Approximation Theorem for Strengthened OneSided Lipschitz Differential Inclusions.
Mathematisches Institut, Universität Bayreuth, School of Mathematical Sciences, Tel Aviv University
Bayreuth; Tel Aviv
,
2023
.  31 S.


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

Abstract
We consider differential inclusions with strengthened onesided Lipschitz (SOSL) righthand sides. The class of SOSL multivalued maps is wider than the class of Lipschitz ones and a subclass of the class of onesided Lipschitz maps. We prove a Filippov stability theorem for the solutions of such differential inclusions with perturbations in the righthand 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 onesided Lipschitz (OSL) righthand sides from 1/2 to 1.
Further data
Item Type:  Preprint, postprint 

Additional notes (visible to public):  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 setvalued maps 3. Filippovtype 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 righthand side Conclusions 
Keywords:  differential inclusions; Filippov theorem; (strengthened) onesided Lipschitz condition; monotonicity; setvalued Euler method; reachable sets 
Subject classification:  Mathematics Subject Classification Code: 47H05, 47H06, 54C60 (26E25, 34A60, 34A36, 49M25) 
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) 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 
Language:  English 
Originates at UBT:  Yes 
URN:  urn:nbn:de:bvb:703epub71606 
Date Deposited:  31 Jul 2023 07:17 
Last Modified:  31 Jul 2023 07:19 
URI:  https://epub.unibayreuth.de/id/eprint/7160 
Available Versions of this Item
 A Filippov Approximation Theorem for Strengthened OneSided Lipschitz Differential Inclusions. (deposited 31 Jul 2023 07:17) [Currently Displayed]