at Google ScholarTitle data
Baier, Robert ; Farkhi, Elza:
A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions.
In: Computational Optimization and Applications.
Vol. 86
(2023)
.
- pp. 885-923.
ISSN 0926-6003
DOI: https://doi.org/10.1007/s10589-023-00517-9
This is the latest version of this item.
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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 approximation 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 of the distance between the approximate and exact solution 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: | Article in a journal |
|---|---|
| Refereed: | Yes |
| Additional notes: | special issue in memory of Asen Dontchev (Open Access)
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 boundedness 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: | 25 Oct 2023 08:41 |
| Last Modified: | 27 Jun 2024 12:36 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/87380 |
Available Versions of this Item
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A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions. (deposited 05 Aug 2023 21:00)
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A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions. (deposited 12 Oct 2023 09:07)
- A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions. (deposited 25 Oct 2023 08:41) [Currently Displayed]
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A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions. (deposited 12 Oct 2023 09:07)