Stability and Convergence of Euler's Method for State-Constrained Differential Inclusions

R. Baier, I.A.Chahma, F. Lempio: Stability and Convergence of Euler's Method for State-Constrained Differential Inclusions
SIAM Journal on Optimization 18 (3; special issue on ``Variational Analysis and Optimization''), 1004 - 1026, 2007

DOI: 10.1137/060661867
MR Nummer: 2345981
Zentralblattnummer: 1262.34021
Keywords: Filippov theorem; set-valued Euler's method; differential inclusions with state constraints; stability and convergence of discrete approximations
Mathematics Subject Classification Code: 49J24 (65L20 34K28 34A60)
Download as PDF


Abstract:

A discrete stability theorem for set-valued Euler's method with state constraints is proved. This theorem is combined with known stability results for differential inclusions withso-called smooth state constraints. As a consequence, order of convergence equal to 1 is proved for set-valued Euler's method, applied to state-constrained differential inclusions.

Contents:

1. Introduction and preliminaries
2. Stability for the unconstrained case
3. Stability analysis for the state-constrained case
4. Convergence analysis
5. Example

Chair -

|  University of Bayreuth -