GALERKIN-LIKE METHOD AND GENERALIZED PERTURBED SWEEPING PROCESS WITH NONREGULAR SETS
Affiliation auteurs | !!!! Error affiliation !!!! |
Titre | GALERKIN-LIKE METHOD AND GENERALIZED PERTURBED SWEEPING PROCESS WITH NONREGULAR SETS |
Type de publication | Journal Article |
Year of Publication | 2017 |
Auteurs | Jourani A, Vilches E |
Journal | SIAM JOURNAL ON CONTROL AND OPTIMIZATION |
Volume | 55 |
Pagination | 2412-2436 |
Type of Article | Article |
ISSN | 0363-0129 |
Mots-clés | differential inclusions, normal cone, Positively alpha-far sets, second-order sweeping process, Subsmooth sets, Sweeping process |
Résumé | In this paper we present a new method to solve differential inclusions in Hilbert spaces. This method is a Galerkin-like method where we approach the original problem by projecting the state into a n-dimensional Hilbert space but not the velocity. We prove that the approached problem always has a solution and that, under some compactness conditions, the approached problems have a subsequence which converges strongly pointwisely to a solution of the original differential inclusion. We apply this method to the generalized perturbed sweeping process governed by nonregular sets (equi-uniformly subsmooth or positively alpha-far). This differential inclusion includes Moreau's sweeping process, the state-dependent sweeping process, and second-order sweeping process for which we give very general existence results. |
DOI | 10.1137/16M1078288 |