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Relaxation of an optimal control problem involving a perturbed sweeping process |
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| Authors: | J.F. Edmond L. Thibault |
| Affiliation: | (1) Département Scientifique Interfacultaire, Campus de Schoelcher, Université des Antilles et de la Guyane, B. P. 7209, 97275 Schoelcher cedex, Martinique, France;(2) Département de Mathématiques, Université Montpellier II, Case Courrier 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France |
| Abstract: | We establish first, in the setting of infinite dimensional Hilbert space, a result concerning the existence of solutions for perturbed sweeping processes whose perturbations are Lipschitz single-valued maps. Then we use this result to extend to the infinite dimensional setting a relaxation result concerning optimal control problems involving such processes. Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday |
| Keywords: | Sweeping process Perturbation Prox-regular set Normal cone Optimal control Relaxation Young measure Set-valued map |
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