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Relaxation of an optimal control problem involving a perturbed sweeping process

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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.

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Authors and Affiliations

  1. Département Scientifique Interfacultaire, Campus de Schoelcher, Université des Antilles et de la Guyane, B. P. 7209, 97275, Schoelcher cedex, Martinique, France

    J.F. Edmond

  2. Département de Mathématiques, Université Montpellier II, Case Courrier 051, Place Eugène Bataillon, 34095, Montpellier Cedex 5, France

    L. Thibault

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  1. J.F. Edmond
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  2. L. Thibault
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Correspondence to L. Thibault.

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Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday

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Edmond, J., Thibault, L. Relaxation of an optimal control problem involving a perturbed sweeping process. Math. Program. 104, 347–373 (2005). https://doi.org/10.1007/s10107-005-0619-y

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  • DOI: https://doi.org/10.1007/s10107-005-0619-y

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