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On the Discretization of Truncated Integro-Differential Sweeping Process and Optimal Control

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Abstract

We consider the Volterra integro-differential equation with a time-dependent prox-regular constraint that changes in an absolutely continuous way in time (a Volterra absolutely continuous time-dependent sweeping process). The aim of our paper is twofold. The first one is to show the solvability of the initial value problem by setting up an appropriate catching-up algorithm (full discretization). This part is a continuation of our paper (Bouach et al. in arXiv: 2102.11987. 2021) where we used a semi-discretization method. Obviously, strong solutions and convergence of full discretization scheme are desirable properties, especially for numerical simulations. Applications to non-regular electrical circuits are provided. The second aim is to establish the existence of optimal solution to an optimal control problem involving the Volterra integro-differential sweeping process.

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Authors and Affiliations

  1. Laboratoire LMPEA, Faculté des Sciences Exactes et Informatique, Université Mohammed Seddik Benyahia, Jijel, B.P. 98, 18000, Jijel, Algeria

    Abderrahim Bouach & Tahar Haddad

  2. Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, 34095, Montpellier Cedex 5, France

    Lionel Thibault

Authors
  1. Abderrahim Bouach
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  2. Tahar Haddad
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  3. Lionel Thibault
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Communicated by Boris S. Mordukhovich.

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Bouach, A., Haddad, T. & Thibault, L. On the Discretization of Truncated Integro-Differential Sweeping Process and Optimal Control. J Optim Theory Appl 193, 785–830 (2022). https://doi.org/10.1007/s10957-021-01991-z

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  • DOI: https://doi.org/10.1007/s10957-021-01991-z

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