On a control dynamical system with maximal monotone operators

Document Type : Original Article

Authors

Nadjiba Abdi ¹

Soumia Saidi ²

¹ LAOTI Laboratory, Faculty of Exact Sciences and Informatics, University of Jijel, 18000 Jijel, Algeria

² LMPA Laboratory, Faculty of Exact Sciences and Informatics, University of Jijel, 18000 Jijel, Algeria

10.22034/kjm.2024.410433.2953

Abstract

This paper studies a minimizing problem subject to a control dynamical system involving two differential inclusions driven by maximal monotone operators and an integral perturbation. First, an existence result, for a mixed partially bounded variation continuous differential system, is obtained via a discretization scheme (in the context of Hilbert spaces). The latter permits us to deduce the well-posedness of the control dynamical system under consideration. Finally, under suitable assumptions on the sets of control maps acting in both the state of the operators and the time-variables of the perturbations, the optimality result is proved.

Keywords

Dynamical system

differential inclusion

maximal monotone operator

integral perturbation

optimal solution

Subjects

• 34 Ordinary differential equations

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