Control and optimization of abstract continuous time evolution inclusions

Hocine Mokhtar-Kharroubi

doi:10.2478/candc-2023-0030

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Control and optimization of abstract continuous time evolution inclusions

Control and Cybernetics

Volume 52 (2023): Issue 1 (March 2023)

By: Hocine Mokhtar-Kharroubi

Open Access

|Feb 2024

Abstract

Abstract controlled evolution inclusions are revisited in the Banach spaces setting. The existence of solution is established for each selected control. Then, the input–output (or, control-states) multimap is examined and the Lipschitz continuous well posedness is derived. The optimal control of such inclusions handled in terms of a Bolza problem is investigated by means of the so-called P_ℱ format of optimization. A strong duality is provided, the existence of an optimal pair is given and the system of optimalty is derived. A Fenchel duality is built and applied to optimal control of convex process of evolution. Finally, it will be shown how the general theory we provided can be applied to a wide class of controled integrodifferental inclusions.

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Articles in this issue

DOI: https://doi.org/10.2478/candc-2023-0030 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569

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Language: English

Page range: 5 - 34

Submitted on: Apr 1, 2022

Accepted on: Mar 1, 2023

Published on: Feb 24, 2024

Published by: Systems Research Institute Polish Academy of Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

system of optimality,

Fenchel duality,

convex process of evolution,

integro-differential inclusions

Related subjects:

Computer sciences,

Computer sciences, other,

Engineering,

Electrical engineering,

Fundamentals of electrical engineering,

Mechanical engineering,

Fundamentals of mechanical engineering,

Mathematics,

General mathematics

© 2024 Hocine Mokhtar-Kharroubi, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 52 (2023): Issue 1 (March 2023)