<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <italic>P</italic><sub>ℱ</sub> 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.</p>
</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 Pℱ 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.

Control and optimization of abstract continuous time evolution inclusions

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Control and optimization of abstract continuous time evolution inclusions"}

Abstract controlled evolution inclusions are revisited in the Banach spaces setting. The existence of solution is established for each selected control. Then,...

Control and optimization of abstract continuous time evolution inclusions

Published Online: Feb 24, 2024

Page range: 5 - 34

Received: Apr 01, 2022

Accepted: Mar 01, 2023

DOI: https://doi.org/10.2478/candc-2023-0030

Keywords
evolution inclusion, well posedness, optimal control, strong duality, system of optimality, Fenchel duality, convex process of evolution, integro-differential inclusions

© 2023 Hocine Mokhtar-Kharroubi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Control and optimization of abstract continuous time evolution inclusions

Published Online: Feb 24, 2024

Page range: 5 - 34

Received: Apr 01, 2022

Accepted: Mar 01, 2023

DOI: https://doi.org/10.2478/candc-2023-0030

Keywordsevolution inclusion, well posedness, optimal control, strong duality, system of optimality, Fenchel duality, convex process of evolution, integro-differential inclusions

© 2023 Hocine Mokhtar-Kharroubi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
evolution inclusion, well posedness, optimal control, strong duality, system of optimality, Fenchel duality, convex process of evolution, integro-differential inclusions