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2 Control and Cybernetics

2 Mokhtar-Kharroubi H.

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Control and optimization of abstract continuous time evolution inclusions

100%

Mokhtar-Kharroubi H.

tom Vol. 52, No. 1

5--34

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.

Characterizations and classification of paraconvex multimaps

100%

Mokhtar-Kharroubi H.

2022

tom Vol. 51, No. 3

303--325

Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on generalized convexities and monotonicities. Several characterizations are then obtained. The links with some generalized convexities for multimaps are examined and a first classification is achieved. In addition, two representation results for 2-paraconvex multimaps are given.