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Control and optimization of abstract continuous time evolution inclusions

Mokhtar-Kharroubi Hocine

Control and Cybernetics

2023

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.

Integrodifferential iclusions in non separable Banach spaces

Cernea A.

Demonstratio Mathematica

2003

Vol. 36, nr 3

591--602

We consider a Cauchy problem for a nonlinear integrodifferential inclusion in non separable Banach spaces under Filippov type assumptions and we prove the existence of solutions. This result allows to obtain a relaxation theorem for the problem considered.

Controllability of nonlinear integrodifferential inclusions in Banach spaces with nonlocal conditions

Benchohra M., Ntouyas S. K.

Fasciculi Mathematici

2001

Nr 31

5-22

In this paper, we shall establish sufficient conditions for the controllability of semilinear integrodifferential inclusions in Banach spaces, with nonlocal conditions. We shall rely of a fixed point theorem for condensing maps due to Martelli.