Geodesic
Regional optimal control problem for a vibrating plate
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Optimal control, Tome 178 (2020), pp. 20-30

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In this paper, we examine the problem on the regional optimal control of a vibrating plate in a spatial domain $\Omega$. We obtain a bounded control that drives such a system from an initial state to a desired state in a finite time, only on a subdomain $\omega$ of $\Omega$. We prove that a regional optimal control exists characterize this control. Also we propose a condition that ensures the uniqueness of an optimal control and develop an algorithm for numerical simulations.
Keywords: distributed bilinear system, plate equation, regional controllability, optimal control. 
@article{INTO_2020_178_a1,
     author = {E. Zerrik and A. Ait Aadi and R. Larhrissi},
     title = {Regional optimal control problem for a vibrating plate},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {20--30},
     publisher = {mathdoc},
     volume = {178},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_178_a1/}
}
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E. Zerrik; A. Ait Aadi; R. Larhrissi. Regional optimal control problem for a vibrating plate. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Optimal control, Tome 178 (2020), pp. 20-30. http://geodesic.mathdoc.fr/item/INTO_2020_178_a1/