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This paper investigates a regional optimal control problem of a plate equation described by a bilinear system evolving in a spacial domain Ω. The control is distributed, bounded and acts on the velocity term. Then, we minimise a functional cost constituted of the deviation between a desired state and the reached one only on a subregion  ω  of Ω and the energy term. The purpose of this study is to prove that a control solution of such problem exists, and characterised as a solution to an optimality system. Numerical approach is given and successfully illustrated by simulations.

Constrained regional control problem of a bilinear plate equation