Bilinear Boundary Optimal Control of a Kirchhoff Plate Equation

EasyChair Preprint 6255

Abstract

This work is devoted to the study of optimal control of a Kirchhoff plate equation, where the control enters the system bilinearly through the boundary such as coefficient like $hz$. The cost functional consists of the energy and the difference between the solution the system at final time, and a desired state in $L^2$-norm. For a closed convex set, we prove the existence of an optimal control that minimizes the cost functional using a priori estimates. Then, using the differentiability of the cost functional with respect of the control, we establish the characterization by deriving necessary conditions that an optimal control must satisfy.

Keyphrases: Boundary bilinear control, Kirchhoff plate equation, optimal control problem

@booklet{EasyChair:6255,
  author    = {Abdelhak Bouhamed and Abella El Kabouss and Hassane Bouzahir},
  title     = {Bilinear Boundary Optimal Control of a Kirchhoff Plate Equation},
  howpublished = {EasyChair Preprint 6255},
  year      = {EasyChair, 2021}}