Optimal active pointwise control of vibrating thin plates
type: Item
instance of: scholarly article
title: Optimal active pointwise control of vibrating thin plates
zbMATH Open document ID: 0803.73051
DOI: 10.1016/S0016-0032(92)90040-N
author: Maria L. Blanton
author: Ibrahim Sadek
published in: Journal of the Franklin Institute
publication date: 1994-03-22T00:00:00Z
review text: The optimal control of thin vibrating plates is studied in the paper. The objective of the control problem is to minimize a given performance index in a prescribed time interval, where the performance index constitutes the total energy of the structure, together with the total force used in open-loop and closed-loop control processes. The orthogonality of the self-adjoint system is used to convert the problem into the optimal control problem for lumped parameter systems. In the first part of the paper, the authors formulate the mathematical control problem, reducing it to a system of integral equations. In the following parts they establish necessary and sufficient conditions for optimality by a variational approach and an algorithm for the determination of control parameters. Finally, they illustrate the effectiveness of the proposed control considering a simply supported plate.
Mathematics Subject Classification ID: 74M05
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 536924
zbMATH Keywords: performance index
zbMATH Keywords: total energy
zbMATH Keywords: total force
zbMATH Keywords: lumped parameter systems
zbMATH Keywords: system of integral equations
zbMATH Keywords: necessary and sufficient conditions for optimality
zbMATH Keywords: simply supported plate
reviewed by: Ştefan Zanfir
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 536924