Maximum principle for optimal boundary control of vibrating structures with applications to beams
type: Item
instance of: scholarly article
title: Maximum principle for optimal boundary control of vibrating structures with applications to beams
zbMATH Open document ID: 0939.49015
DOI: 10.1023/A:1008208727964
author: J. M. Sloss
author: J. C. jun. Bruch
author: Ibrahim Sadek
author: S. Adali
published in: Dynamics and Control
publication date: 1999-06-13T00:00:00Z
review text: The paper considers the optimal boundary control of a transversely vibrating beam. The state equation is of the form \[ w_{tt}+ L_1\Biggl(x, {\partial\over\partial x}\Biggr)[w_t]+ L_2\Biggl(x, {\partial\over\partial x}\Biggr)[w]= 0,\quad (x,t)\in(0, T)\times (0,1), \] with fourth-order differential operators \(L_1\) and \(L_2\), and with a general linear boundary condition. The necessary optimality conditions in the form of the maximum principle are obtained for a quadratic cost functional. A method of solution of the problem, based on the expansions in series of the eigenfunctions of the operators \(L_2\) (for the case \(L_1\equiv 0\)), is proposed and some numerical results are presented.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 1236229
zbMATH Keywords: optimal boundary control
zbMATH Keywords: vibrating beam
zbMATH Keywords: necessary optimality conditions
zbMATH Keywords: maximum principle
reviewed by: Uldis Raitums
MaRDI profile type: Publication
full work available at URL: a:1008208727964
OpenAlex ID: W47244192
description: scientific article; zbMATH DE number 1236229