Compositions of passive boundary control systems
type: Item
instance of: scholarly article
title: Compositions of passive boundary control systems
zbMATH Open document ID: 1272.47015
author: Atte Aalto
author: Jarmo Malinen
published in: Mathematical Control and Related Fields
publication date: 2013-03-21T00:00:00Z
review text: The subject of this paper is best described by an example from acoustics given by the authors. The basic entity is a graph of interconnected segments. Propagation on each edge (wave guide) is governed by the linear wave equation \[ {\partial^2 \psi \over \partial t^2} = c^2 {\partial^2 \psi \over \partial x^2} \, . \] At the vertices of the graph, there are two linear boundary conditions which involve the solution at the wave guides making up the vertex; one states the equality of \(\partial \psi / \partial t\) for all these solutions at the vertex, the other equates to zero a linear combination of \(\partial \psi / \partial x\) at the vertex. In the acoustic application in mind, \(\psi\) is a velocity potential, \(\partial \psi / \partial t\) is (a multiple of) the perturbation pressure and \(\partial \psi / \partial x\) is the perturbation velocity. The input or control \(u(t)\) is applied at a vertex where only two wave guides meet; \(u(t)\) is the common value of \(\partial \psi / \partial t.\) Finally, the output is a linear combination of \(\partial \psi / \partial x\) for the two waveguides. The objective is to show that, under adequate assumptions, the dynamical system \(u \to y\) (which is a boundary control system in a generalized sense) is well posed and conservative. The authors solve the problem by means of an operator setup that encompasses this and other examples, such as a model of the acoustics of the human vocal tract.
reviewed by: Hector O. Fattorini
Mathematics Subject Classification ID: 47A48
Mathematics Subject Classification ID: 35R02
Mathematics Subject Classification ID: 47N70
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 6147689
zbMATH Keywords: boundary control systems
zbMATH Keywords: passive systems
zbMATH Keywords: input-output systems
zbMATH Keywords: well-posedness
zbMATH Keywords: conservative systems
MaRDI profile type: Publication
full work available at URL: mcrf.2013.3.1
OpenAlex ID: W2334820552
DOI: 10.3934/MCRF.2013.3.1
description: scientific article; zbMATH DE number 6147689