Open dynamical systems and their control
type: Item
instance of: scholarly article
title: Open dynamical systems and their control
zbMATH Open document ID: 0915.93004
published in: Documenta Mathematica
publication date: 1998-08-06T00:00:00Z
full work available at URL: https://eudml.org/doc/233073
full work available at URL: Willems.MAN.html
review text: The behavioral approach is followed in this paper and some of the main features of the theory of open dynamical systems are described. Linear time-invariant differential systems receive special attention. Object-oriented mathematical modelling of complex systems leads to a model that relates the variables whose dynamic relation one wants to model (called manifest variables) to auxiliary variables (called latent variables) that have been introduced in the modelling process. By using kernel representations, the manifest behavior and latent variable representations in the linear time-invariant case, the elimination theorem is proved. This theorem means that the latent variables may be eliminated and that the number of equations can be reduced to no more than the number of manifest variables. Again for linear time-invariant differential systems, various equivalences for controllability are proved, anwering questions such as: ''What conditions on the parameters of a system representation imply controllability?'' and ''Do controllable systems admit a particular representation in which controllability becomes apparent?''. The theory of observability, running parallel to that of controllability, is only briefly touched upon in the paper. The paper ends with a discussion of control, which is viewed as system interconnection.
Mathematics Subject Classification ID: 93A30
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 1184406
zbMATH Keywords: open dynamical systems
zbMATH Keywords: control
zbMATH Keywords: behavioral approach
zbMATH Keywords: linear time-invariant differential systems
zbMATH Keywords: kernel representations
zbMATH Keywords: latent variable
zbMATH Keywords: elimination theorem
zbMATH Keywords: controllability
author: Jan C. Willems
reviewed by: Frieda Theron
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184406