Aggregation of a class of large-scale, interconnected, nonlinear dynamical systems
type: Item
instance of: scholarly article
title: Aggregation of a class of large-scale, interconnected, nonlinear dynamical systems
zbMATH Open document ID: 1008.93007
DOI: 10.1155/S1024123X01001697
author: S. Darbha
author: K. R. Rajagopal
published in: Mathematical Problems in Engineering
publication date: 2003-04-06T00:00:00Z
full work available at URL: https://eudml.org/doc/49883
review text: Given, in general, a countable collection of large-scale, interconnected nonlinear dynamical systems, the aim of this paper is the construction of a ``meaningful'' average in terms of a function \(w(t)\) whose evolution is proved to be described by a ``reduced order'' differential equation. In this respect, a statement of the problem along with auxiliary results are presented in Section 2, so that the main results are then shown in Section 3. More precisely, given the string of equations, \[ \dot X(i)= f\bigl( X(i), X(i-1),\dots, X(i-r+1), u(t)\bigr);\;X(j)(t)= X(1)(t),\;j\leq 1; \;i=1,2, \dots, \] a function \(w(t)\) is a ``meaningful'' average for the given collection of interconnected systems if and only if it satisfies the differential equation \[ \dot w=f(w,w, \dots,w,u) \] provided \(f\) satisfies certain appropriate conditions. Finally, some concluding remarks are also given in Section 4.
Mathematics Subject Classification ID: 93A15
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 1790999
zbMATH Keywords: aggregation
zbMATH Keywords: string stability
zbMATH Keywords: average dynamical system
zbMATH Keywords: reduced order differential equation
zbMATH Keywords: large-scale, interconnected nonlinear dynamical systems
reviewed by: Pablo González-Vera
MaRDI profile type: Publication
OpenAlex ID: W2069452175
description: scientific article; zbMATH DE number 1790999