Linear programming based routing design for a class of positive systems with integral and capacity constraints

Heather Arneson, Cédric Langbort

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present techniques to design routing parameters for positive compartmental conservative systems. Such systems capture the dynamics of some material owing through a network of interconnected reservoirs and have become popular, in particular, as models of air traffic fows. These techniques use Linear Programs (LP) to design static routing parameters for single destination networks with the following objectives: (a) minimize delay, (b) minimize delay and satisfy additional delay constraints which are formulated as integral constraints on the states of the network, and (c) satisfy capacity constraints. For each of these problems, we prove that the resulting closed loop systems are stable, positive, conservative and exhibit a user defined interconnection of sections. Additionally, problems (a) and (b) are shown to minimize delay over all choices of routing parameters such that the closed loop system exhibits these characteristics.

Original languageEnglish (US)
Title of host publication1st IFAC Workshop on Estimation and Control of Networked Systems, NecSys'09
Pages352-357
Number of pages6
EditionPART 1
DOIs
StatePublished - 2009
Event1st IFAC Workshop on Estimation and Control of Networked Systems, NecSys'09 - Venice, Italy
Duration: Sep 24 2009Sep 26 2009

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
Volume1
ISSN (Print)1474-6670

Other

Other1st IFAC Workshop on Estimation and Control of Networked Systems, NecSys'09
Country/TerritoryItaly
CityVenice
Period9/24/099/26/09

Keywords

  • Air traffic ow management
  • Capacity constraints
  • Linear programming
  • Network routing design
  • Positive systems

ASJC Scopus subject areas

  • Control and Systems Engineering

Fingerprint

Dive into the research topics of 'Linear programming based routing design for a class of positive systems with integral and capacity constraints'. Together they form a unique fingerprint.

Cite this