A linear programming approach to routing control in networks of constrained linear positive systems

Heather Arneson; Cédric Langbort

doi:10.1016/j.automatica.2012.02.001

A linear programming approach to routing control in networks of constrained linear positive systems

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Abstract

We study routing control in dynamic continuous-time networks in which each node is described by a linear internally positive system. We derive a linear programming (LP) characterization of optimal constant routing policies for the infinite-horizon routing problem under weighted l ₁ constraints and objective. For finite horizon problems with piecewise constant state constraints, we provide sufficient feasibility conditions, which also take the form of an LP problem. We illustrate the solution for the finite horizon problem in an application example.

Original language	English (US)
Pages (from-to)	800-807
Number of pages	8
Journal	Automatica
Volume	48
Issue number	5
DOIs	https://doi.org/10.1016/j.automatica.2012.02.001
State	Published - May 2012

Keywords

Control of networks
Controller constraints and structure
Linear programming
Positive systems

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

Online availability

10.1016/j.automatica.2012.02.001

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title = "A linear programming approach to routing control in networks of constrained linear positive systems",

abstract = "We study routing control in dynamic continuous-time networks in which each node is described by a linear internally positive system. We derive a linear programming (LP) characterization of optimal constant routing policies for the infinite-horizon routing problem under weighted l 1 constraints and objective. For finite horizon problems with piecewise constant state constraints, we provide sufficient feasibility conditions, which also take the form of an LP problem. We illustrate the solution for the finite horizon problem in an application example.",

keywords = "Control of networks, Controller constraints and structure, Linear programming, Positive systems",

author = "Heather Arneson and C{\'e}dric Langbort",

note = "Funding Information: This work was funded in part by a NASA Illinois Space Grant Consortium seed grant and NSF grant #0826469 to C. Langbort, and University of Illinois College of Engineering SURGE Fellowship , and NASA Aeronautics Scholarship Program Fellowship to H. Arneson. The material in this paper was partially presented at the 1st IFAC Workshop on Estimation and Control of Networked Systems, September 24–26, 2009, Venice, Italy and the IEEE American Control Conference, June 29–July 1, 2011, San Francisco, CA. This paper was recommended for publication in revised form by Associate Editor Maria Elena Valcher under the direction of Editor Roberto Tempo. ",

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AU - Langbort, Cédric

N1 - Funding Information: This work was funded in part by a NASA Illinois Space Grant Consortium seed grant and NSF grant #0826469 to C. Langbort, and University of Illinois College of Engineering SURGE Fellowship , and NASA Aeronautics Scholarship Program Fellowship to H. Arneson. The material in this paper was partially presented at the 1st IFAC Workshop on Estimation and Control of Networked Systems, September 24–26, 2009, Venice, Italy and the IEEE American Control Conference, June 29–July 1, 2011, San Francisco, CA. This paper was recommended for publication in revised form by Associate Editor Maria Elena Valcher under the direction of Editor Roberto Tempo.

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AB - We study routing control in dynamic continuous-time networks in which each node is described by a linear internally positive system. We derive a linear programming (LP) characterization of optimal constant routing policies for the infinite-horizon routing problem under weighted l 1 constraints and objective. For finite horizon problems with piecewise constant state constraints, we provide sufficient feasibility conditions, which also take the form of an LP problem. We illustrate the solution for the finite horizon problem in an application example.

KW - Control of networks

KW - Controller constraints and structure

KW - Linear programming

KW - Positive systems

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A linear programming approach to routing control in networks of constrained linear positive systems

Abstract

Keywords

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