Consensus Problems with Distributed Delays, with Application to Traffic Flow Models

This paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics. In the application problems the distributed delay, whose kernel is a γ-distribution with a gap, represents the human drivers' behavior in the ave...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2009-01, Vol.48 (1), p.77-101
Main Authors: Michiels, Wim, Morarescu, Constantin-Irinel, Niculescu, Silviu-Iulian
Format: Article
Language:English
Subjects:
Automatic Control Engineering
Byproducts
Computer Science
Delay
Distributed processing
Drivers
Dynamical systems
Kernels
Linear equations
Linear systems
Mathematical models
Studies
Traffic flow
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Summary:This paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics. In the application problems the distributed delay, whose kernel is a γ-distribution with a gap, represents the human drivers' behavior in the average. The aim of the paper is to give a characterization of the regions in the corresponding delay parameter space, where a consensus is reached for all initial conditions. The structure and properties of the system are fully exploited, which leads to explicit and computationally tractable expressions. As a by-product a stability theory for distributed delay systems with a γ-distribution kernel is developed. Also explicit expressions for the consensus function(al) of time-delay systems with constant and distributed delays that solve a consensus problem are provided. Several illustrative examples complete the presentation. [PUBLICATION ABSTRACT]
ISSN:0363-0129
1095-7138
DOI:10.1137/060671425