Consensus Problems with Distributed Delays, with Application to Traffic Flow Models
Consensus Problems with Distributed Delays, with Application to Traffic Flow Models
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DOI：
10.1137/060671425
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发表时间：
2009-02
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影响因子：
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通讯作者：
W. Michiels;I. Morǎrescu;S. Niculescu
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文献类型：
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作者：
W. Michiels;I. Morǎrescu;S. Niculescu
研究了交通流动力学建模中遇到的一类具有分布时滞的线性系统的一致性问题。在应用问题中，分布延迟，其核心是一个$\gamma$-分布的差距，代表人类驾驶员的行为的平均值。本文的目的是在相应的延迟参数空间，其中达成共识的所有初始条件的区域的特征。系统的结构和属性被充分利用，这导致明确的和计算上易于处理的表达式。作为一个副产品的分布延迟系统的稳定性理论与$\gamma$分布核。还提供了解决一致性问题的常时滞和分布时滞时滞系统的一致性函数（al）的显式表达式。几个说明性的例子完成介绍。
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 $\gamma$-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 $\gamma$-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.