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Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata

机译:基于动态图混合自动机的城市高速公路网络建模与密度估计

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In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research.
机译:在本文中,为了描述复杂的网络系统,我们首先提出了一种将动态图与混合自动机相结合的通用建模框架,因此将其命名为动态图混合自动机(DGHA)。然后,我们通过将小区传输模型(CTM)嵌入到DGHA中,将该框架应用于城市高速公路网络上的交通流建模。通过建模程序,我们采用路网结构的二元图来描述道路拓扑,使用线性混合自动机来描述路段中的动态密度的多种模式,并将两路段之间传输的交通流的非线性表达式转化为在多模式切换方面的分段线性函数。该建模过程是模块化和基于规则的,因此可以借助用于交通流动态的组合算法轻松扩展。它可以描述具有任意拓扑结构和大小的城市高速公路网络上交通流的动态。接下来,我们在整个高速公路网络的模型中分析模式类型和数量,并推导分段仿射线性系统(PWAL)模型。此外,基于PWALS模型,设计了一种多模式切换状态观察器来估计高速公路网络的交通密度,其中使用李雅普诺夫函数方法来计算一组观察器增益矩阵。例如,我们利用PWALS模型和相应的切换状态观察器来控制北京三环上的交通流量。为了清楚地解释所提出方法的原理并避免计算复杂性,我们采用北京三环路的简化版本。在未来的研究中,将通过分散建模方法和分布式观测器设计来实现大规模道路网络的实际应用。

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