Modeling freeway network by using dynamic graph hybrid automata and estimating its states by designing state observer

Chen, Yangzhou; Guo, Yuqi; Wang, Ying; Li, Wei

doi:10.1109/cac.2015.7382503

Cited by 7 publications

(13 citation statements)

References 30 publications

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“…An early version of the model was given in references [19,20,21]. In what follows, we restate it in the way of parallel composition of hybrid automata.…”

Section: Preliminariesmentioning

confidence: 99%

“…We apply the proposed model and state observer to the outer ring freeway. According to consistency rule of cells [21], the outer ring freeway can be partitioned into 128 cells. As shown in Section 3, if a centralized Equation (15) is used for the freeway with 128 cells, there exist

8.44342 \times 10^{48}

combination modes, which results in high computational complexity.…”

Section: Application To Beijing Third Ring Freewaymentioning

confidence: 99%

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

Chen

Guo

Wang

2017

Sensors

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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.

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“…An early version of the model was given in references [19,20,21]. In what follows, we restate it in the way of parallel composition of hybrid automata.…”

Section: Preliminariesmentioning

confidence: 99%

8.44342 \times 10^{48}

combination modes, which results in high computational complexity.…”

Section: Application To Beijing Third Ring Freewaymentioning

confidence: 99%

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

Chen

Guo

Wang

2017

Sensors

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“…The outer ring is approximately 33 km long and includes 37 on-ramps and 53 off-ramps. According to the homogeneous rule of cell division [8], the outer ring freeway can be divided into 100 cells, and the whole road network was partitioned into 4 sections. Each one can be seen as one subsystem which contains 25 cells, and the cell lengths are listed in Appendix A.…”

Section: Data Collection and Parameter Settingsmentioning

confidence: 99%

“…Canudas-de-Wit et al [6] proposed the graph constrained-CTM observer and applied it to reconstruct the densities of the Grenoble south ring, and in [7] they further introduced a robust mode selector for the uncertain graph constrained switching mode model and applied it to highway traffic densities estimation via a switched state observer. Chen and Guo et al [8,9] deduced a piecewise affine linear system (PWALS) by combining the cell transmission model (CTM) with the dynamic graph hybrid automata (DGHA), and then based on the model designed switched state observer to estimate traffic densities. In addition, Wang and Papageorgiou [10] proposed a general stochastic macroscopic traffic flow model of freeway stretches, and based on this model the extended Kalman filter was designed to estimate traffic state in freeway stretches.…”

Section: Introductionmentioning

confidence: 99%

Decentralized State-Observer-Based Traffic Density Estimation of Large-Scale Urban Freeway Network by Dynamic Model

2017

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In order to estimate traffic densities in a large-scale urban freeway network in an accurate and timely fashion when traffic sensors do not cover the freeway network completely and thus only local measurement data can be utilized, this paper proposes a decentralized state observer approach based on a macroscopic traffic flow model. Firstly, by using the well-known cell transmission model (CTM), the urban freeway network is modeled in the way of distributed systems. Secondly, based on the model, a decentralized observer is designed. With the help of the Lyapunov function and S-procedure theory, the observer gains are computed by using linear matrix inequality (LMI) technique. So, the traffic densities of the whole road network can be estimated by the designed observer. Finally, this method is applied to the outer ring of the Beijing's second ring road and experimental results demonstrate the effectiveness and applicability of the proposed approach.

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“…Chen et al proposed a dynamic graph hybrid automata modeling framework [7,8] by combining the dynamic graph [9] with the hybrid automata theory [10,11] and deduced the piecewise affine system model (PWASM) of the traffic network [12]. Based on the PWASM, a series of switched state observers [13,14,15,16,17] and Kalman filters [18] were studied to solve the issues of traffic density estimation and congestion identification for traffic networks of any size and with any topology structures.…”

Section: Introductionmentioning

confidence: 99%

A New Switched State Jump Observer for Traffic Density Estimation in Expressways Based on Hybrid-Dynamic-Traffic-Network-Model

Zha

Guo

et al. 2019

Sensors

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When faced with problems such as traffic state estimation, state prediction, and congestion identification for the expressway network, a novel switched observer design strategy with jump states is required to reconstruct the traffic scene more realistically. In this study, the expressway network is firstly modeled as the special discrete switched system, which is called the piecewise affine system model, a partition of state subspace is introduced, and the convex polytopes are utilized to describe the combination modes of cells. Secondly, based on the hybrid dynamic traffic network model, the corresponding switched observer (including state jumps) is designed. Furthermore, by applying multiple Lyapunov functions and S-procedure theory, the observer design problem can be converted into the existence issue of the solutions to the linear matrix inequality. As a result, a set of gain matrices can be obtained. The estimated states start to jump when the mode changes occur, and the updated value of the estimated state mainly depends on the estimated and the measured values at the previous time. Lastly, the designed state jump observer is applied to the Beijing Jingkai expressway, and the superiority and the feasibility are demonstrated in the application results.

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Modeling freeway network by using dynamic graph hybrid automata and estimating its states by designing state observer

Cited by 7 publications

References 30 publications

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

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

Decentralized State-Observer-Based Traffic Density Estimation of Large-Scale Urban Freeway Network by Dynamic Model

A New Switched State Jump Observer for Traffic Density Estimation in Expressways Based on Hybrid-Dynamic-Traffic-Network-Model

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