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Bifurcation control of optimal velocity model through anticipated effect and response time-delay feedback methods

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  • Guan, Xueyi
  • Cheng, Rongjun
  • Ge, Hongxia

Abstract

In order to further improve the adaptability of the optimal velocity model (OVM) in actual traffic flow, the paper introduces a feedback control with considering both driver’s anticipated time and response time-delay. Through the linear analysis and bifurcation analysis, we obtain stability conditions and the balance point of dual time-delay control OVM. Aiming at restraining the Hopf bifurcation caused by small disturbance, a bifurcated controller is designed to reduce the number of unstable eigenvalues of the characteristic equation and determine the definite stability interval under the combination of anticipation and response time-delay. Then followed by the simulated verification for more vehicles, the simulation results show that the controller can effectively suppress traffic congestion without changing the balance point, and significantly improve traffic efficiency and traffic stability. In addition, utilizing NGSIM data to calibrate the controlled model so as to explore the feasibility and advantages of the model.

Suggested Citation

  • Guan, Xueyi & Cheng, Rongjun & Ge, Hongxia, 2021. "Bifurcation control of optimal velocity model through anticipated effect and response time-delay feedback methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    • Handle: RePEc:eee:phsmap:v:574:y:2021:i:c:s0378437121002442
    DOI: 10.1016/j.physa.2021.125972
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    References listed on IDEAS

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    1. Zhang, Yicai & Xue, Yu & Zhang, Peng & Fan, Deli & di He, Hong, 2019. "Bifurcation analysis of traffic flow through an improved car-following model considering the time-delayed velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 133-140.
    2. Sun, Yuqing & Ge, Hongxia & Cheng, Rongjun, 2019. "An extended car-following model considering driver’s memory and average speed of preceding vehicles with control strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 752-761.
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    6. Jin, Sheng & Wang, Dian-Hai & Huang, Zhi-Yi & Tao, Peng-Fei, 2011. "Visual angle model for car-following theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1931-1940.
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    Cited by:

    1. He, Haoming & Xiao, Min & Lu, Yunxiang & Wang, Zhen & Tao, Binbin, 2023. "Control of tipping in a small-world network model via a novel dynamic delayed feedback scheme," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Lixia Duan & Shuangshuang Fan & Danyang Liu & Zhonghe He, 2022. "Two-parameter bifurcation and energy consumption analysis of the macro traffic flow model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(12), pages 1-12, December.

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