Abstract
In order to alleviate unstable factor-caused bifurcation and reduce oscillations in traffic flow, a feedback control with consideration of time delay is designed for the solid angle model (SAM). The stability and bifurcation condition of the new SAM is derived through linear analysis and bifurcation analysis, and then accurate range of stable region is obtained. In order to explore the mechanism of the influence of multiple parameter combinations on the stability of controlled systems, a definite integral stabilization method is provided to determine the stable interval of time delay and feedback gain. Numerical simulations are explored to verify the feasibility and effectiveness of the proposed model, which also demonstrate that feedback gain and delay are two key factors to alleviate traffic congestion in the SAM.
摘要
目的
随着城市化进程的不断发展,交通事故和交通拥堵越来越成为城市发展的障碍。本文旨在设计一种响应延迟反馈控制来抑制不稳定因素引起的分岔,从而抑制交通流量振荡并提高模型对车辆轨迹的拟合程度。
创新点
1. 采用定积分方法来确定反应延迟和反馈增益的稳定区间;2. 设计一种抑制交通拥堵和稳定交通流量的控制策略。
方法
1. 通过对线性分析和分岔分析的比较,确定稳定区的临界范围;2. 运用定积分的方法模拟各参数联合控制下的精确和稳定范围;3. 通过校准得到的最优反馈增益和时滞参数位于控制系统的稳定区域,从而验证该控制系统的合理性和可行性。
结论
1. 本文设计的响应延迟反馈控制系统可以用来抑制或削弱交通系统的分岔,从而抑制交通拥堵;2. 校准得到的最优反馈增益和时滞参数位于控制系统的稳定区域;3. 合理的反馈增益和延迟设置可以有效地提高交通流量的稳定性。
This is a preview of subscription content, log in via an institution to check access.
References
Andersen GJ, Sauer CW, 2007. Optical information for car following: the driving by Visual Angle (DVA) model. Human Factors: The Journal of the Human Factors and Ergonomics Society, 49(5):878–896. https://doi.org/10.1518/001872007X230235
Bando M, Hasebe K, Nakayama A, et al., 1995. Dynamical model of traffic congestion and numerical simulation. Physical Review E, 51(2):1035–1042. https://doi.org/10.1103/PhysRevE.51.1035
Bando M, Hasebe K, Nakanishi K, et al., 1998. Analysis of optimal velocity model with explicit delay. Physical Review E, 58(5):5429–5435. https://doi.org/10.1103/PhysRevE.58.5429
Cheng RJ, Liu FX, Ge HX, 2017. A new continuum model based on full velocity difference model considering traffic jerk effect. Nonlinear Dynamics, 89(1):639–649. https://doi.org/10.1007/s11071-017-3477-2
Das S, Maurya AK, 2022. A car-following model considering driver’ s instantaneous reaction delay in nonlane-based traffic environments. Journal of Transportation Engineering, Part A: Systems, 148(8):1–13. https://doi.org/10.1061/JTEPBS.0000709
Fang YL, Shi ZK, Cao JL, 2015. Congestion phenomenon analysis and delayed-feedback control in a modified coupled map traffic flow model containing the velocity difference. Communications in Nonlinear Science and Numerical Simulation, 23(1–3): 175–184. https://doi.org/10.1016/j.cnsns.2014.11.007
Ge HX, Zheng PJ, Lo SM, et al., 2014. TDGL equation in lattice hydrodynamic model considering driver’s physical delay. Nonlinear Dynamics, 76(1):441–445. https://doi.org/10.1007/s11071-013-1137-8
Geroliminis N, Karlaftis MG, Skabardonis A, 2009. A spatial queuing model for the emergency vehicle districting and location problem. Transportation Research Part B: Methodological, 43(7):798–811. https://doi.org/10.1016/j.trb.2009.01.006
Guan XY, Cheng RJ, Ge HX, 2022. Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior. Chinese Physics B, 31:070507. https://doi.org/10.1088/1674-1056/ac5606
Helbing D, Treiber M, 1998. Gas-kinetic-based traffic model explaining observed hysteretic phase transition. Physical Review Letters, 81(14):3042–3045. https://doi.org/10.1103/PhysRevLett.81.3042
Helbing D, Tilch B, 1998. Generalized force model of traffic dynamics. Physical Review E, 58(1): 133–138. https://doi.org/10.1103/PhysRevE.58.133
Herman R, Montroll EW, Potts RB, et al., 1959. Traffic dynamics: analysis of stability in car following. Operations Research, 7(1):86–106. https://doi.org/10.1287/opre.7.1.86
Jiang N, Yu B, Cao F, et al., 2021. An extended visual angle car-following model considering the vehicle types in the adjacent lane. Physica A: Statistical Mechanics and Its Applications, 566:125665. https://doi.org/10.1016/j.physa.2020.125665
Jiang R, Wu QS, Zhu ZJ, 2001. Full velocity difference model for a car-following theory. Physical Review E, 64(1):017101. https://doi.org/10.1103/PhysRevE.64.017101
Jin S, Wang DH, Huang ZY, et al., 2011. Visual angle model for car-following theory. Physica A: Statistical Mechanics and Its Applications, 390(11): 1931–1940. https://doi.org/10.1016/j.physa.2011.01.012
Jin YF, Xu M, 2016. Stability analysis in a car-following model with reaction-time delay and delayed feedback control. Physica A: Statistical Mechanics and Its Applications, 459: 107–116. https://doi.org/10.1016/j.physa.2016.04.038
Kong DW, Sun LS, Li J, et al., 2021. Modeling cars and trucks in the heterogeneous traffic based on car-truck combination effect using cellular automata. Physica A: Statistical Mechanics and Its Applications, 562:125329. https://doi.org/10.1016/j.physa.2020.125329
Konishi K, Hirai M, Kokame H, 1998. Decentralized delayed-feedback control of a coupled map model for open flow. Physical Review E, 58(3):3055–3059. https://doi.org/10.1103/PHYSREVE.58.3055
Konishi K, Kokame H, Hirata K, 1999. Coupled map car-following model and its delayed-feedback control. Physical Review E, 60(4):4000–4007. https://doi.org/10.1103/PhysRevE.60.4000
Konishi K, Kokame H, Hirata K, 2000. Decentralized delayed-feedback control of an optimal velocity traffic model. The European Physical Journal B-Condensed Matter and Complex Systems, 15(4):715–722. https://doi.org/10.1007/s100510051176
Ma DF, Han YY, Jin S, 2020. Solid angle car following model. Chinese Physics B, 29(6):060504. https://doi.org/10.1088/1674-1056/ab862c
Michaels RM, Cozan LW, 1963. Perceptual and field factors causing lateral displacement. Highway Research Record, 25:1–13.
Milanés V, Shladover SE, 2014. Modeling cooperative and autonomous adaptive cruise control dynamic responses using experimental data. Transportation Research Part C: Emerging Technologies, 48:285–300. https://doi.org/10.1016/j.trc.2014.09.001
Ngoduy D, Li TL, 2021. Hopf bifurcation structure of a generic car-following model with multiple time delays. Transportmetrica A: Transport Science, 17(4):878–896. https://doi.org/10.1080/23249935.2020.1818002
Ossen S, Hoogendoorn SP, Gorte BGH, 2006. Interdriver differences in car-following: a vehicle trajectory-based study. Transportation Research Record, 1965(1):121–129. https://doi.org/10.1177/0361198106196500113
Sun J, Zheng ZD, Sun J, 2018. Stability analysis methods and their applicability to car-following models in conventional and connected environments. Transportation Research Part B: Methodological, 109:212–237. https://doi.org/10.1016/j.trb.2018.01.013
Treiber M, Kesting A, Helbing D, 2006. Delays, inaccuracies and anticipation in microscopic traffic models. Physica A: Statistical Mechanics and Its Applications, 360(1):71–88. https://doi.org/10.1016/j.physa.2005.05.001
van Winsum W, 1999. The human element in car following models. Transportation Research Part F: Traffic Psychology and Behaviour, 2(4):207–211. https://doi.org/10.1016/S1369-8478(00)00008-5
Wiedemann R, 1974. Simulation of Road Traffic in Traffic Flow. University of Karlsruhe, Karlsruhe, Germany.
Xie DF, Zhao XM, He ZB, 2019. Heterogeneous traffic mixing regular and connected vehicles: modeling and stabilization. IEEE Transactions on Intelligent Transportation Systems, 20(6):2060–2071. https://doi.org/10.1109/TITS.2018.2857465
Yu SW, Liu QL, Li XH, 2013. Full velocity difference and acceleration model for a car-following theory. Communications in Nonlinear Science and Numerical Simulation, 18(5): 1229–1234. https://doi.org/10.1016/j.cnsns.2012.09.014
Zhang XZ, Shi ZK, Chen JZ, et al., 2023. A bi-directional visual angle car-following model considering collision sensitivity. Physica A: Statistical Mechanics and Its Applications, 609: 128326. https://doi.org/10.1016/j.physa.2022.128326
Zhang YC, Xue Y, Zhang P, et al., 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, 514:133–140. https://doi.org/10.1016/j.physa.2018.09.012
Zhao XM, Gao ZY, 2006. A control method for congested traffic induced by bottlenecks in the coupled map car-following model. Physica A: Statistical Mechanics and Its Applications, 366:513–522. https://doi.org/10.1016/j.physa.2005.11.004
Acknowledgments
This work is supported by the National Key Research and Development Program of China (No. 2017YFE9134700), the Natural Science Foundation of Zhejiang Province, China (No. LY22G010001), the Program of Humanities and Social Science of Education Ministry of China (No. 20YJA630008), the Ningbo Natural Science Foundation of China (Nos. 2021J235 and 2021J111), the Fund of Healthy & Intelligent Kitchen Engineering Research Center of Zhejiang Province, and the K.C. Wong Magna Fund in Ningbo University, China.
Author information
Authors and Affiliations
Contributions
Rongjun CHENG designed the research. Hao LYU and Hang YANG processed the corresponding data. Qun JI wrote the first draft of the manuscript. Hao LYU helped to organize the manuscript. Hang YANG revised and edited the final version. Qi WEI is responsible for numerical simulation and language polishing.
Corresponding author
Ethics declarations
Qun JI, Hao LYU, Hang YANG, Qi WEI, and Rongjun CHENG declare that they have no conflict of interest.
Additional information
Electronic supplementary materials
Sections S1 and S2, Eqs. (S1)-(S13)
Electronic supplementary materials
Rights and permissions
About this article
Cite this article
Ji, Q., Lyu, H., Yang, H. et al. Bifurcation control of solid angle car-following model through a time-delay feedback method. J. Zhejiang Univ. Sci. A 24, 828–840 (2023). https://doi.org/10.1631/jzus.A2300026
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.A2300026