考虑多辆自动驾驶车平均速度和自时滞反馈的离散时间时滞跟驰模型

康成俊; 苗卉

doi:10.21656/1000-0887.450223

考虑多辆自动驾驶车平均速度和自时滞反馈的离散时间时滞跟驰模型

doi: 10.21656/1000-0887.450223

康成俊^1,,
苗卉^2, ,

1.
山西工程科技职业大学计算机工程学院，山西晋中 030600
2.
山西财经大学应用数学学院，太原 030000

基金项目:

山西省基础研究计划 202403021221218

详细信息

作者简介:
康成俊(1987—)，男，讲师，博士(E-mail: chengjun0102@126.com)

通讯作者:
苗卉(1987—)，女，副教授，博士(通讯作者. E-mail: miaohuixju@163.com)

中图分类号: U491
计量
- 文章访问数: 81
- HTML全文浏览量: 27
- PDF下载量: 10
- 被引次数: 0
出版历程
- 收稿日期: 2024-08-01
- 修回日期: 2024-09-23
- 刊出日期: 2025-10-01

A Discrete-Time Delayed Car-Following Model Considering the Average Velocity of Multiple Autonomous Vehicles and Self-Delayed Feedback

KANG Chengjun^1
,,
MIAO Hui^{2
, ,}

1.
School of Computer Engineering, Shanxi Vocational University of Engineering Science and Technology, Jinzhong, Shanxi 030600, P.R.China
2.
School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030000, P.R.China

摘要

摘要: 为了更好地探究自动驾驶车辆的跟驰特征和车流稳定性特性，在最优速度跟驰模型的基础上，结合自动驾驶车辆，通过车辆之间相互通讯共享收集到的交通信息，提出一种改进的离散时间时滞跟驰模型，该模型考虑了前方自动驾驶车辆与当前自动驾驶车辆的交互信息，前方多辆自动驾驶车辆的平均速度. 此外，还考虑了自时滞速度和车头间距控制策略. 通过控制理论方法和Lyapunov稳定性理论，建立了自动驾驶车流的稳定性条件. 进而, 在扰动影响下，通过数值模拟直观地展示了自动驾驶车流的时空演化模式，进一步验证了理论分析，揭示了自动驾驶车辆通过车辆之间的信息交互、前方多车辆平均速度、速度信息和车头间距信息传感过程中的时滞因素以及自时滞速度和车头间距控制策略对自动驾驶车流稳定性的影响. 结果表明：车辆之间的信息交互、前方多车辆平均速度的获取均可提高自动驾驶车流的稳定性；自时滞速度和车头间距控制策略可以有效地提高自动驾驶车流的稳定性，抑制交通拥堵；然而，速度信息和车头间距信息传感过程中的时滞因素不利于自动驾驶车流的稳定性.
- 跟驰模型 /
- 平均速度 /
- 自时滞控制 /
- 稳定性
Abstract: Based on the optimal velocity car-following model and combined with the traffic information collected by autonomous vehicles through mutual communication, an improved discrete-time time-delayed car-following model was proposed to better explore the car-following performances and stability characteristics of autonomous vehicles, with the interaction information between the front autonomous vehicle and the current autonomous vehicle, and the average velocity of multiple front autonomous vehicles considered. In addition, the self-delayed velocity and the space headway control strategy was analyzed. With the control theory method and the Lyapunov stability theory, the stability condition for traffic flow was established. Furthermore, under disturbance, the spatio-temporal evolution of the autonomous vehicle flow was intuitively demonstrated through numerical simulation, to further validate the theoretical analysis and reveal the effects of the autonomous vehicles on the traffic flow stability through the information interaction between vehicles, the average velocity of multiple front vehicles, the time delay factors in the sensing process of velocity and space headway information, and the self-delayed velocity and space headway control strategy. The results show that, the information exchange between vehicles and the acquisition of the average velocity of multiple front vehicles can improve the traffic flow stability. At the same time, the self-delayed velocity and space headway control strategy can effectively improve the traffic flow stability and restrain traffic congestion. However, the time delay factor in the sensing process of velocity and space headway information is not conducive to the traffic flow stability.
- car-following model /
- average velocity /
- self-delayed control /
- stability

HTML全文

图 1 车辆之间的最优速度、前方多车辆平均速度影响的速度时空演化

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 1. The spatiotemporal evolution of velocity influenced by the optimal velocity between vehicles and the average velocity of multiple vehicles ahead

下载: 全尺寸图片幻灯片

图 2 时滞因素影响的速度时空演化

Figure 2. The spatiotemporal evolution of velocity influenced by time-delay factors

下载: 全尺寸图片幻灯片

图 3 自时滞速度和车头间距影响的速度时空演化

Figure 3. The spatiotemporal evolution of velocity influenced by the self-delayed velocity and the space headway

下载: 全尺寸图片幻灯片

参考文献(21)

[1]	BANDO M, HASEBE K, NAKAYAMA A, et al. Dynamical model of traffic congestion and numerical simulation[J]. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1995, 51(2): 1035-1042.
[2]	HELBING D, TILCH B. Generalized force model of traffic dynamics[J]. Physical Review E, 1998, 58(1): 133-138. doi: 10.1103/PhysRevE.58.133
[3]	JIANG R, WU Q, ZHU Z. Full velocity difference model for a car-following theory[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2001, 64: 017101. doi: 10.1103/PhysRevE.64.017101
[4]	TANG T, WANG Y, YANG X, et al. A new car-following model accounting for varying road condition[J]. Nonlinear Dynamics, 2012, 70(2): 1397-1405. doi: 10.1007/s11071-012-0542-8
[5]	WEN H, RONG Y, ZENG C, et al. The effect of driver's characteristics on the stability of traffic flow under honk environment[J]. Nonlinear Dynamics, 2016, 84(3): 1517-1528. doi: 10.1007/s11071-015-2585-0
[6]	LI S, YANG L, GAO Z, et al. Stabilization strategies of a general nonlinear car-following model with varying reaction-time delay of the drivers[J]. ISA Transactions, 2014, 53(6): 1739-1745. doi: 10.1016/j.isatra.2014.08.017
[7]	GE H X, DAI S Q, DONG L Y, et al. Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2004, 70: 066134. doi: 10.1103/PhysRevE.70.066134
[8]	KUANG H, XU Z P, LI X L, et al. An extended car-following model accounting for the average headway effect in intelligent transportation system[J]. Physica A: Statistical Mechanics and Its Applications, 2017, 471: 778-787. doi: 10.1016/j.physa.2016.12.022
[9]	ZHU W X, ZHANG L D. A new car-following model for autonomous vehicles flow with mean expected velocity field[J]. Physica A: Statistical Mechanics and Its Applications, 2018, 492: 2154-2165. doi: 10.1016/j.physa.2017.11.133
[10]	MA M, MA G, LIANG S. Density waves in car-following model for autonomous vehicles with backward looking effect[J]. Applied Mathematical Modelling, 2021, 94: 1-12. doi: 10.1016/j.apm.2021.01.002
[11]	YU B, ZHOU H, WANG L, et al. An extended two-lane car-following model considering the influence of heterogeneous speed information on drivers with different characteristics under honk environment[J]. Physica A: Statistical Mechanics and Its Applications, 2021, 578: 126022. doi: 10.1016/j.physa.2021.126022
[12]	陈龙, 刘孟协, 蔡英风, 等. 车路协同环境下考虑坡度与前车信息的跟驰模型[J]. 东南大学学报(自然科学版), 2022, 52(4): 787-795. CHEN Long, LIU Mengxie, CAI Yingfeng et al. A following model considering slope and information of the vehicle ahead under vehicle-road coordination environment[J]. Journal of Southeast University(Natural Science Edition), 2022, 52(4): 787-795. (in Chinese)
[13]	PENG G H, JIA T T, KUANG H, et al. A novel car-following model by sharing cooperative information transmission delayed effect under V2X environment and its additional energy consumption[J]. Chinese Physics B, 2022, 31(5): 058901. doi: 10.1088/1674-1056/ac422a
[14]	PENG G, JIA T, ZHAO H, et al. Integrating the historical evolution information integral effect in car-following model under the V2X environment[J]. Physica A: Statistical Mechanics and Its Applications, 2023, 627: 129125. doi: 10.1016/j.physa.2023.129125
[15]	PENG G, WANG K, ZHAO H, et al. Integrating cyber-attacks on the continuousdelay effect in coupled map car-following model under connected vehicles environment[J]. Nonlinear Dynamics, 2023, 111(14): 13089-13110. doi: 10.1007/s11071-023-08508-5
[16]	尹砚铎, 龙科军, 谷健. 考虑驾驶员记忆的多前车速度差跟驰模型研究[J]. 交通科学与工程, 2024, 40(2): 127-137. YIN Yanduo, LONG Kejun, GU Jian. A multi-vehicle speed difference car-following model considering driver memory[J]. Journal of Transport Science and Engineering, 2024, 40(2): 127-137. (in Chinese)
[17]	房雅灵, 史忠科. 离散交通流模型的反馈线性化与拥堵控制[J]. 应用数学和力学, 2015, 36(5): 474-481. doi: 10.3879/j.issn.1000-0887.2015.05.003 FANG Yaling, SHI Zhongke. Feedback linearization and congestion control for a discrete traffic flow model[J]. Applied Mathematics and Mechanics, 2015, 36 (5): 474-481. (in Chinese) doi: 10.3879/j.issn.1000-0887.2015.05.003
[18]	ZHU W X, ZHANGL D. Discrete car-following model and its feedback control scheme[J]. Asian Journal of Control, 2020, 22(1): 182-191. doi: 10.1002/asjc.1867
[19]	CUI B Y, ZHANG G, MA Q L. A stable velocity control strategy for a discrete-time car-following model[J]. Physica A: Statistical Mechanics and Its Applications, 2021, 571: 125846. doi: 10.1016/j.physa.2021.125846
[20]	KANG C, QIAN Y, ZENG J, et al. Analysis of stability, energy consumption and CO₂ emissions in novel discrete-time car-following model with time delay under V2V environment[J]. Physica A: Statistical Mechanics and Its Applications, 2024, 634: 129480. doi: 10.1016/j.physa.2023.129480
[21]	BOYD S, EL GHAOUI L, FERON E, et al. Linear Matrix Inequalities in System and Control Theory[M]. Philadelphia: Society for Industrial and Applied Mathematics, 1994.