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Journal of Zhejiang University SCIENCE A
ISSN 1673-565X(Print), 1862-1775(Online), Monthly
2023 Vol.24 No.9 P.828-840
Bifurcation control of solid angle car-following model through a time-delay feedback method
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.
Key words: Solid angle model (SAM); Time-delay; Hopf bifurcation; Feedback control; Parameter calibration
机构：1宁波大学，海运学院，中国宁波，315211；2宁波财经学院，中国宁波，315175
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。
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DOI:
10.1631/jzus.A2300026
CLC number:
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On-line Access:
2023-06-20
Received:
2023-01-12
Revision Accepted:
2023-03-02
Crosschecked:
2023-09-20