Abstract
In this paper, a double time-delay feedback control of an optimal velocity model (OVM) is investigated. Double time-delay means that there exist two different state feedback control signals in the controlled OVM system, which are related to the velocity difference and the optimal velocity difference, respectively. Through linear stability analysis, the critical condition of Hopf bifurcation for the controlled OVM is derived. Utilizing the characteristics of Hopf bifurcation and the improved definite integral method, appropriate double time-delay feedback control strategy is designed in term of the number of unstable eigenvalues of the characteristic equation to suppress the stop-and-go waves generated by the uncontrolled OVM. Note that when the number of unstable eigenvalues is equal to zero, the controlled OVM is stable, otherwise, it is unstable. Numerical simulations are executed to validate the accuracy and feasibility of the design of double time-delay control strategy. Finally, case studies approximating the actual traffic situation are given, and the appropriate combination of control parameters is selected through the verified design steps. In addition, the measured data from NGSIM are also considered.
Highlights
Time delays have a non-negligible impact on the evolution of traffic flow and driving performance whether human-driven vehicles or self-driven vehicles, which is still a worthy issue for discussion
A double time-delayed feedback control is proposed to alleviate the traffic congestion produced by the uncontrolled optimal velocity model (OVM): dvn (t dt where un (t − 1) and en (t − 2 ) denote two different control signals related to time delay which are expressed as follows: un (t − 1 ) = 1 vn (t ) − vn (t − 1 )
The stability analysis of the OVM with double time-delayed feedback control is executed to investigate the characteristics of bifurcation
Summary
Time delays have a non-negligible impact on the evolution of traffic flow and driving performance whether human-driven vehicles or self-driven vehicles, which is still a worthy issue for discussion. Orosz et al [13] implemented bifurcation analysis on a nonlinear car-following model with peculiar attention to driver’s reaction-time delay Their results demonstrated that Hopf bifurcation can give rise to a transformation in stability where oscillations suddenly occur. In the process of investigating the bifurcation characteristics of a platoon of vehicles, Kamath et al [15] proposed an improved OVM model with attention to delayed feedback They proved that the stability analysis results agreed well with the Hopf bifurcation boundary. Zhang et al [16] presented an extended OVM accounting for time-delayed velocity difference Their experimental results showed that the occurrence of Hopf bifurcation will destroy the stability of traffic flow.
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