Bifurcation Control in an Optimal Velocity Model via Double Time-Delay Feedback Method

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.