Dynamical analysis of an optimal velocity model with time-delayed feedback control

Abstract

In this paper, the dynamical behaviors of an optimal velocity model (OVM) with delayed feedback control of velocity difference is studied. By analyzing the transcendental characteristic equation, the stable region of controlled OVM is obtained and the critical condition for Hopf bifurcation is derived. To stabilize the unstable traffic flow and control the bifurcations, the definite integral stability method can be applied to determine the first stable intervals of time delay and feedback gain by calculating the number of all unstable eigenvalues of the characteristic equation. That is, when the time delay and the feedback gain are chosen from the corresponding stable intervals, the controlled OVM is stable and the stop-and-go traffic waves disappear. The numerical simulations in the case studies indicate that the proposed control strategy can suppress the traffic jams effectively and enhance the stability of traffic flow significantly.