Self-stabilizing analysis of an extended car-following model with consideration of expected effect

Abstract

In this paper, an extended car-following model considers expected effects and self-stabilizing control. The self-stabilizing control is applied to the new model by employing the anticipation velocity and the anticipation optimal velocity of the considered vehicle. The theoretical analysis and numerical simulation are combined to carry out this paper, the stability conditions can be derived from linear stability analysis. Moreover, by using nonlinear analysis method, the time-dependent Ginzburg–Landau (TDGL) equation and the modified KdV equation near critical point is derived by the reductive perturbation method. Finally, theoretical results are in agreement with numerical simulation results, confirming the correctness of the theoretical analysis results. We demonstrate that self-stabilizing control plays a positive part in restraining traffic congestion. The results reveal that the expected time between the current velocity and the expected velocity has an important impact on the stability of traffic flow.