Bifurcation analysis and control study of improved full-speed differential model in connected vehicle environment

Abstract

In recent years, the traffic congestion problem has become more and more serious, and the study of traffic system control has become a new hot spot. Studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable pivots can alleviate the traffic congestion problem from a new perspective. In this paper, the full-speed differential model considering the vehicle network environment is improved to adjust the traffic flow from the perspective of bifurcation control. This paper theoretically proves the existence conditions of Hopf bifurcation and saddle-node bifurcation in the model, and finds the stability mutation point for the stability of the transportation system. For the unstable bifurcation point, a nonlinear system feedback controller is designed using Chebyshev polynomial approximation and stochastic feedback control method. The advancement, postponement, and elimination of Hopf bifurcation are achieved without changing the system equilibrium point, and the mutation behavior of the transportation system is controlled so as to alleviate the traffic congestion. In this paper, the changes in the stability of complex traffic systems are explained from the perspective of bifurcation analysis, which can better capture the characteristics of the traffic flow. By adjusting the control parameters in the feedback controllers, the influence of the boundary conditions on the stability of the traffic system is adequately described, and the effects of the unstable focuses and saddle points on the system are suppressed to slow down the traffic flow. In addition, the unstable bifurcation points can be eliminated and the Hopf bifurcation can be controlled to advance, delay, and disappear, so as to realize the control of the stability behavior of the traffic system, which can help to alleviate the traffic congestion as well as describe the actual traffic phenomena.