The Control Theory Analysis In The Car-following And Lattice Hydrodynamic Models

Control theory is concerned with system of information transformation and control proce-dures, the applications of control in traffic flow has significance for solving traffic jams. Recently years, articles solving traffic jams with car-following model with control method have prolifer-ated in traffic flow. Through the analysis of the theory and simulation, the feedback control have a good effect with traffic congestions. At present, some researchers involved have made some achievement with analysis with control theory. However, it is rare that feedback control is applied to solving two lane car following model and the lattice hydrodynamic model, but the research of multiple vehicles’feedback signals was seldom reported. Moreover, the application of the feedback control theory in lattice hydrodynamic models is blank at present, in view of the similarity between the car-following models and lattice hydrodynamic models, we introduce the method of the feedback control theory to the lattice hydrodynamic models. The primary coverage of this essay constitutes by three models:an extended the car-following model with the control method by considering the headway of arbitrary number of vehicles that precede and the relative velocity, two-lane traffic model considering lane-changing behavior with the velocity difference control signal and the lattice hydrodynamic model of traffic flow considering the flux difference. We analysis the models with control theory, the stability condition was also deduced. Finally, the results show that those models with the feedback control signals can effectively alleviate traffic congestion.