The Control Theory Analysis In The Car-following Model Of Traffic Flow

With the rapid development of economy, traffic congestion has become more and moreserious，especially in the big cities. The traffic congestion problem is more and more prominent.In1961, Newell presented a car-following model described by diferential equation of frst orderand defned the optimal velocity (for short, OV) function for the frst time. After that, manyscholars were interested in OV model. The coupled map (for short, CM) car-following modelplayed an important role in suppressing traffic jams. For the past few years, studies have beendone more for the CM traffic model by using control method. The feedback control signalis used regularly. However, little attention has been paid to study car-following model usingcontrol method. The main contents of this paper is to solve the traffic jam problem in thecar-following model using control theory. We will give the diferential equation of OV model ina single lane. Full velocity diference model and two velocity diference model are considered.The stability conditions are based on a simple control method. Besides, we presented a modifedcar following model that the speed considering the infuence of the vehicle in front and rear. Thecorresponding theoretical analysis and numerical simulations are proposed, traffic flow stabilityconditions are obtained.The thesis is arranged as follows:Chapter1Make a brief introduction about the background and signifcance of theresearch of traffic flow. We introduce the traffic flow research and development status, and thenelaborate several typical microscopic traffic flow model.Chapter2The control theory is applied to solve the traffic jam of car-following model.The diferential equation of OV model for a single lane is given in this chapter. On the basis offull velocity diference model, we consider the infuence of the front of the vehicle speed usingfeedback control signs of Zhao Xiaomei and Gao Ziyou. The stability conditions is obtainedwhere control signals can alleviate the traffic disturbance. We compare the result of our controltheory with no control signal by the numerical simulation.Chapter3Ge Hongxia presented the the two velocity diference model, which consideredthe efect of two vehicle velocity diference in front. Based on this model, the stability condi-tions are derived using this control method under periodic boundary condition. According tonumerical simulation, it can be concluded that our control method can be used to suppress thetraffic jam in car-following model. Chapter4On the basis of the feedback control theory of Zhao xiaomei and Gao Ziyou,a modifed car following model is put forward. This model not only considers the infuence ofvehicle speed in front, but also the vehicle speed behind the the current car. We propose themodifed diferential equation of OV model. The use of feedback control theory, we give stabilityconditions after the system disturbs for a short time. Our control method suppresses the trafficjam successfully by numerical simulation.