Feedback-based control for coupled map car-following model with time delays on basis of linear discrete-time system

In order to suppress traffic jams and make traffic flow smooth, we propose feedback-based control strategy for the coupled map car-following model with time delays on basis of linear discrete-time system. In this new kind of model, time delay is incorporated into dynamic equation of vehicles. The traffic system is analyzed based on Gerschgorin disk theorem and general Nyquist stability criterion. The sufficient condition for the existence of coupled map car-following model with time delays is given. Considering time delays, the proposed control scheme can be competent to alleviate traffic congestion. Numerical examples are given to illustrate the effectiveness of the proposed control method.