Dynamical analysis for a car-following model with delayed-feedback control of both velocity and acceleration differences

In this paper, based on an existing car-following model, a novel delayed-feedback control scheme depending on both velocity and acceleration differences is proposed to stabilize the unstable steady state and suppress traffic jam. The controller of each vehicle is constructed to use the difference information i.e., velocity difference and acceleration difference between the present state and the past state, and the velocity and the acceleration of other vehicles in the platoon are not required. Using stability switching and definite integral stability methods, the stable intervals of time delays and feedback gains are obtained by calculating the number of all unstable eigen-values of the characteristic equation. Then, the unstable traffic flow can be stabilized through choosing the proper time delays and feedback gains from the corresponding stable intervals. Compared with the delayed-feedback control of velocity difference, the proposed control method expands the stable delay interval and improves the robust performance. Numerical simulations under periodic and open boundary are demonstrated to verify the theoretical results.