Discrete Car-Following Model and its Feedback Control Scheme

Abstract

In this paper, we discretize continuous car-following model into a difference equation. With the use of discrete control theory, the discrete car-following model was linearized and the impulse transfer function was obtained. Based on the definition of traffic jam, one Lemma was proposed to judge system stability and two theorems were given to judge the non-jam conditions for controlled and uncontrolled systems. Moreover, the feedback gain was designed for a controlled system. Numerical simulations were conducted to show the validity of the discrete car-following model and control scheme. The results are in agreement with the theoretical results.