A Stabilizing Controller for the Modified Optimal Velocity Model

Abstract

We address the issue of assisting a human driver in maintaining safety for a highwaylike scenario. To that end, we consider a human-driven vehicle following a lead vehicle on a straight road. We model the response of the human driver using a recently-proposed non-linear time-delayed car-following model called the Modified Optimal Velocity Model (MOVM). Our study is motivated by the MOVM’s loss of local stability via a Hopf bifurcation for increased reaction delays of the driver, which may manifest as collisions. For analytical tractability, we first approximate the MOVM by applying a semi-discretization method on the driver’s reaction delay. Next, using this approximation, we propose a stabilizing output-feedback controller that does not require specifics of (i) the system non-linearity that models driver behavior, and (ii) the driver’s reaction delay. Lastly, we numerically verify the stabilizing effect of the proposed controller on the MOVM. The proposed controller is shown to ensure system stability for increased reaction delays. Thus, such a controller may prove useful in aiding a human driver ensure safety.