Extending the adaptive time gap car-following model to enhance local and string stability for adaptive cruise control systems

In this paper, we extend the nonlinear adaptive time gap car-following model to enhance the local and string stability for adaptive cruise control systems considering a time-lag in the lower level vehicle dynamics and a sensor time-delay. Both over-damped local and string stability analyses are performed mathematically and examined by simulation. The over-damped string stability criterion fulfills all the Lp stability norms, where $p\in \left[1,\infty \right].$ Here we consider a time-lag operating in the lower level of the longitudinal control system’s architecture, a sensor time-delay, and heterogeneity in the vehicle dynamics of the platoon. The adaptive time gap model without these attributes is intrinsically stable. However, it turns out that the introduction of a lag, a delay, or heterogeneity in the lower vehicular level reduces the performance in terms of stability, yielding unsafe damped oscillating collective behaviors. Henceforth we extend the model to enhance the stability by transforming the model to a homogeneous structure, without changing the fundamental dynamics. The results show that the extended model satisfies over-damped criteria for both local and string stability, considering actuator time-lag, sensor time-delay, and heterogeneity in the lower level vehicle dynamics. Such features are expected for automated driving systems.