On Disturbance Propagation in Vehicular Platoons with Different Communication Ranges

In the control of vehicular platoons, the disturbances acting on one vehicle can propagate and affect other vehicles. If the disturbances do not amplify along the vehicular string, then it is called string stable. However, it is usually difficult to achieve string stability with a distributed control setting, especially when a constant spacing policy is considered. This note considers the string unstable cases and studies disturbance propagation in a nonlinear vehicular platoon consisting of $n+1$ vehicles where the (virtual) leading vehicle provides the reference for a constant spacing policy. Apart from the communications between consecutive vehicles, we also assume that each vehicle can receive information from $r$ neighbors ahead, that is, the vehicular platoon has communication range $r$. For the maximal overshoot of the inter-vehicular spacing errors, we explicitly show that the effect of disturbances, including the external disturbances acting on each vehicle and the acceleration of the leading vehicle, is scaled by $O(\sqrt{ \left \lceil \frac{n}{r} \right \rceil})$ for a fixed $n$. This implies that disturbance propagation can be reduced by increasing communication range. Numerical simulation is provided to illustrate the main results.