Convergence Analysis for Platooning Over Coloured Additive Noise Channels

We consider a platooning control problem where the communication channels between vehicles are subject to coloured additive noises. Due to the stochastic nature of these channels, our analysis delves into examining the convergence of both the mean and variance of the vehicle tracking errors. We study the convergence as both time and number of vehicles grow unbounded. Our results include necessary and sufficient conditions for convergence and reveal that the colour of the noise does not impact the convergence characteristics of the error statistics, although it affects the values of the tracking error variances. Our findings offer insights into string stabilization. Numerical examples illustrate our results.