Disturbance propagation in strings of vehicles with limited leader information

This paper considers the problem of disturbance propagation in a string of vehicles, where each vehicle has access to the position error with respect to its preceding vehicle. In addition, the followers in the string may receive coded information sent by the leader over finite capacity side channels. A lower bound on the integral of the sensitivity function of the position errors with respect to a stochastic disturbance acting on the lead vehicle is presented. This bound depends on the open-loop unstable modes of the system, as in the classical Bode integral formula for single-input single-output systems. However, in this case, the bound also depends on the capacities of the side communication channels. Simulation results illustrating the tightness of the proposed bound are presented.