On disturbance propagation in leader-follower systems with limited leader information

This paper studies the problem of disturbance propagation in a string of vehicles aiming to proceed along a given trajectory while keeping a constant distance between each vehicle and its successor. It is assumed that each vehicle can control its position based on the spacing error with respect to the preceding vehicle in the string, as well as on coded information transmitted by the lead vehicle. Using information–theoretic techniques, this paper establishes a lower bound to the integral of the sensitivity function of spacing errors with respect to a stochastic disturbance acting on the lead vehicle. The derived bound depends on the open-loop poles and zeros of the vehicles’ dynamics as well as on the (possibly non-linear) controller used at each vehicle. The lower bound is shown to be tight for a specific class of systems and controllers.