Disturbance propagation analysis in vehicle formations: An information-theoretic approach

We consider the problem of disturbance propagation in a control system where a group of vehicles aims to move in a formation with a tree topology. The control law at every vehicle depends on its position error with respect to its parent vehicle in the tree as well as on coded information transmitted by other vehicles across side communication channels. A lower bound on the integral of the log sensitivity function of the position errors for any vehicle with respect to a stochastic disturbance acting on the lead vehicle is presented. The effect of the side information channels is illustrated through some examples. It is also shown that in some cases the lower bound is achievable through appropriate design of the controllers and encoder/decoder pairs.