Optimal tracking over an additive white Gaussian noise channel

This paper studies the optimal reference tracking problems of finite-dimensional, linear, time-invariant (LTI) systems with an additive white Gaussian noise (AWGN) channel between the controller and the plant. We consider two types of the reference signal: a random variable and a Brownian motion. The power of the tracking error is adopted as the measure of the performance and is to be minimized over all stabilizing two-parameter controllers. We assume the power of the channel input is limited and seek to solve the constrained optimization problem explicitly. It is shown that, besides the power constraint, the lowest power of the tracking error hinges closely on non-minimum phase zeros, the unstable poles and the plant gain.