Minimum Variance Control Over a Gaussian Communication Channel

We consider the problem of minimizing the response of a plant output to a stochastic disturbance using a control law that relies on the output of a noisy communication channel. We discuss a lower bound on the performance achievable at a specified terminal time using nonlinear time-varying communication and control strategies and show that this bound may be achieved using strategies that are linear. We also consider strategies that are defined over an infinite horizon that may achieve better transient response that those that are optimal for the terminal time problem.