LQG Control with Communication Constraints

The average cost control problem for linear stochastic systems with Gaussian noise and quadratic cost is considered in the presence of communication constraints. The latter take the form of finite alphabet codewords, being transmitted to the controller with ensuing delay and distortion. It is shown that if instead of the state observations an associated “innovations process” is encoded and transmitted, then the separation principle holds, leading to an optimal control linear in state estimate. An associated “off-line” optimization problem for code length selection is formulated. Some possible extensions are also pointed out.