Computation and System Identification of a Lower Bound on Scalar LQG Control via a Noisy Communication Link with Delayed CaSI at the Decoder

We consider a closed-loop control problem where a fully observable plant modeled as a time-invariant scalar- valued Gauss-Markov process is connected to a controller via a communication link. We examine the impact of the communication link on the performance of the closed-loop system when its decoder accepts with unit delay some causal side information (CaSI) (correlated to the system's dynamics) modeled as an impair measurement of the state process and the performance criterion is the linear quadratic (LQ) cost. We use the separation principle between the control and estimation that applies in our setup to obtain the following results: i) a lower bound on the optimal linear quadratic cost; ii) the optimal linear policies that achieve this lower bounds. We compare our bound to similar known bounds in the literature.