LQG-like control of scalar systems over communication channels: The role of data losses, delays and SNR limitations

In this work we address the problem of feedback control design for scalar systems in the presence of a non-ideal communication channel, which gives rise to tightly coupled limitations in terms of quantization errors, decoding/computational delays and packet loss affecting the closed loop control performance. We restrict our analysis to the context of LQG-like control, where the estimator and controller gains are forced to be constant, subject to SNR limitations, packet loss, and constant delay, and we derive their impact on the optimal design of the controller parameters. In particular, we show that the stability of the closed loop system depends on a tradeoff among SNR, packet loss probability and delay. Through this analysis we are also able to recover, as special cases, several results already available in the literature that have treated packet loss, quantization error and delay separately. We also show that the estimator and controller cannot be designed independently even if the controller has full knowledge of the packet loss sequence and the control inputs to the plant. In fact the optimal control gain, when accounting for the communication constraints is, in general, different from the optimal gain derived under the classical LQG scenario, which is recaptured when the SNR over the channel goes to infinity.