Step reference tracking in signal-to-noise ratio constrained feedback control

In this paper we address the problem of step reference tracking in the context of signal-to-noise ratio (SNR) constrained feedback control. We study the presence of a channel model in the feedback loop either over the measurement path, between the plant and the controller, or the control path, between the controller and the plant. We start the analysis by considering the memoryless additive white Gaussian noise (AWGN) channel model, and follow-up with the additive coloured Gaussian noise (ACGN) channel with memory model. We observe that the standard SNR constrained feedback loop configuration, when tracking step references, will result in an infinite channel SNR. We show that this situation can be ameliorated by extending the feedback loop configuration with an encoder and decoder. The proposed configurations result in a finite SNR that converges back to the infimal SNR for regulation when the amplitude of the reference signal tends to zero.