Optimal transmitters for control over a noisy link with imperfect feedback

We consider a control loop which is closed over an additive noise communication channel. The quantity of interest is the Signal-to-Noise Ratio (SNR) of the channel such that control objectives like stabilization or minimal tracking error are met. We investigate a transmitter that uses observations of the plant output and the channel output which are fed back to the transmitter. Recently, a transmitter has been proposed which uses linearly filtered channel output feedback and the analytical expression for the minimal value of the SNR has been determined. In the present work, we derive the transmitter in a general framework using noisy channel output feedback. This allows for the investigation of the connection between the quality of imperfect feedback information and performance improvement due to this information. Additionally, other performance criteria than SNR can be used for transmitter design.