On the use of one bit quantizers in networked control

This paper addresses the following problem in networked control: “If a control law is implemented over a channel that supports a certain fixed bit rate what is the best choice for the control update rate and, consequently, the number of bits carried in each sample?” A restricted architecture in which linear filters are used for the encoder/decoder is considered and a quantizer with linear feedback is deployed. Subject to these restrictions, a procedure for designing the controller and associated filters is presented. These filters are then deployed to choose the best number of bits per control update. It is shown, subject to the above restrictions, that it is generally best to use one bit per sample, in which case, the control update rate is equal to the bit rate. Our analysis has two points of departure from contemporary literature in this area. Firstly, we focus on bits per unit time, as opposed to bits per sample. Secondly we use a fixed number of bits in every time period as opposed to an average bit rate.