Robust quantization for digital finite communication bandwidth (DFCB) control

In this paper, we consider a scalar model of DFCB control that accommodates time-varying data rate constraints, such as might occur with intermittent network congestion, and asynchronism of sampling and control actuation. Because of the possibly unpredictable fluctuation of the data rate, we are interested in feedback control designs that tolerate significantly constrained data-rates on feedback loops, while providing acceptable performance when such data rate constraints are not in force. In light of a very basic notion of acceptable performance, we show that control designs with different number of quantization levels tolerate constrained data rates differently. This leads to the conclusion that binary control represents the most robust control quantization under data rate constraints imposed by time-varying congestion on the feedback communication channel. The advantage margin of binary control is further investigated numerically with and without the sampling-control asynchronism being considered. We show that the advantage margin is more substantial when the sampling-control asynchronism is significant.