Optimal Block Length for Data-Rate Minimization in Networked LQG Control

We consider a discrete-time networked LQG control problem in which state information must be transmitted to the controller over a noiseless binary channel using prefix-free codewords. Quantizer, encoder and controller are jointly designed to minimize average data-rate while satisfying required LQG control performance. We study the effects of selecting large block-lengths (data transmission intervals) from the perspectives of information-theoretic advantage due to coding efficiency and control-theoretic disadvantage due to delay. In particular, we demonstrate that the performance of networked control scheme by Tanaka et al. (2016) can be improved by adjusting the block-length optimally. As a byproduct of this study, we also show that the data-rate theorem for mean-square stability similar to Nair and Evans (2004) can be recovered by considering sufficiently large block-lengths.