Limited-communication control theory
We consider the problem of stabilizing a linear system when communication constraints limit how often the controller learns the state of the system. We introduce a communications framework that accounts for the fact that the absence of communication nevertheless conveys information (i.e., nothing communication-worthy occurred). In this framework, we explore the relationship between the encoder’s average bit-rate, its average consumption of communication resources, and the ability of the controller and encoder/decoder pair to stabilize the process. We present a necessary and sufficient condition for the existence of a stabilizing controller and encoder/decoder pair, which depends on the encoder’s average bit-rate, its average resource consumption, and the unstable eigenvalues of the process. We presented these results at the IEEE Conference on Decision and Control and later wrote an article in the IEEE journal Transactions on Automatic Control.