Decomposition of Data Rate Allocation for Stabilization over Networks

We consider the problem of stabilizing a network consisting of linear time-invariant plants, sensors, controllers, and relays, where the links can be rate-limited. A previous result shows how to characterize such networks for which stabilizing controllers exist, and then shows how to synthesize coding and control laws to stabilize the network. A key component is finding pseudorates, which determine how much of a given network link is used to help stabilize a given unstable mode on the network. In this paper, we seek to determine these pseudorates using only local information, and show that this can be achieved using dual decomposition for most objectives of interest. For a 1-norm objective that often allows a sparse portion of the network to be used for stabilization, we instead develop a method using techniques similar to ADMM and show that all but one step of the algorithm can be decomposed.