Low-Rank and Low-Order Decompositions for Local System Identification
For researchers in distributed system identification, this work provides a novel heuristic for separating local and global dynamics, though it is presented as a promising approach without concrete results.
The paper addresses local system identification in large distributed systems, showing that the full interconnection case is easily solved with existing methods, and proposes a nuclear norm minimization heuristic for the hidden interconnection case by exploiting low-order local and low-rank global dynamics.
As distributed systems increase in size, the need for scalable algorithms becomes more and more important. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. We show that in what we term the "full interconnection measurement" setting, this task is easily solved using existing system identification methods. We also propose a promising heuristic for the "hidden interconnection measurement" case, in which contributions to local measurements from both local and global dynamics need to be separated. Inspired by the machine learning literature, and in particular by convex approaches to rank minimization and matrix decomposition, we exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization.