Observability-blocking control using sparser and regional feedback for network synchronization processes

Abstract

The design of feedback control systems to block observability in a network synchronization model, i.e. to make the dynamics unobservable from measurements at a subset of the network’s nodes, is studied. First, a general design algorithm is presented for blocking observability at any group of m nodes, by applying state feedback controls at m+2 specified actuation nodes. The algorithm is based on a method for eigenstructure assignment, which allows surgical modification of particular eigenvectors to block observability while preserving the remaining open-loop eigenstructure. Next, a sparser design is obtained, which leverages low-cardinality vertex cutsets separating the actuation and measurement locations in the network’s graph to reduce the required number of actuation nodes for observability blocking. Also, the design is modified to encompass regional feedback controls, which only use data from accessible nodes. The regional feedback design does not maintain the open-loop eigenstructure, but can be guaranteed to preserve stability via a time-scale argument. The sparser and regional feedback designs are illustrated with numerical examples.