Observability-Blocking Controllers for Network Synchronization Processes

The design of local state-feedback control systems in dynamical networks to block observability at remote nodes is studied, in the context of a canonical linear network synchronization model. A general design algorithm is presented first, which can be used to ensure unobservability at any group of m nodes using m + 1 local controllers. The algorithm is based on a method for joint eigenvalue-eigenvector assignment, and serves to prevent observability while leaving all eigenvalues and all but one eigenvector of the open loop unchanged. Next, the topological structure of the network is exploited to reduce the number of controllers required for blocking observability; the result is based on blocking observability on node cutsets separating the actuation locations and nodes that must be made unobservable. The results are illustrated with a numerical example.