Observability-Blocking Control using Sparser and Regional Feedback for Network Synchronization Processes

TL;DR

This paper develops a control design method to block observability in network synchronization models using sparse regional feedback, reducing control complexity while ensuring stability, with practical numerical demonstrations.

Contribution

It introduces a novel eigenstructure assignment-based algorithm for blocking observability at specified nodes using minimal controllers, and extends it to regional feedback controls considering network topology.

Findings

The algorithm effectively blocks observability at targeted nodes.

Regional feedback controls can preserve stability despite not maintaining open-loop eigenstructure.

Network topology can be exploited to minimize the number of controllers needed.

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 specified 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, 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 the nodes associated with a vertex-cutset separating the actuation and measurement locations. Also, the design is modified to encompass regional feedback controls, which only use data from a subset of 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 results are illustrated with numerical examples.