Observability-Blocking Controls for Double-Integrator and Higher Order Integrator Networks

TL;DR

This paper develops control strategies to prevent observability at remote nodes in integrator networks, using eigenstructure techniques and network topology to optimize the number of controllers needed.

Contribution

It introduces a novel eigenstructure-based design algorithm for blocking observability in double integrator networks and generalizes the approach to higher order integrator networks.

Findings

The algorithm requires m+2 actuation nodes for DIN to block observability.

Network topology can reduce the number of controllers needed.

Design principles are extended to N-th order integrator networks.

Abstract

The design of state-feedback controls to block observability at remote nodes is studied for double integrator network (DIN) and higher order integrator network models. A preliminary design algorithm is presented first for DIN that requires $m+2$ actuation nodes to block observability for the measurement obtained from a set of $m$ nodes. The algorithm is based on eigenstructure assignment technique and leverages the properties of the eigenvectors in DIN. Next, the topological structure of the network is exploited to reduce the number of controllers required for blocking observability. The number of actuation nodes in sparser design depends on the cardinality of a cutset separating the actuation and measurement locations. Later, the design principles are generalized for blocking observability in $N$-th order integrator network models.