Minimum Sensor Placement for Robust Observability of Structured Complex Networks

TL;DR

This paper investigates the minimum sensor placement problem in complex networks to ensure robust structural observability against sensor or connection failures, proposing an approximation approach due to NP-hardness.

Contribution

It introduces a two-step method combining minimum sensor placement with a set covering approach for robustness, providing feasible approximations with guarantees.

Findings

The problems are NP-hard, indicating no efficient exact solutions.

A two-step approach effectively approximates robust sensor placement.

Feasible solutions with optimality guarantees can be obtained in polynomial time.

Abstract

This paper addresses problems on the robust structural design of complex networks. More precisely, we address the problem of deploying the minimum number of dedicated sensors, i.e., those measuring a single state variable, that ensure the network to be structurally observable under disruptive scenarios. The disruptive scenarios considered are as follows: (i) the malfunction/loss of one arbitrary sensor, and (ii) the failure of connection (either unidirectional or bidirectional communication) between a pair of agents. First, we show these problems to be NP-hard, which implies that efficient algorithms to determine a solution are unlikely to exist. Secondly, we propose an intuitive two step approach: (1) we achieve an arbitrary minimum sensor placement ensuring structural observability; (2) we develop a sequential process to find minimum number of additional sensors required for robust observability. This step can be solved by recasting it as a weighted set covering problem. Although this is known to be an NP-hard problem, feasible approximations can be determined in polynomial-time that can be used to obtain feasible approximations to the robust structural design problems with optimality guarantees.