# Monitoring Link Faults in Nonlinear Diffusively-coupled Networks

## TL;DR

This paper develops methods for detecting and isolating link faults in multi-agent systems with passive dynamics by analyzing steady-state outputs and using data-driven convergence protocols, with graph-theoretic guarantees.

## Contribution

It introduces asymptotic and data-driven convergence assertion protocols for fault detection and isolation in nonlinear diffusively-coupled networks, leveraging network optimization theory.

## Key findings

- Effective fault detection in multi-agent systems using steady-state analysis.
- Graph-theoretic guarantees on fault isolation capabilities.
- Successful demonstration through a case study.

## Abstract

Fault detection and isolation is an area of engineering dealing with designing on-line protocols for systems that allow one to identify the existence of faults, pinpoint their exact location, and overcome them. We consider the case of multi-agent systems, where faults correspond to the disappearance of links in the underlying graph, simulating a communication failure between the corresponding agents. We study the case in which the agents and controllers are maximal equilibrium-independent passive (MEIP), and use the known connection between steady-states of these multi-agent systems and network optimization theory. We first study asymptotic methods of differentiating the faultless system from its faulty versions by studying their steady-state outputs. We explain how to apply the asymptotic differentiation to detect and isolate communication faults, with graph-theoretic guarantees on the number of faults that can be isolated, assuming the existence of a "convergence assertion protocol", a data-driven method of asserting that a multi-agent system converges to a conjectured limit. We then construct two data-driven model-based convergence assertion protocols. We demonstrate our results by a case study.