  The conventional solutions for fault-detection, identification, and
reconstruction (FDIR) require centralized decision-making mechanisms which are
typically combinatorial in their nature, necessitating the design of an
efficient distributed FDIR mechanism that is suitable for multi-agent
applications. To this end, we develop a general framework for efficiently
reconstructing a sparse vector being observed over a sensor network via
nonlinear measurements. The proposed framework is used to design a distributed
multi-agent FDIR algorithm based on a combination of the sequential convex
programming (SCP) and the alternating direction method of multipliers (ADMM)
optimization approaches. The proposed distributed FDIR algorithm can process a
variety of inter-agent measurements (including distances, bearings, relative
velocities, and subtended angles between agents) to identify the faulty agents
and recover their true states. The effectiveness of the proposed distributed
multi-agent FDIR approach is demonstrated by considering a numerical example in
which the inter-agent distances are used to identify the faulty agents in a
multi-agent configuration, as well as reconstruct their error vectors.
