Distributed Error-Identification and Correction using Block-Sparse Optimization

Abstract

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.