Resilient Initial-Dependent Coordination via Transformed Consensus and Distributed Compensation

Abstract

This paper addresses the challenge of resilient initial-dependent coordination in multi-agent systems with abnormal nodes. Initial-dependent coordination refers to the process where each node's final value converges to the transformed average of the initial values, with inter-node relationships modeled using augmented transformation matrices. This formulation captures a broad class of coordination and information fusion tasks involving coordinate transformations. We propose a resilient transformed consensus protocol and define the conditions required to achieve initial-dependent coordination in the presence of abnormal nodes. To implement these conditions, we design a distributed accounting and compensation mechanism. Specifically, each node maintains a private ledger that records real-time interaction data with its neighbors. Abnormal behaviors are detected by reconciling accounts with neighboring nodes, leveraging historical interaction information. The accounting mechanism provides a more flexible and effective detection condition. To recover from the impact of abnormal behaviors, we design a distributed compensation scheme that guides normal nodes to adjust their states, mitigating the adverse effects caused by abnormal nodes. Finally, numerical simulations in a sensor network under various abnormal behaviors validate the effectiveness of our approach.