Resilient Synchronization of Networked Lagrangian Systems in Adversarial Environments

This paper considers the resilient synchronization problems of multiple Euler-Lagrange (EL) systems, where the communication network is affected by the external attacks or internal non-participant agents. The considered adversarial environments can cover several types of cyber-attacks, such as misbehaving agents and false data injection attacks. The remaining normal agents aim to reach a common decision despite the influence of faulty agents. To this end, a "safe kernel" based secure control scheme is proposed for the networked Lagrangian systems. According to the scheme, each healthy agent generates a convex hull based on the states of its neighbors and updates its reference state toward this kernel only in each sampling instant to reduce the computational burden. The "average sampling interval" is used to define the number of sampling instants for faster convergence. With an assumption on the number of misbehaving agents, the proposed scheme guarantees consensus of Euler-Lagrange systems even in adversarial environments. Mathematical proofs and a numerical example are presented to verify the resilience and validity of the proposed scheme.