Distributed Cooperative Optimization for Continuous‐Time Multi‐Agent Systems Against Byzantine Attacks

ABSTRACT

This work investigates distributed cooperative optimization for continuous‐time multi‐agent systems (MASs) in the presence of unknown Byzantine agents. Byzantine agents can transmit falsified information to neighbours, termed Byzantine edge attacks (BEAs), or manipulate input signals, termed Byzantine node attacks (BNAs). To counter these threats, we propose a resilient optimization algorithm based on a two‐layered framework: a virtual twin layer (TL) and a cyber‐physical layer (CPL). On the TL, a Zeno‐free event‐triggered Byzantine detection and isolation strategy is developed to disconnect compromised communication links, preventing the spread of falsified data. A secure correction mechanism further restores isolated agents, with an upper bound on correction response time analysed. On the CPL, a decentralized adaptive controller is designed using recursive backstepping and attack compensation mechanisms to mitigate execution deviations caused by BNAs. This controller suppresses disturbances from unknown malicious inputs while ensuring accurate tracking of the virtual optimization signals generated by the TL. The proposed approach thus achieves robust convergence and resilience against Byzantine attacks. Effectiveness is validated through Lyapunov stability analysis and numerical simulations, demonstrating secure optimization in adversarial environments.