Distributed resilient consensus for heterogeneous fractional-order multi-agent systems against hybrid attacks

Consensus in multi-agent systems (MASs) relies on connectivity of communication topology and integrity of information, which are also the primary targets of cyber-attacks. Under such attacks, the hereditary property of fractional-order dynamics causes attack effects to accumulate over time, posing additional challenges to the protocol design and stability analysis. Accordingly, this paper investigates heterogeneous fractional-order MASs subject to hybrid attacks, including Denial-of-Service (DoS) attacks and deception attacks. A fractional-order attack-resilient control framework, comprising a distributed resilient control protocol, fractional-order state observers and attack estimators, is proposed to ensure leader-following consensus with cooperative uniformly ultimately bounded (UUB). Moreover, sufficient conditions are rigorously derived from a switching perspective, among which an order-dependent attack tolerance condition is established. Lastly, the effectiveness of the proposed control framework is validated, and the influence of the fractional order on the attack tolerance capability and system performance is revealed through an illustrative example.