Consensus of multi-agent systems with noise-based delayed communications under dynamic Denial-of-Service attacks

This work formulates stochastic consensus with probability one (SC-PO) of multi-agent systems (MSs) by proposing noise-based delayed communication protocols under dynamic Denial-of-Service (D-DoS) attacks. The developed consensus protocols are composed of two cases: (1) interference attacker induces transmission defeats on full inter-agent communication; (2) the attacker interrupts a subset of communication links. During activation period, the communication from neighbors of each agent can be successfully jammed in a certain probability, that is, the Denial-of-Service attacker acts randomly, which fits better to the reality. Different from existing results about the SC-PO of MSs incorporating noise and time delays, this paper delves into the SC-PO through creating a delay-free companion system, which removes the underlying assumption of mean square consensus. By leveraging Lyapunov method, graph theory and stochastic analysis, SC-PO criteria are formulated, which is intricately connected with topology structure, noise intensity, D-DoS frequency and the probability of successful attack. Moreover, on the basis of the criterion, bounds on the attack parameters that can be tolerated and the communication delay are estimated. It is demonstrated that the noise in our work plays a positive role in consensus. Finally, a numerical simulation case for a specific class of robot manipulators is provided to authenticate the feasibility and validity of the theoretical derivations.