Unified Adaptive Consensus Framework for Fractional-Order Multi-Agent Systems Under Mixed Communication Delays and Denial-of-Service Attacks

Abstract

This paper investigates the resilient leader–follower consensus problem for a class of memory-dependent fractional-order multi-agent systems (FOMASs) with mixed communication delays, uncertain nonlinear dynamics, norm-bounded parametric uncertainties, and intermittent Denial-of-Service (DoS) attacks. The goal is to ensure that the follower agents follow the leader’s path even in the event of weak links, network changes, and lost communications. An adaptive radial basis function neural network (RBFNN) is used as an online approximator to cover the unmodeled nonlinearity. The two complementary delay configurations studied are a discrete-delay protocol, which features a fixed delay on the state, communication channel, and control input; and a distributed-delay protocol, which carries a memory of past states on the control input but a cumulative memory of past states on the DoS-induced input disturbance. In both scenarios, adequate linear matrix inequality (LMI) conditions are obtained in a Lyapunov–Razumikhin stability setting ensuring leader-following consensus, plus a less demanding version of the LMI conditions expressed in terms of eigenvalues, tailored for Kronecker-structured, large-scale networks. A condition of an average dwell-time is used to establish an average condition on the frequency of DoS attack to certify the robustness against intermittent communication disruption. The effectiveness of the proposed RBFNN-based resilient consensus framework is demonstrated by numerical simulation on a network of six followers, with the discrete-delay and distributed-delay configurations each validated separately; the scalability of the eigenvalue-based feasibility-verification test relative to the full LMI synthesis is examined with growing network size, and an ablation study is carried out to isolate the effect of the RBFNN compensation and the dwell-time-consistent gain design. The fully combined discrete-and-distributed-delay case is formulated but not numerically simulated in this work.