Resilient consensus of multi-agent systems with time-varying topologies and unmodeled dynamics

Most existing resilient consensus algorithms for multi-agent systems under Byzantine attacks are developed for integrator-type or linear dynamics, rely on a known input-to-state mapping, and impose restrictive graph conditions under time-varying topologies. These limitations hinder their application to nonlinear systems with unmodeled dynamics. This paper studies resilient consensus for nonlinear multi-agent systems over time-varying topologies under Byzantine attacks. The model reference adaptive control framework is enhanced by neural networks and adaptive high-gain terms, so that the residual effects of nonlinearities and unmodeled dynamics are represented as vanishing disturbances in the reference-model dynamics. A zero-order hold model is further introduced to represent topology variations as irregular communication delays over a fixed union graph, thereby enabling consensus analysis via stochastic matrix theory. To characterize the required graph condition, the notion of weak joint robustness is proposed, which focuses on the robustness of the union graph formed by edges that repeatedly appear over bounded intervals, rather than on the structure of the edge set at any instant as in existing notions. This notion is shown to be implied by existing notions, but not vice versa, thereby providing a relaxed robustness characterization for time-varying topologies. Based on this notion, a necessary and sufficient graph condition for achieving resilient consensus under the proposed algorithm is established. Case studies illustrate the effectiveness of the proposed algorithm.