Practical bipartite flocking and velocity alignment in quasi-structurally balanced signed networks under malicious attacks
摘要
Practical bipartite flocking for second-order multi-agent systems over signed cooperation–competition networks under malicious node attacks is studied in this paper. A leader–follower Cucker–Smale model is considered, in which malicious neighbors are first screened by a gauge-lifted, trimmed, substochastic detector and the resulting normal-agent network is required to retain a quasi-structural balance pattern. To describe this detector-induced resilience, a compact residual-graph certificate is used, and graph-theoretic sufficient conditions are derived to guarantee that the residual signed structure remains usable. On the dynamics side, a gauge-based contraction analysis is developed, by which the signed closed-loop system is turned into a tractable absolute-value form and an explicit practical (non-zero-radius) velocity-alignment bound is obtained. It is shown that quasi-structural balance guarantees practical bipartite velocity alignment rather than full flocking with spatial cohesion, while structural balance is recovered as a special case yielding exact bipartite flocking. It is also quantified how imperfect screening enlarges the residual deviation. The distributed screening rule is summarized as a per-agent algorithm whose per-step cost is linear in the number of communication links. Theoretical results are supported by numerical studies on 24-agent structurally balanced, quasi-structurally balanced, non-balanced, detector-isolated, leakage-perturbed, and large-scale signed-network settings, including detector diagnostics and an explicit comparison between the theoretical bounds and the observed steady-state errors.