关键词: 空天防御, 协同控制, 拓扑异构性, 动力学系统, 节点失效鲁棒性, 李雅普诺夫稳定性

Abstract:

To overcome the limitations of existing cooperative control theories in addressing the topological heterogeneity of military command systems and evaluating the cooperative effectiveness of equipment， this paper proposes a dual-driven dynamic modeling framework that integrates local neighborhood cooperation and global command traction. The framework systematically reveals the quantitative influence law of the coupling mechanism of network topological parameters on the system-level cooperative performance. By constructing matrix-form differential equations to uniformly describe the dynamic behaviors of three typical combat topologies， namely fully-connected， star-shaped， and ring-shaped， the global asymptotic stability and the uniqueness of the equilibrium point of the system under undirected connected topological configurations are strictly proved， and an explicit relationship between algebraic connectivity and convergence rate is established. According to the simulation examples， the cooperative effectiveness indicators and internal laws under different topological configurations are analyzed in detail， and the system robustness under phased target traction， link failure， and node failure is investigated. The research results can provide useful references for improving the global cooperative effectiveness of heterogeneous equipment groups in complex combat systems， and provide computable theoretical tools for the topological optimization and adaptive control of aerospace defense systems.

Key words: aerospace defense, cooperative control, topological heterogeneity, dynamical systems, node failure robustness, Lyapunov stability