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

Abstract: Aiming at the limitations of existing cooperative control theories in addressing topological heterogeneity in military command architectures and evaluating equipment collaborative effectiveness, this paper proposes a dual-driven dynamic modeling framework that integrates local neighborhood coordination and global command guidance. This framework systematically reveals the quantitative impact of coupled network topology parameters on system-wide collaborative performance. By constructing matrix-form differential equations to uniformly characterize the dynamic behaviors of three typical combat topologies (fully-connected, star, and ring), the study rigorously proves the global asymptotic stability and existence-uniqueness of equilibrium points in undirected connected topologies, while establishing an explicit relationship between algebraic connectivity and convergence rate. Numerical simulations are conducted to analyze collaborative effectiveness metrics and their inherent patterns under different topological configurations. The results demonstrate that the proposed methodology provides valuable insights for enhancing global collaborative efficiency of heterogeneous equipment groups in complex combat systems, offering computable theoretical tools for topology optimization and adaptive control in aerospace defense systems. This work contributes a unified analytical framework for addressing multi-topology interactions in military applications, with particular significance for air defense coordination, anti-missile networks, and unmanned swarm control.

Key words: Aerospace Defense,, Cooperative Control,, Topological Heterogeneity,, Dynamical Systems,, Lyapunov Stability