The optimal selection of pinning nodes for multi-agent flocking is a challenging NP-hard problem. Current pinning node selection strategies mainly rely on centrality measures of complex networks, which lack rigorous mathematical proof for effective flocking control. This paper proposes a pinning node selection strategy based on matrix eigenvalue theory. First, the effect of the pinning node on the eigenvalue of the Laplacian matrix is analyzed. Then, a synchronization index representing the topology uniformity of the multi-agent system is proposed to exert maximum influence on the system synchronizability. A practical optimal pinning node selection method based on the synchronization index is proposed and analyzed using the eigenvalue perturbation method. Finally, simulations demonstrate that the convergence rate of the system obtained using the optimal synchronizability pinning node selection method is better than that achieved with the maximum degree centrality node selection strategy.

In GPS-denied environments, the spatio-temporal coupling of errors caused by dynamic network topologies poses a fundamental challenge to cooperative localization, presenting existing methods with a dilemma: approaches pursuing global optimization lack dynamic adaptability, while those focusing on local adaptation struggle to guarantee global convergence. To address this challenge, this paper proposes ST-DCL, a cooperative localization framework based on a novel principle of closed-loop spatio-temporal decoupling. The core of ST-DCL comprises two modules: a Dynamic Weighted Multidimensional Scaling (DW-MDS) optimizer, responsible for providing a globally consistent coarse estimate with provable convergence, and a specially designed Spatio-Temporal Graph Neural Network (ST-GNN) corrector, tasked with compensating for local nonlinear errors. The DW-MDS effectively suppresses interference from historical errors via an adaptive sliding window and confidence weights derived from our error propagation model. The key innovation of the ST-GNN lies in its two newly designed components: a Dynamic Topological Attention Module for actively modulating neighbor aggregation to inhibit spatial error diffusion, and a Dilated Causal Convolution Module for modeling long-term temporal dependencies to curb error accumulation. These two modules form a closed loop via a confidence feedback mechanism, working in synergy to achieve continuous error suppression. Theoretical analysis indicates that the framework exhibits bounded-error convergence under dynamic topologies. In simulations involving 200 nodes, velocities up to 50 m/s, and 15% NLOS links, the ST-DCL achieves a normalized root mean square error (NRMSE) of 0.0068, representing a 21% performance improvement over state-of-the-art methods. The practical efficacy and real-time capability are further validated through real-world flight experiments with a 10-UAV swarm in complex, GPS-denied scenarios.