A Distributed Cluster Economic Dispatch Scheme for Cross-regional Microgrids Induced by Well-designed Communication Weights

What the math gives to ML

The paper offers a constructive directed-network mechanism: communication weights are designed so that the adjacency matrix has a prescribed Perron eigenvector, with equal centrality values inside each desired cluster. This creates leader-follower multiconsensus rather than forcing every agent into one global consensus, while the non-dominant eigenvalues determine convergence behavior. A transferable neural-network version is a Perron-weighted cluster-consensus optimizer or modular architecture in which replicas or experts share parameters within clusters, preserve distinct cluster-level states, and use spectral constraints to guarantee stable communication updates.