AI 中文总结
针对矩阵加权网络强结构可控性的最小领导者选择这一NP-难问题，本文提出含三类破对称算法的两阶段数学框架，经理论证明与数值评估验证了方法的有效性。
AI 中文摘要
选择最小领导者集以保证矩阵加权网络的强结构可控性（SSC）的逆综合问题仍是未解决的NP-难挑战。本文提出严格数学框架求解该问题，证明结构不可控性仅源于维度特定的可达性孤立和拓扑对称等价性。为克服这些瓶颈，本文构建两阶段综合方法：首先通过可达性前提识别结构根，再采用三种不同的破对称算法（贪心Weisfeiler-Lehman选择、子模边界最大化、划分熵最大化）。数学证明保证该方法对不变子空间和结构扩张的免疫性，且通过不同拓扑下的大量数值评估验证了其有效性。
英文摘要
The inverse synthesis problem of selecting a minimal leader set to guarantee strong structural controllability (SSC) in matrix-weighted networks remains an unresolved NP-hard challenge. This paper proposes a rigorous mathematical framework to solve this. We prove that structural uncontrollability stems exclusively from dimension-specific reachability isolation and topological symmetry equivalence. To overcome these bottlenecks, we formulate a two-phase synthesis: a reachability prerequisite to identify structural roots, followed by three distinct symmetry-breaking algorithms (Greedy Weisfeiler-Lehman Selection, Submodular Bound Maximization, and Partition Entropy Maximization). Mathematical proofs guarantee immunity to invariant subspaces and structural dilation, validated by extensive numerical evaluations across diverse topologies.
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