Distributed Pinning Control: Stabilizing Large Boolean Networks Subjected to Perturbations
研究了用分布式牵制控制策略维持受扰动的大规模布尔网络的稳定性，提出了两种控制器设计方法，大幅降低了计算复杂度，并在类风湿关节炎滑膜成纤维细胞基因网络模型上验证了有效性。
Stability maintenance in systems refers to the capacity to preserve inherent stability characteristics. In this article, stability maintenance of large boolean networks (BNs) subjected to perturbations is investigated using a distributed pinning control (PC) strategy. The concept of edge removal as a form of perturbation is introduced, and several criteria for achieving global stability are established. Two forms of distributed PCs, one implemented before perturbation occurs and the other after, are introduced. It is noteworthy that the designs of the controllers are solely dependent on the system’s in-neighbors. The proposed method significantly decreases the computational complexity, reducing it from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(2^{2|\texttt {V}|})$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(|\texttt {V}|+ |\texttt {E}| + \kappa \cdot 2^{K})$ </tex-math></inline-formula>, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$|\texttt {V}|, |\texttt {E}|$ </tex-math></inline-formula> denotes the cardinality of vertices and arcs of the adjacent graph of BN, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> is the number of the pinning nodes, and K represents the maximum in-degree of the network. In the worst-case scenario, the computational complexity is bounded by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(|\texttt {V}|+ |\texttt {E}| + \kappa \cdot 2^{|\texttt {V}|})$ </tex-math></inline-formula>. To validate the effectiveness of the proposed methods, results from multiple gene networks are presented, including a model representing the human rheumatoid arthritis synovial fibroblast, among which only 12 of the 359 nodes are deemed essential.