用于选择大规模网络系统控制节点的可控性分数
Controllability scores for selecting control nodes of large-scale network systems
AI总结：
针对大规模网络系统的控制节点选择问题，提出基于可控性 Gramian 凸优化的体积与平均能量可控性分数，并用投影梯度算法高效求解，实验证明其效率和节点重要性识别效果更优。
摘要：
为恰当地选择大规模网络系统的控制节点，我们提出了两种控制中心性，分别称为体积可控性分数和平均能量可控性分数。这些分数是利用可控性 Gramian 构建的凸优化问题的唯一解。其唯一性在稳定情形以及包含多智能体系统的不稳定情形中均得到证明。我们表明，通过使用所提出的、基于到标准单纯形上投影梯度法的算法，可以高效计算这些分数。数值实验表明，所提算法比现有内点法更高效，并且所提分数能够正确捕捉每个状态节点在可控性方面的重要性，优于现有的控制中心性。
英文摘要：
To appropriately select control nodes of a large-scale network system, we propose two control centralities called volumetric and average energy controllability scores. The scores are the unique solutions to convex optimization problems formulated using the controllability Gramian. The uniqueness is proven for stable cases and for unstable cases that include multi-agent systems. We show that the scores can be efficiently calculated by using a proposed algorithm based on the projected gradient method onto the standard simplex. Numerical experiments demonstrate that the proposed algorithm is more efficient than an existing interior point method, and the proposed scores can correctly capture the importance of each state node on controllability, outperforming existing control centralities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
