相依网络连锁故障的贪婪控制
Greedy control of cascading failures in interdependent networks
摘要：
复杂系统的控制具有挑战性，因为系统以非线性方式响应控制器，通常包含反馈机制。系统的相互依赖性带来了额外的困难，因为跨系统连接使恶意活动能够在各层之间传播，增加了系统风险。在本文中，我们探讨了相互依赖的网络系统中的级联故障的最优控制的条件。具体来说，我们研究了巴克唐Wiesenfeld沙堆模型纳入控制机制，这会影响级联发生在各个层的频率。这种修改使我们能够探索的临界状态附近的沙堆样的动力学，与超临界区对应的罕见的大级联和亚临界区的特点是频繁的小雪崩。网络之间的拓扑耦合引入了各个层中采用的控制设置的依赖性，导致给定层的控制策略受到其他连接网络中做出的选择的影响。我们发现，在超临界状态下运行的层的最佳控制策略是耦合到一个层在亚临界区中运行，因为这样的条件对应于降低造成雪崩的概率。然而，这种情况描述了一种寄生关系，其中只有一层受益。第二种最优配置是互惠配置，其中两层采用相同的控制策略。这项工作表明，在相互依赖的网络系统中的控制协议需要考虑到系统的高阶组织，不能独立设计，最大限度地提高效益，只为他们的个别层。
英文摘要：
Complex systems are challenging to control because the system responds to the controller in a nonlinear fashion, often incorporating feedback mechanisms. Interdependence of systems poses additional difficulties, as cross-system connections enable malicious activity to spread between layers, increasing systemic risk. In this paper we explore the conditions for an optimal control of cascading failures in a system of interdependent networks. Specifically, we study the Bak-Tang-Wiesenfeld sandpile model incorporating a control mechanism, which affects the frequency of cascades occurring in individual layers. This modification allows us to explore sandpile-like dynamics near the critical state, with supercritical region corresponding to infrequent large cascades and subcritical zone being characterized by frequent small avalanches. Topological coupling between networks introduces dependence of control settings adopted in respective layers, causing the control strategy of a given layer to be influenced by choices made in other connected networks. We find that the optimal control strategy for a layer operating in a supercritical regime is to be coupled to a layer operating in a subcritical zone, since such condition corresponds to reduced probability of inflicted avalanches. However this condition describes a parasitic relation, in which only one layer benefits. Second optimal configuration is a mutualistic one, where both layers adopt the same control strategy. This work demonstrates that control protocols in systems of interdependent networks need to take into account higher-order organization of the system and cannot be designed independently, maximizing benefits only for their individual layers.
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