Controllability of Complex Networks

我们对自然发生或人工系统的理解程度可以通过我们控制它们的能力来观察。越来越多地用于分析的此类系统的一种抽象表示是复杂网络。复杂网络存在于许多领域（例如生物学和网络），这些网络的控制是一个已经开始引起越来越多研究关注的研究课题。虽然工程学提供了开发控制系统的工具，可以迫使系统遵循特定的状态轨迹，但不存在用于控制复杂的、可能自组织的网络的框架。该提案的主要目标是确定复杂网络中可以进行控制的条件，并为网络可控性领域内的示例问题开发控制解决方案。这项研究的新颖之处在于它探索了交互问题的解决方案，即决定控制网络中的哪些节点以及将哪些信号注入选定的网络节点，以实现特定的时间相关目标。 复杂网络的可控性 [1] 导致我们对网络控制问题 (NCP) [2] 进行形式化。早期迹象表明，在多种情况下都可以实现可控性。开发了简单的神经网络控制器；我们建议深度学习和强化学习应该在从[2]中概述的分类法中抽取的 NCP 实例中进行评估。特别令人感兴趣的是基于分布的控制（DbC），这是一类网络控制问题，试图维持网络节点状态的分布接近目标分布；例如，防止社交网络观点变得过于极端。通过分析，我们建议开发类似于景观分析的技术来评估 DbC 难度。通过检查节点影响力和各种网络主题（例如可识别的社区），我们期望对重要结构有更深入的理解。最后，我们将 DbC 视为避免灾难或泡沫的重要方法。在这里，市场由代理人的社交网络支持，这些代理人的行为是相互依赖的。我们的目标是检验 DbC 作为市场控制机制的有效性。 综上所述，该提案将在复杂网络可控性领域做出贡献；最显着的是基于分布的控制领域。首席研究员已经为 NCP 研究界做出了贡献 [2]，并看到了所提出的研究在市场控制应用中的巨大潜力。 [1] Y.-Y。刘，J.-J。斯洛廷，A.-L. Barabsi，“复杂网络的可控性”，《自然》，卷。 473，没有。 7346，第 167173 页，2011 年。 [2] A. Runka 和 T. White，“走向社交网络中影响扩散的智能控制”，社交网络分析与挖掘，卷。 5、没有。 2015 年 1 月。

A measure of our understanding of naturally occurring or artificial systems can be observed in our ability to control them. One abstract representation of such systems that is increasingly been used for analysis is that of a complex network. Complex networks are found in many domains (e.g., Biology and the Web) and the control of these networks is a research topic that has started to draw increasing research attention. While engineering has provided tools for developing control systems which can force a system to follow a particular state trajectory, no framework exists for control of complex, possibly self-organizing, networks. The main objective of this proposal is to identify conditions under which control is possible in complex networks and develop control solutions for exemplar problems within the domain of network controllability. The novelty of this research is in its exploration of the solution to the interacting problems of deciding which nodes in the network to control and which signals to inject into the selected network nodes in order to achieve a particular time dependent objective. Controllability of complex networks [1] led to our formalization of the Network Control Problem (NCP) [2]. Early indications are that controllability is possible in a wide range of scenarios. Simple neural network controllers have been developed; we propose that deep learning and reinforcement learning should be evaluated on exemplar NCP instances drawn from the taxonomy outlined in [2]. Of particular interest is distribution-based control (DbC), a class of network control problem that attempts to maintain the distribution of network node states close to a target distribution; e.g., preventing social network opinions from becoming too extreme. Analytically, we propose the development of techniques similar to landscape analysis to assess DbC difficulty. By examining node influence and various network motifs such as identifiable communities we expect that a deeper understanding of structures of importance will be forthcoming. Finally, we see DbC as an important approach to catastrophe or bubble avoidance. Here, a market place is backed by a social network of agents whose actions are interdependent. Our objective would be to examine the effectiveness of DbC as a market place control mechanism. To summarize, this proposal will make contributions in the area of complex network controllability; most notably in the area of distribution-based control. The principal investigator has already contributed to the NCP research community [2] and sees great potential in the application of the proposed research to market control. [1] Y.-Y. Liu, J.-J. Slotine, and A.-L. Barabsi, “Controllability of complex networks,” Nature, vol. 473, no. 7346, pp. 167173, 2011. [2] A. Runka and T. White, “Towards Intelligent Control of Influence Diffusion in Social Networks,” Social Network Analysis and Mining, vol. 5, no. 1, 2015.