Controllability of Complex Networks

我们对自然发生的或人工的系统的理解程度可以从我们控制它们的能力中观察到。这种系统越来越多地被用于分析的一种抽象表示是复杂网络的表示。复杂网络存在于许多领域(如生物学和网络)，对这些网络的控制已经开始引起越来越多的研究关注。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，但还不存在控制复杂的、可能是自组织的网络的框架。这项建议的主要目标是确定在复杂网络中可能进行控制的条件，并针对网络可控性领域内的典型问题开发控制解决方案。这项研究的新颖性在于它探索了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依赖目标的交互问题的解决方案。 复杂网络的可控性[1]导致了我们对网络控制问题(NCP)的形式化[2]。早期迹象表明，可控性在许多情况下都是可能的。简单的神经网络控制器已经开发出来；我们建议深度学习和强化学习应该在从[2]中概述的分类中提取的样本NCP实例上进行评估。特别感兴趣的是基于分布的控制(DBC)，这是一类网络控制问题，其试图将网络节点状态的分布保持在接近目标分布的位置；例如，防止社交网络观点变得过于极端。在分析方面，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，如可识别的社区，我们预计将对重要结构有更深的理解。最后，我们认为DBC是避免灾难或泡沫的重要途径。在这里，一个市场是由一个由代理人组成的社会网络支持的，这些代理人的行为是相互依赖的。我们的目标是研究DBC作为一种市场监管机制的有效性。 总而言之，这项提议将在复杂网络可控性领域做出贡献；最显著的是在基于分布式的控制领域。首席研究员已经为NCP研究界做出了贡献[2]，并看到了将拟议的研究应用于市场控制的巨大潜力。 [1]刘永元，J.J.斯洛廷，A.-L.巴拉布西，《复杂网络的可控性》，《自然》，第473卷，第7346期，167173页，2011年。 [2]A.Runka和T.White，《走向社会网络中影响力扩散的智能控制》，《社会网络分析与挖掘》，第5卷，第1期，2015年。

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.