Controllability of Complex Networks

我们对自然发生或人工系统的理解程度可以从我们控制它们的能力中观察到。越来越多地用于分析的这种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）和控制这些网络是一个研究课题，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，但不存在控制复杂的、可能自组织的网络的框架。这个建议的主要目标是确定条件下，控制是可能的，在复杂的网络和开发控制解决方案的范例问题的域内的网络可控性。本研究的新奇在于其探索的解决方案，以决定哪些节点在网络中控制和信号注入到选定的网络节点，以实现一个特定的时间相关的目标的相互作用的问题。 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]。早期的迹象表明，可控性是可能的，在广泛的情况。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示例NCP实例上进行评估。特别令人感兴趣的是基于分布的控制（DbC），这是一类试图保持网络节点状态的分布接近目标分布的网络控制问题;例如，防止社交网络上的观点变得过于极端。在分析上，我们提出了类似于景观分析技术的发展，以评估DbC的难度。通过研究节点的影响力和各种网络图案，如可识别的社区，我们预计，更深入地了解结构的重要性将即将到来。最后，我们认为DbC是避免灾难或泡沫的重要方法。在这里，一个市场是由一个社会网络的代理人的行动是相互依赖的。我们的目标是检查DbC作为市场控制机制的有效性。 总而言之，这个建议将在复杂网络可控性领域做出贡献;最值得注意的是在基于分布的控制领域。首席研究员已经为NCP研究社区做出了贡献[2]，并看到了将拟议研究应用于市场控制的巨大潜力。 [1]Y.-- Y.刘杰- J. Slotine和A.- L. Barabsi，“Controllability of complex networks，”Nature，vol. 473，no. 7346，pp. 167173，2011年。 [2]A. Runka和T.白色，“走向智能控制的影响力扩散在社交网络，”社会网络分析和挖掘，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.