Controllability of Complex Networks

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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.