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# Controllability and Networks

Dr. Philipp Hövel:

Research of control has many origins ranging from physics, nonlinear dynamics, and mathematics to engineering and even beyond and accordingly, its applications are manifold. Recently, the question of controllability entered also the interdisciplinary eld of networks. In my presentation, I will discuss an analytical framework to address this question [1]. The goal is to determine the minimal set of controllers, i.e., driver nodes, in an arbitrary complex network with directed links such that any desired state can be realized within the given network topology. The crucial idea is to nd a set of edges that form the functional backbone of the considered network. Based on this decomposition, one can easily identify the nodes best suited for control input by additional driver nodes.

The derivation of the general, algorithmic method will be complemented by considering theoretical network models, e.g., random Erdös-Rényi and scale-free networks, as well as real-world networks. The latter are chosen as examples from social, technological, and biological contexts.

[1] Y.-Y. Liu, J.-J. Slotine, and A.-L. Barabási: Controllability of complex networks, Nature 473, 167 (2011).