Controllability Metrics, Limitations and Algorithms for Complex Networks

By Fabio Pasqualetti, Sandro Zampieri, Francesco Bullo. IEEE Transactions on Control of Network Systems, 2013

639 citations recorded by the source corpus.

This paper studies the problem of controlling complex networks, i.e., the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem, 1) we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, 2) we derive bounds based on the system dynamics (network topology and weights) to characterize the tradeoff between the control energy and the number of control nodes, and 3) we propose an open-loop control strategy with performance guarantees. In our strategy, we select control nodes by relying on network partitioning, and we design the control input by leveraging optimal and distributed control techniques. Our findings show several control limitations and properties. For instance, for Schur stable and symmetric networks: 1) if the number of control nodes is constant, then the control energy increases exponentially with the number of network nodes; 2) if the number of control nodes is a fixed fraction of the network nodes, then certain networks can be controlled with constant energy independently of the network dimension; and 3) clustered networks may be easier to control because, for sufficiently many control nodes, the control energy depends only on the controllability properties of the clusters and on their coupling strength. We validate our results with examples from power networks, social networks and epidemics spreading.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/924e74ba865401b774960d3388c08b10f3e438d9

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Citations in the corpus

On Submodularity and Controllability in Complex Dynamical Networks (2014, methodology): “have also defined a different network centrality measure based on the controllability Gramian [34].”
Small-World Brain Networks Revisited (2016, background): “But what have we learnt more speciﬁ-cally about brain small-worldness since 2006, and what do we still have to learn?”
Synchronization in complex networks and its application - A survey of recent advances and challenges (2014, background): “Additionally, optimal control theory can also be applied to characterize the relationship between convergence speed, energy cost and features of complex networks (Rugh, 1996), which has been neglected in Yan et al. (2012), Yuan et al. (2013), Pasqualetti et al. (2014).”
Signals on Graphs: Uncertainty Principle and Sampling (2015, background): “As illustrated in [38], the dynamics of the power generators give rise to smooth graph signals, so that the bandlimited assumption is justified, although in approximate sense.”
Minimal Controllability Problems (2013, background): “(See [25], [32]–[34], and [37] for work on this problem.”
Learning in brain-computer interface control evidenced by joint decomposition of brain and behavior (2019, methodology): “Here, we use tools from network control theory to satisfy these conditions [84].”