THE ACTUATION SPECTRUM OF SPATIOTEMPORAL NETWORKS WITH POWER-LAW TIME DEPENDENCIES

Qi Cao, Guilherme Ramos (), Paul Bogdan () and Sérgio Pequito ()
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Qi Cao: Department of Industrial and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
Guilherme Ramos: Institute for Systems and Robotics, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
Paul Bogdan: Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA
Sérgio Pequito: Department of Industrial and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

Advances in Complex Systems (ACS), 2020, vol. 22, issue 07n08, 1-19

Abstract: The ability to steer the state of a dynamical network towards a desired state within a time horizon is intrinsically dependent on the number of driven nodes considered, as well as the network’s topology. The trade-off between time-to-control and the minimum number of driven nodes is captured by the notion of the actuation spectrum (AS). We study the actuation spectra of a variety of artificial and real-world networked systems, modeled by fractional-order dynamics that are capable of capturing non-Markovian time properties with power-law dependencies. We find evidence that, in both types of networks, the actuation spectra are similar when the time-to-control is less or equal to about 1/5 of the size of the network. Nonetheless, for a time-to-control larger than the network size, the minimum number of driven nodes required to attain controllability in networks with fractional-order dynamics may still decrease in comparison with other networks with Markovian properties. These differences suggest that the minimum number of driven nodes can be used to determine the true dynamical nature of the network. Furthermore, such differences also suggest that new generative models are required to reproduce the actuation spectra of real fractional-order dynamical networks.

Keywords: Complex networks; control theory; fractional calculus and dynamical systems; network controllability; minimum number of driven nodes (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219525919500231

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