Journal
ANNUAL REVIEWS IN CONTROL
Volume 53, Issue -, Pages 147-160Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.arcontrol.2022.04.005
Keywords
Network dynamical systems; Synchronization; Pinning control; Coevolving networks
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Funding
- University of Naples Federico II, Italy and Compagnia di San Paolo, Istituto Banco di Napoli -Fondazione, Italy, project ACROSS
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This manuscript presents a mathematical model of coevolving networks and studies the conditions for synchronization and pinning control. The theoretical results are applied to design synchronization and pinning control protocols in two specific applications.
Network dynamical systems are often characterized by the interlaced evolution of the node and edge dynamics, which are driven by both deterministic and stochastic factors. This manuscript offers a general mathematical model of coevolving network, which associates a state variable to each node and edge in the network, and describes their evolution through coupled stochastic differential equations. We study the emergence of synchronization, be it spontaneous or induced by a pinning control action, and provide sufficient conditions for local and global convergence. We enable the use of the Master Stability Function approach for studying coevolving networks, thereby obtaining conditions for almost sure local exponential convergence, whereas global conditions are derived using a Lyapunov-based approach. The theoretical results are then leveraged to design synchronization and pinning control protocols in two select applications. In the first one, the edge dynamics are tailored to induce spontaneous synchronization, whereas in the second the pinning edges are activated/deactivated and their weights modulated to drive the network towards the pinner's trajectory in a distributed fashion.
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