Open AccessSynchronisation for multi‐network with two types of inter‐network coupling faults: pinning control effects
Author(s) -
Ren Tao,
Sun Shixiang,
YanJie Xu,
Zhe Li,
Wang Ranran,
Cheng Xiaoyan,
Dimirovski Georgi Marko
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.0842
Subject(s) - lyapunov stability , coupling (piping) , control theory (sociology) , complex network , controller (irrigation) , computer science , stability (learning theory) , dimension (graph theory) , topology (electrical circuits) , control (management) , mathematics , engineering , artificial intelligence , mechanical engineering , agronomy , combinatorics , machine learning , world wide web , pure mathematics , biology
Investigation of simultaneous occurrence of permanent and/or recoverable faults of coupled nodes within different networks in a larger network structure is an appealing timely research topic. For the modelling of such a multi‐network structure, the coupling terms in the same network and the coupling terms among different networks are described separately in order to explain clearly the multi‐network feature here. The dimension‐transformation matrix is used to deal with the mismatched dimensions of nodes in the different networks. Then a synchronisation controller is designed from the underlying theory of pinning control schemes. Furthermore, following the ideas of Lyapunov stability theory, a sufficient stability condition under the pinning control is derived which guarantees nodes in the same network synchronisation. Computer simulation results for a numerical case study of three coupled networks with nodes that possess rather complex non‐linear dynamics demonstrate that the proposed controllers can enforce synchronisation despite different types of faults being occurred in the multi‐network. It is also shown that the specific pinning control scheme is more effective than the random pinning.