Synchronisation for multi‐network with two types of inter‐network coupling faults: pinning control effects
Tao Ren, Shixiang Sun, Xu YanJie, Zhe Li, Ranran Wang, Xiaoyan Cheng, Georgi Marko Dimirovski · IET Control Theory and Applications · 2020
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.