Distributed Adaptive Cluster Synchronization for Linearly Coupled Nonidentical Dynamical Systems

This brief studies the cluster synchronization problem for networks of linearly coupled systems where the dynamical system models in different clusters are nonidentical. To ensure scalability and reconfigurability of networks, a distributed adaptive law is proposed to update the intra-cluster coupling strengths. Concretely, each system is required to update its own coupling strength with its cluster members, instead of using a common strength for all systems. The adaptive updating law applied by each system depends on relative states with respective to connected cluster members which are locally available information. Moreover, the parameters involved in the adaptive law of each system allow decentralized off-line computations. Both generic linear systems which are partial-state coupled and nonlinear oscillators which are full-state coupled are considered, respectively.

Automated summary

This brief study addresses the cluster synchronization problem in networks of linearly coupled systems with nonidentical dynamical system models in different clusters. By proposing a distributed adaptive law to update the intra-cluster coupling strengths, scalability and reconfigurability of networks are ensured. The results show that this method is applicable to both generic linear systems with partial-state coupling and nonlinear oscillators with full-state coupling.