Adaptive pinning synchronization of complex networks with a target system subject to external inputs

Abstract

This paper addresses the global pinning synchronization problem of complex networks with a single target system being subject to nonzero external control inputs. When pinning synchronization in such complex networks is achieved, the states of the nodes in the present networks may evolve onto the predesigned trajectory which may not be a solution of the isolated node system as the target system is subject to external control inputs. A challenging in solving the present pinning synchronization problem is that the external inputs acting on the target system are totally unknown to any node within the networks. To realize global pinning synchronization, a kind of fully distributed adaptive coupling law is constructed for each node to guarantee that the states of these nodes can track those of the target system asymptotically when the network topology is undirected. By appropriately constructing a Lyapunov function and using tools from stability theory, some sufficient conditions for achieving global pinning synchronization are obtained. For the case with directed network topology, a class of centralized adaptive coupling laws is designed and utilized to ensure global pinning synchronization.