Recently, some researchers investigated the topology identification for complex networks via LaSalle's invariance principle. The principle cannot be directly applied to time-varying systems since the positive limit sets are generally not invariant. In this paper, we study the topology identification problem for a class of weighted complex networks with time-varying node systems. Adaptive identification laws are proposed to estimate the coupling parameters of the networks with and without communication delays. We prove that the asymptotic identification is ensured by a persistently exciting condition. Numerical simulations are given to demonstrate the effectiveness of the proposed approach. © 2010 American Institute of Physics. ͓doi:10.1063/1.3421947͔The topology identification, as an inverse problem, is a significant issue in the study of complex networks. For example, if a major malfunction occurs in a communication network, power network, or the Internet, it is very important to quickly detect the location of the faulty line. This paper proposes a novel adaptive identification approach for the topology identification of the weighted complex dynamical networks. We show that the concept of persistent excitation plays a key role in the process of topology identification. Our result overcomes the limitation of previous methods, which rely on the use of LaSalle's invariance principle, and is applicable to networks with time-varying node systems and diverse time-varying coupling delays.

Inspired byVicsek's model, in this paper we propose two decentralized heading consensus algorithms for nonlinear multi-agent systems. The first algorithm, called WHCA, can be seen as a weighted Vicsek's model. The second algorithm, named LBHCA, is a leader-follower strategy based on the WHCA. It is proved that, under a well-known connectivity assumption, the algorithm WHCA can ensure almost global consensus of the headings, except for the situation where they are initially balanced. For the LBHCA, the global heading consensus is guaranteed under the same connectivity assumption. Simulation results are provided to justify the proposed algorithms.

This paper proposes relaxed sufficient conditions for the consensus of multi-agent systems by the averaging protocols with time-varying system topology. Bidirectional information exchange between neighboring agents is considered and both the discrete-time and continuous-time consensus protocols are studied. It is shown that the consensus is reached if there exists an unbounded time sequence such that two agents who own the maximum and minimum states at each time instant in the sequence will be jointly connected at some future time. Further, this result is applied to the original nonlinear Vicsek model, and a sufficient condition for the heading consensus of the group with restricted initial conditions is obtained.