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This paper investigates the problem of synchronization in complex dynamical networks. Based on the stability theory for impulsive differential equations, an impulsive control scheme is proposed to achieve impulsive synchronization for complex dynamical networks with unknown coupling. The synchronization strategy considers the influence of all nodes in the dynamical network and the effect intensity of every node to network synchronization relies on its weight in the network. For practical problems, by choosing appropriately the weights of the nodes in the network, network synchronization can be achieved by only a few useful nodes. Simulated examples are provided by using the chaotic Chua system as nodes of the dynamical network, and the effectiveness of the proposed impulsive control are demonstrated.

In this article, a new method, which constructs a coupling scheme with cooperative and competitive weight-couplings, is used to stabilize arbitrarily selected cluster synchronization patterns with several clusters for connected chaotic networks. By the coupling scheme, a sufficient condition about the global stability of the selected cluster synchronization patterns is derived. That is to say, when the sufficient condition is satisfied, arbitrarily selected cluster synchronization patterns in connected chaotic networks can be achieved via an appropriate coupled scheme. The effectiveness of the method is illustrated by an example.

It is well known that nonlinear multi-agent systems (MASs) with a directed topology can reach a consensus if the global coupling coefficient is strong enough. In this paper, we propose a novel distributed protocol based on the subgroup structure. Our results demonstrate that the MAS design can follow a part-to-whole approach, starting with subgroups and gradually building up to a more complex system. We firstly consider two cases for the MASs: one with a single leader and one with a leader group, where agents within the leader group can communicate with each other, but cannot receive the information of other group. We show that followers can track the leader or group leaders if intra-coupling within the subgroup and information strength received by the root node are above a certain threshold. Next, we investigate cluster consensus and practical cluster consensus for the Laplacian matrix with unequal row sum, equal row sum, and mixing of partitioned matrices. Our results reveal that row sum and community structure of the partitioned matrix are crucial in determining the final state of each agent. Our proposed control protocol is highly flexible and relies only on the cluster structure and information received by the root node, rather than global information. Moreover, our method is not limited to tracking problems, cooperative control, or multi-objective control, and can accommodate new group agents joining the system, making it highly adaptable. We provide illustrative examples to demonstrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Aiming to solve the cluster lag consensus (CLC) problem of networked nonlinear agents with a switching topologies, this paper proposes a control algorithm based on the measurements of position and velocity. When the network has several clusters of agents, under the conditions that each cluster is a strongly connected digraph including isolated agents, and at least one agent in each cluster can communicate with the common leader each time, a sufficient condition is derived for reaching CLC. Finally, a numerical simulation is demonstrated to validate the proposed control algorithm and the developed conditions. [ABSTRACT FROM AUTHOR]

In this article, the problem of cluster synchronization in the complex networks with nonidentical nonlinear dynamics is considered. By Lyapunov functional and M-matrix theory, some sufficient conditions for cluster synchronization are obtained. Moreover, the least number of nodes which should be pinned is given. It is shown that when the root nodes of all the clusters are pinning-controlled, cluster synchronization with adaptive coupling strength can be achieved. Different from the constraints of many literatures, the assumption is that each row sum for all diagonal submatrices of the Laplacian matrix is equal to zero. Finally, a numerical simulation in the network with three scale-free subnetwork is provided to demonstrate the effectiveness of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 380-387, 2016 [ABSTRACT FROM AUTHOR]

Lag consensus is a phenomenon where followers track the trajectory of the leader with a time delay. By using lag consensus, a protocol is designed for agents to behind the leader at different times, so as to avoid congestion. In this paper, aiming to the lag consensus of second-order nonlinear multi-agent systems, a control protocol for each follower based on local information of neighboring agents is proposed, and an adaptive feedback control protocol is also given. Moreover, the multi-agent systems with noisy environment are considered. The results suggest that our protocol is robust to the noise. Finally, simulation examples are given to illustrate our theoretical analysis. [ABSTRACT FROM AUTHOR]