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Lag consensus is an essential dynamic behavior in nature and practical systems, which means that the trajectory of followers lags behind the leader owing to a track time-delay. In this paper, the lag consensus problem under event-triggered control is investigated for leader-following multi-agent systems with nonlinear dynamics. A novel static event-triggered control strategy based on combined measurement is presented to avoid continuous information interaction between agents by introducing a track time-delay. It should be emphasized that this control protocol is fully distributed, that is, the global information in the network is not involved. In addition, for each agent, the information transmission and the updates of control protocol only arise at its own triggering instants. Based on stability theory, a sufficient condition is derived for leader-following multi-agent systems with nonlinear dynamics to achieve lag consensus. Moreover, it is exhibited that Zeno behavior is excluded by proving the existence of a positive lower bound for the triggering interval. Finally, the correctness of theoretical results is verified via numerical simulations. [ABSTRACT FROM AUTHOR]

Firstly, the definition of clustering component synchronization is given (that is, all nodes in each cluster realize partial component synchronization). Then, both stability theory and matrix analysis are used to study the group dynamics of a class of unconnected networks via pinning control. Furthermore, a sufficient condition on clustering component synchronization in the network is derived, and the correctness of the theoretical results is verified by numerical simulation. The advantage of the control scheme is that, by adjusting the dynamics of a very small number of pinning nodes, some clusters can be merged in the network, and then the presetting synchronous patterns can emerge. Compared with cluster synchronization and partial component synchronization, clustering component synchronization is a weaker group dynamics behavior. • The definition of clustering component synchronization is given for the first time. • Clustering component synchronization is a weaker group dynamics behavior. • A sufficient condition for clustering component synchronization is derived. [ABSTRACT FROM AUTHOR]

The multiagent system has the advantages of simple structure, strong function, and cost saving, which has received wide attention from different fields. Consensus is the most basic problem in multiagent systems. In this paper, firstly, the problem of partial component consensus in the first-order linear discrete-time multiagent systems with the directed network topology is discussed. Via designing an appropriate pinning control protocol, the corresponding error system is analyzed by using the matrix theory and the partial stability theory. Secondly, a sufficient condition is given to realize partial component consensus in multiagent systems. Finally, the numerical simulations are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Partial component consensus means that some components of all state variables in a multi-agent system tend to be convergence as time tends to be infinite. It is a dynamics behavior that is weaker than identical consensus. In this paper, partial component consensus of nonlinear multi-agent systems via intermittent pinning control is investigated for the first time, and the intermittent signal can be aperiodic. With the help of permutation matrix method, the corresponding error system is reduced to a new error system. Then, partial component consensus in the multi-agent system is converted into the stability of the new error system with respect to partial variables. Based on matrix theory, graph theory and stability theory of partial variables, some sufficient conditions to guarantee exponential partial component consensus are derived. Finally, numerical simulations are shown to demonstrate correctness of the theoretical results. • Partial component consensus dependence on exponential partial variable stability is discussed for the first time. • The internal communication network between agents is a directed graph. • Aperiodically and periodically intermittent pinning control are taken into account, respectively. • Some novel criteria for partial component consensus via intermittent pinning control protocols are derived. [ABSTRACT FROM AUTHOR]

Successive lag synchronization (SLS) is a novel and important synchronization pattern, whose control problem has been deeply investigated in the past several years. However, the impact of noise perturbation on the control of SLS is still unclear. To this end, this paper focuses on the intermittent pinning control of SLS on a dynamical network with noise perturbation. In order to push the SLS to a desired trajectory, we design an intermittent pinning control scheme that is active only on controlled intervals and a small proportion of nodes. By applying the stability theory of stochastic differential equation, we obtain sufficient conditions under which the network can realize the SLS with exponential stability in mean square. According to these conditions, we can determine which nodes should be controlled or not, the minimum control ratio and the impact of noise perturbation on the SLS. An interesting finding is that performing the control on at least half of each subinterval can ensure the stochastic stability of SLS, which is independent of any network parameters. The effectiveness of proposed intermittent pinning control scheme is verified by the network of coupled Chua's circuits. [ABSTRACT FROM AUTHOR]

Partial component consensus is a phenomenon that some components of agents reach identity, but the others components are not the same. In this paper, the partial component consensus problem of second-order and third-order nonlinear multi-agent systems has been investigated. Some concepts and results of partial component consensus are given through partial component stability theory and pinning control protocol. Numerical simulations are finally given to verify the theoretical results. • Investigating the partial component consensus problems in second-order and third-order nonlinear leader-following systems. • Deriving some sufficient conditions of partial component consensus for high-order multi-agent systems. • Illustrating the effectiveness of the results through second-order and third-order systems. [ABSTRACT FROM AUTHOR]

In recent years, the successive lag synchronization (SLS) has been deeply analyzed, however, the control theory of SLS on complex networks with noise perturbation is lacking. To this end, this paper focuses on the pinning control of SLS on a dynamical network with noise perturbation. Both the constant pinning control law and adaptive pinning control law are designed respectively to push the network to achieve the desired SLS. By utilizing the Lyapunov stability theory of stochastic differential equations, several sufficient conditions for the controlled networks to achieve the SLS are obtained. The influences of network structure, noise strength and coupling strength on the realization of SLS are also discussed. We find that the noise can suppress or even destroy the realization of SLS. Meanwhile, we attain the index set of pinned nodes, which can tell us whether a node should be controlled or not. In particular, those nodes with zero in-degree must be controlled to achieve SLS, while those nodes with non-zero in-degree need not to be controlled if the coupling strength is large enough. All theoretical results are verified by numerical simulations. • A dynamical network with noise perturbation is introduced to realize the SLS. • Stochastic stability conditions of SLS on the controlled networks are obtained. • The noise can suppress or even destroy the SLS. • The pinned nodes are determined by solving 1-dimensional inequalities. [ABSTRACT FROM AUTHOR]