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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]

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]

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]

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]

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]

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]