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Summary: Event‐triggered consensus of multi‐agent systems (MASs) under directed topology is investigated in this paper. First, one shortcoming about the event‐trigger conditions in some recent results is pointed out through a counterexample. Then, two reasonable event‐trigger conditions are proposed and analyzed. Meanwhile, a novel dynamic event‐trigger strategy is applied in the two designed event‐trigger conditions, in which an auxiliary term is introduced for each agent to regulate its threshold dynamically. It is proved that the dynamic term plays an essential role in excluding Zeno behavior. The case of strongly connected topology is first investigated. Then, the results are extended to the more general topology containing a spanning tree. Numerical example is provided to illustrate the effectiveness of the designed event‐trigger conditions. [ABSTRACT FROM AUTHOR]

Consensus of multi-agent systems (MASs) with general linear dynamics is investigated. In order to reduce communication frequency and avoid dependence on global information, adaptive event-triggered strategy is applied. A kind of dynamic event-triggered strategy, which is more flexible in giving event-trigger threshold, is proposed. An event-trigger condition based on continuous relative measurement is first designed. Then, the event-trigger condition is improved to only utilize event-triggered information. Sufficient criteria are derived to guarantee consensus. Moreover, it is proved that the designed event-trigger conditions can exclude Zeno behavior. Numerical simulation is performed to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper constructs a lower dimensional multi-agent system (MAS) utilizing the structural decomposition of system matrix. Through equivalent transformation, it has been proven that the sampling controllability of the original system is inherited by the lower dimensional system, allowing us to further obtain a criterion for determining the sampling controllability based on topology structure and sampling period. The paper also applies state feedback to the protocol design of MAS during the sampling period, achieving that the sampled-data MAS can still maintain controllability in uncontrollable topologies, and controllability is unaffected by the sampling period. Finally, numerical examples are provided for verification. [ABSTRACT FROM AUTHOR]

This article investigates the controllability of path and star graphs under the protocol of second-order neighbours. With identified special control nodes, a sufficient condition is first derived for the controllability of path graph by taking advantage of the protocol of second-order neighbours. Then necessary and sufficient conditions are developed respectively for the single and multiple leaders. Some differences between the protocol of second-order neighbours and first-order neighbours are also presented for path graph. Finally, a necessary and sufficient condition is proposed for the controllability of star graph by taking advantage of the protocol of second-order neighbours. [ABSTRACT FROM AUTHOR]

The event-triggered consensus problems of multi-agent systems without and with time delay under directed topology are investigated, respectively. The event-checkings are only implemented at periodic time instants. Under the designed consensus algorithm, the sampling period is permitted to be arbitrarily large. Another advantage of the designed consensus algorithm is that, for systems with time delay, consensus can be achieved for any finite delay only with the requirement that it is bounded by the sampling period. The case of strongly connected topology is first investigated. Then, the result is extended to the most general topology which only needs to contain a spanning tree. A novel method based on positive series is introduced to analyze the convergence of the closed-loop systems. A numerical example is provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, event-triggered leader-following consensus of general linear multiagent systems under both fixed topology and switching topologies is studied. First, centralised and decentralised event-triggered control strategies based on neighbors' state estimation are proposed under fixed topology, in which the controller is only updated at the time of triggering. Obviously, compared with the continuous time control algorithms, the event-triggered control strategies can reduce the communication frequency among agents effectively. Meanwhile, event-triggering conditions are derived for systems to achieve consensus by using the Lyapunov stability theory and model transformation method. Then, the theoretical results obtained under the fixed topology are extended to the switching topologies, and the sufficient conditions for the system to achieve leader-following consensus under the switching topologies are given. However, different from fixed topology, the control input of each agent is updated both at event-triggering and topology switching time. Finally, Zeno behaviors can be excluded by proving that the minimum triggering interval of each agent is strictly positive, and the effectiveness of the event-triggered protocol is verified by simulation experiments. [ABSTRACT FROM AUTHOR]

In this paper, the optimal topology structure is studied for hybrid-weighted leader-follower multiagent systems (MASs). The results are developed by taking advantage of linear quadratic regulator (LQR) theory. We show that the multiagent star composite structure is the optimal topology which can enable the MAS to achieve the bipartite consensus. In particular, we prove that the optimal topology corresponding to the multiagent system with the first-order static leader and the second-order dynamic leader is, respectively, a hybrid-weighted star composite structure and an unevenly hybrid-weighted star composite structure. The results of the paper indicate that, in addition to the necessary information communication between leader and followers, the information exchange among followers increases the control cost of the system. [ABSTRACT FROM AUTHOR]

This paper studies the controllability of multiagent systems based on path and cycle graphs. For paths or cycles, sufficient and necessary conditions are presented for determining the locations of leaders under which the controllability can be realized. Specifically, the controllability of a path is shown to be determined by a set generated only from its odd factors, and the controllability of a cycle is determined by whether the distance between 2 leaders belongs to a set generated from its even (odd) factors when the number of its nodes is even (odd). For both graphs, the dimension of the controllable subspace is also derived. Moreover, the technique used in the derivation of the above results is further used to get sufficient and necessary conditions for several different types of graphs generated from path and cycle topologies. These types of graphs can be regarded as typical topologies in the study of multiagent controllability, and accordingly the obtained results have meaningful enlightenment for the research in this field. [ABSTRACT FROM AUTHOR]

In this paper, the controllability of multi-agent systems is studied under leader-follower framework, where the interconnection between agents is directed. The concept of leader-follower connectedness is first introduced for directed graph to check controllability, and some graph-theoretic conditions are derived for constructively designed topologies. Then, distance partition and almost equitable partition are employed to quantitatively study the controllable subspaces. Moreover, the relationship between the state invariance of multi-agent systems and the existence of almost equitable partition is discussed. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Recently, graphical characterization of multiagent controllability has been studied extensively. A major effort in the study is to determine controllability directly from topology structures of communication graphs. In this paper, we proposed the concept of controllability destructive nodes, which indicates that the difficulty in graphical characterization turns out to be the identification of topology structures of controllability destructive nodes. It is shown that each kind of double and triple controllability destructive nodes happens to have a uniform topology structure which can be defined similarly. The definition, however, is verified not to be applicable to the topology structures of quadruple controllability destructive (QCD) nodes. Even so, a design method is proposed to uncover topology structures of QCD nodes for graphs with any size, and a complete graphical characterization is presented for the graphs consisting of five vertices. One advantage of the established complete graphical characterization is that the controllability of any graph with any selection of leaders can be determined directly from the identified/defined destructive topology structures. The results generate several necessary and sufficient graphical conditions for controllability. A key step of arriving at these results is the discovery of a relationship between the topology structure of the controllability destructive nodes and a corresponding eigenvector of the Laplacian matrix. [ABSTRACT FROM PUBLISHER]

The event-based broadcasting containment control problem for both first-order and second-order multi-agent systems under directed topology is investigated. Based on certain event, each agent decides when to transmit its current states to its neighbours and the agents’ distributed control algorithms are based on these sampled state measurements, which can significantly decrease the number of the controllers’ updates. All the agents are divided into two groups, namely, the leaders and the followers. The formation control is introduced. The leaders exchange their information to converge to a formation. The followers utilise the information from both their leader neighbours and their follower neighbours and are driven to the convex hull of the leaders using the proposed control algorithms. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM PUBLISHER]

As an efficient collective response of multi-agent systems, the realization of stabilizability needs appropriate information transfer among agents, thus the topology structure is paramount. To investigate the influences of network topology on stabilizability, the concept of quotient graph (equivalent transformation of original graph) is proposed to realize the stabilizability of large-scale network systems which can be reduced to a small-scale quotient graph. As a cornerstone of topology graph transformation, N S i graph division, which is proposed for the first time in this paper, plays a crucial role in stabilizability analysis and has far-reaching impact. It establishes an equivalent connection between the stabilizability of the original topology graph and the quotient graph. Results reveal a nontrivial relationship between stabilizability of uncontrollable multi-agent systems and network topology (i.e., the stabilizability of uncontrollable multi-agent systems is not only related to the selection of leaders, but also depends on uncontrollable modes.), which is established by quotient graph as a visual generalization of the original network topology. Surprisingly, structural balance is not always good, and unbalance has a positive effect on the stabilizability of the system. Finally, the simulation experiments demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the controllability of first-order and second-order discrete-time multi-agent systems with directed topology and input delay. The problem is studied in the leader–follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents. Sufficient and necessary conditions are derived for the controllability of first-order discrete-time multi-agent systems. With sampling period and feedback gain satisfying certain conditions, it is proved under three different protocols that the controllability of second-order discrete-time multi-agent systems is equivalent to that of a pair of submatrices of Laplacian matrix. In addition, the controllability of both first-order and second-order discrete-time multi-agent systems with input delay is shown, through some transformations, to be equivalent to that of the transformed non-delayed systems. Finally, some simulation examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: By controllability of multi-agent systems, we mean the property that all agents can be driven to arbitrary configurations only through regulating a few leaders externally, while the rest of the agents are subject to the nearest-neighbor-law. It is known that the controllability of multi-agent systems depends not only on the communication topologies among agents but also on the selection of leaders. The main objective of this paper aims to characterize the virtue that leaders should have from the perspective of algebraic and graphical conditions. We begin with a heuristic observation for tree graph. To gain more insights, necessary and sufficient conditions are then proposed in terms of downer branch and subgraphs, respectively. In particular, it is shown for path topologies that controllability completely depends on the leaders’ location. The obtained results may help us to pave the way towards a new method of formation and reconfiguration control in swarming robots. [Copyright &y& Elsevier]

In this paper, we study the strong targeted controllability of multi-agent systems with time-varying topologies over finite fields from a graph theoretic perspective. We consider leader–follower networks, where only some of the agents are governed by external control inputs, namely the leaders. We develop a graph-theoretic characterization for strong targeted controllability of multi-agent systems with time-varying topologies over finite fields. Specifically, we show that a time-varying multi-agent system is strongly targeted controllable over any finite field if the graphs of the system satisfy certain properties. Our main results are applicable to time-varying topologies with arbitrary fields and coupling weights. We also present a necessary and sufficient condition for the strong structural controllability of the time-invariant multi-agent systems. [ABSTRACT FROM AUTHOR]