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This paper investigates the adaptive consensus problem of general linear multi‐agent systems. Finite‐time consensus and fixed‐time consensus are both discussed. In order to remove the dependence on global information about system topology, distributed adaptive mechanisms are introduced. Compared with the existing asymptotic consensus results, the system's convergence speed is improved by the proposed distributed finite‐time consensus protocol. Furthermore, a distributed fixed‐time consensus protocol is proposed to remove the dependence on system's initial state. Under the fixed‐time consensus protocol, it is proved that an upper bound of the system's convergence time can be estimated. Sufficient conditions are given to ensure that all agents can achieve consensus in finite time and fixed time, respectively. Finally, the effectiveness of the proposed protocols is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

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]

In this article, the effects of different models on the controllability of leader‐follower dynamics system based on Laplacian matrix are studied, and the controllability results applicable to general model are obtained. Our research is based on three different control modes, namely, broadcast control, UI$$ {U}_I $$ control, and non‐broadcast control, which cover all the control modes in the general model. Specifically, we first identify the relation of different UI$$ {U}_I $$ control, that is, if the system is controllable under i1$$ {i}_1 $$ different control signals, then increasing the number of control signals does not change the controllability of the system. Furthermore, it is proved that in a fixed topology, when the number of control inputs is increased, the controllability of the system is not correlated with the controllability of the original system, which appears counter‐intuitive. But the spectral radius of the Gramian matrix of the controllable system is increased. In addition, we analyze the condition number of Gramian matrix. Based on the above conclusions, we put forward the concept of hierarchical equivalent partition (HEP), and prove that under the general model, the existence of HEP makes the system uncontrollable. Finally, we expect to find a way to make the system controllable under the general model. Therefore, we obtain sufficient conditions for the system to be controllable. As a by‐product, we find that there is no completely uncontrollable graph when the general model with broadcast control is removed. [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]