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In this paper, the $ H_{\infty } $ H ∞ consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and $ (x, u, v) $ (x , u , v) -dependent noises is studied. Firstly, the $ H_{\infty } $ H ∞ consensus problem is transformed into a standard $ H_{\infty } $ H ∞ control problem by model transformation. Then, a dynamic output feedback control protocol is constructed by solving a set of linear matrix inequalities to ensure that the closed-loop system achieves the mean square consensus and meets the specified $ H_{\infty } $ H ∞ performance level. After that, both delay-independent and delay-dependent stochastic bounded real lemmas are established by taking advantage of the Lyapunov–Krasovskii function method and the generalised It $ \hat {\rm {o}} $ o ^ formula. Finally, we illustrate the validity of the developed method with numerical simulations. [ABSTRACT FROM AUTHOR]

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]

In this paper, we study the controllability of multi-agent systems by equitable partition and automorphism. For the case that cells are incompletely connected outside but completely connected inside, a necessary condition for controllability is given from the perspective of the rank of connection matrix. For the case of multiple cells being completely connected outside and incompletely connected inside, in terms of the eigenvalues and eigenvectors of L and L π , several sufficient and necessary conditions for controllability are presented. Once the quotient graph is controllable under single input or all nodes in nontrivial cells are leaders, the lower bound of controllable subspace is determined. Finally, we give the gap between the necessary condition and the sufficient condition for controllability from the aspect of equitable partition. One highlight of the results in this paper is that we show sufficient conditions to judge controllability by equitable partition and automorphism, which, for specific cases, provides one method that how to break through the defect that equitable partition can only obtain necessary conditions. [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]

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]

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 is concerned with adaptive event-triggered consensus of general linear multi-agent systems (MASs). Leaderless consensus and leader-following consensus are both considered. In order to avoid dependence on global information about system topology and reduce communication frequency, distributed adaptive event-triggered consensus protocols are designed. Through model transformation, the consensus problems of MASs are transformed into the stability problems of the corresponding error systems. By using algebraic graph theory and Lyapunov stability theory, some sufficient criteria for MASs to achieve consensus are obtained. Meanwhile, it is proved that the proposed event-trigger conditions can exclude Zeno behaviour effectively. One simulation example is provided to validate the effectiveness of obtained theoretical 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]

In this article, by analyzing the eigenvalues and eigenvectors of Laplacian $L$ , we investigate the controllability of multiagent systems under equitable partitions. Two classes of nontrivial cells are defined according to the different numbers of links between them, which are completely connected nontrivial cells (CCNCs) and incompletely connected nontrivial cells. For the system with CCNCs, a necessary condition for controllability is found to be choosing leaders from each nontrivial cell, the number of which should be one less than the cardinality of the cell. It is shown that the controllability is affected by three factors: 1) the number of the links between nontrivial cells; 2) the rank of the connection matrix; and 3) the odevity of the capacity of the nontrivial cells. In the case of nontrivial cells under the equitable partition, there are automorphisms of interconnection graph $\mathcal {G}$ , which induce the eigenvectors of $L$ with zero entries. For the system with automorphisms, by taking advantage of the property of eigenvectors associated with $L$ , we propose several graphical necessary conditions for controllability. In addition, by the PBH rank criterion, the controllable subspaces of the system with different classes of nontrivial cells are compared. Finally, a necessary and sufficient condition for controllability under minimum inputs is given. [ABSTRACT FROM AUTHOR]

The consensus problem of multi-agent systems with general second-order dynamics is studied. A distributed event-triggering strategy is proposed to reduce the communication frequency of agents and the update frequency of event-triggering controller. Under the fixed topology, a consensus protocol and event-triggering function are designed for each agent. The sufficient conditions of consensus are obtained by the stability theory, and the theoretical proof of excluding Zeno behaviour is presented. Finally, a simulation example is given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In view of the problems of large consumption of communication and computing resources in the control process, this paper studies a fundamental property for a class of multi-agent systems under event-triggered strategy: the S-stabilizability of a group of multi-agent systems with general linear dynamics under weakly connected directed topology. The results indicate that the S-stabilizability can be described in some way that the stabilizability region and feedback gain can evaluate the performance of the protocol. Firstly, a new distributed event-triggered protocol is proposed. Under this protocol, a kind of hybrid static and dynamic event-triggered strategy are presented, respectively. In particular, by using Lyapunov stability theory and graph partition tool, it is proved that the proposed event-triggered control strategy can guarantee the closed-loop system achieve S-stabilizability effectively, if at least one vertex in each iSCC (independent strongly connected component) cell receives information from the leader, which reflects the ability of distributed control law. Further, we demonstrate that the stabilizability can be realized if the initial system matrix A is Hurwitz. Moreover, it is confirmed that the designed static event-triggered condition is a limit case of dynamic event condition and can guarantee Zeno-free behavior. Finally, the validity of the theoretical results is proved by numerical simulation. [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]

This paper studies the stabilizability and formation control problems of multi-agent systems with antagonistic interactions. The agents run a bipartite consensus protocol using a signed Laplacian which is different from the conventional one. By taking advantage of the proposed structurally balanced independent strongly connected components(SBiSCCs) of the signed graph, a sufficient and necessary condition is presented to solve the decentralized stabilizability problem of multi-agent systems with antagonistic interactions. Besides, formation control is considered and the sufficient and necessary condition is provided by applying the proposed results. Several simulations are given to illustrate the theoretical results. • SBiSCCs based necessary and sufficient conditions are derived for the rank of Laplacian. • Stabilizability condition and the decentralized control are proposed. • A necessary and sufficient condition is provided for formation control. [ABSTRACT FROM AUTHOR]

The consensus problem of first-order multi-agent systems with time delay is investigated. The periodic sample and event hybrid control method is applied. Specifically, each agent samples its own states periodically and decides when to transmit its sampled states to its neighbors based on certain event. The agents’ distributed consensus algorithms are based on these hybrid sampled and event-triggered state measurements, which can significantly decrease the number of the controllers’ updates. The Zeno behavior which is discussed in most works considering event-based consensus of multi-agent systems is excluded automatically since the span between two contiguous event-triggering time instants is not less than the sampling period. The cases of directed and undirected topologies are both considered. The obtained results improve the existing ones in the literature. A numerical simulation is provided to illustrate the effectiveness of the obtained theoretical results. [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]

This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM PUBLISHER]

In this paper, the influences of negative weights on the consensus problems of multi-agent systems are investigated. While the system is subject to external attacks or agents in the system break down, there are errors in information transmission between agents. As a result, for non-negative systems, the connection weights between agents may change, or even change from positive to negative. In this paper, we provide a unified approach to deal with the problem of how to ensure the consensus of the system when the connection weight becomes negative. It is found that the consensus of multi-agent systems and general linear multi-agent systems will be guaranteed while the weights change to a certain extent without changing the protocol and feedback gains. We obtain a necessary and sufficient condition to ensure that the system can still reach asymptotic consensus when the connection weight is negative. The result is applicable to first-order, high-order integrator type of multi-agent systems as well as the general linear multi-agent system. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the formation control problem of the network of multiple agents is studied in terms of controllability, where the network is of the leader–follower structure with some agents taking leaders role and others being followers interconnected via the neighbor-based rule. It is shown that the controllability of a multi-agent system can be uniquely determined by the topology structure of interconnection graph, for which the investigation comes down to that for a multi-agent system with the interconnection graph being connected. Based on these observations, two kinds of uncontrollable interconnection topologies are characterized, and a necessary and sufficient eigenvector-based condition is presented. Our studies also touch upon the selection of leaders. [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]