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The second-order scalar-weighted consensus problem of multiagent systems has been well explored. However, in some practical antagonistic interaction networks, the interdependencies of multidimensional states of the agents must be described by matrix coupling. In order to highlight the influence of matrix coupling in the antagonistic interaction network, we investigate the second-order matrix-weighted bipartite consensus problem on undirected structurally balanced signed networks. Under the proposed bipartite consensus protocol, an algebraic condition is obtained for achieving second-order bipartite consensus via utilizing matrix-valued Gauge transformation and stability theory. Then, using the obtained criteria, a more direct algebraic graph condition is given for reaching bipartite consensus. Besides, because of the existence of negative (positive) semidefinite connections, the matrix-weighted network may have clustering phenomena, which means that matrix weights play a critical role in achieving consensus. An algebraic graph condition for admitting cluster bipartite consensus is provided. By designing matrix weights in practical scenarios, the required number of clusters can be obtained. Finally, the theoretical results are verified by five simulation examples. [ABSTRACT FROM AUTHOR]

The issue of bipartite time-varying formation (BTVF) tracking for linear multiagent systems (MASs) with a leader of unknown input on signed digraphs is investigated. An adaptive nonsmooth protocol is taken in this article that utilizes only the local output feedback information among neighbors and, thus, can avoid employing the eigenvalue information of the Laplacian matrix of the graph. It is proven that if the interaction network of agents containing a spanning tree is structurally balanced, the BTVF tracking can be achieved with a leader of the bounded input via the proposed scheme. This leader-following BTVF includes two time-varying subformations, whose relationship is antagonistic. A convergence analysis of the proposed protocol for MASs is reflected by the Lyapunov method. Finally, the validly numerical simulations are illustrated to show the performance of the proposed schemes. [ABSTRACT FROM AUTHOR]

In this article, we study the consensus issues of multiagent systems (MASs) without any information of the system model by using the reinforcement learning (RL) method and event-based control strategy. First, we design an adaptive event-based consensus control protocol using the local sampled state information so that the consensus errors of all agents are uniformly ultimately bounded. The validity of the above event-triggered adaptive control protocol is confirmed by excluding the Zeno behavior within finite time. Then, based on the RL approach, we present a model-free algorithm to get the feedback gain matrix, and accomplish constructing the adaptive event-triggered control strategy without the knowledge of model information. Distinct with the existing related works, this RL-based event-triggered adaptive control algorithm only relies on the local sampled state information, irrelevant to any model information or global network information. Finally, we provide some examples to demonstrate the validity of the above adaptive event-based consensus algorithm. [ABSTRACT FROM AUTHOR]

This article studies the consensus control problem of second-order multiagent systems with switching dynamics, which consist of a continuous-time and a discrete-time subsystem. A novel control protocol is proposed for fixed digraphs by using the same control strategy for two subsystems so that the controller can keep the control strategy unchanged when systems switch. Moreover, this control strategy uses only sampled position data at the current sampling time and the previous sampling time to deal with this possible situation when speed information is difficult to be measured, which is also robustness and low cost. Some necessary and sufficient conditions to achieve consensus are derived about the network topology, structure and sampling period. At last, a few simulation examples are given. [ABSTRACT FROM AUTHOR]

In this article, bipartite consensus is investigated for linear multi‐agent systems (MASs) via adaptive asynchronous intermittent control. Adaptive asynchronous intermittent bipartite consensus protocols are proposed for MASs with antagonistic links under both fixed and connected switching topologies. By using gauge transformation and stability theory, convergency analysis is given and some conditions of bipartite consensus are obtained. It is turned out that bipartite consensus can be realized if the communication rate is no less than a threshold under the assumption that the network is connected and structurally balanced. Finally, two simulation examples are provided to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This article concerns the robust consensus problem of continuous-time linear multiagent systems (MASs) with uncertainty and discrete-time measurement information, where the output measurement information is in the data-sampled form. Distributed output-feedback protocol with or without controller interaction is proposed for each agent. Specifically, the output-feedback protocol runs in continuous time with an output error correction term mixed with the discrete-time measurement information. The concrete algorithm is given for the construction of the feedback matrices. Then, by using the delay-input approach, sufficient conditions are provided for the robust consensus of this kind of MASs interacting over networks described by the directed graphs. Finally, numerical simulations are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

A consensus control issue is studied for general second-order multiagent systems via Q-learning method in this article. A novel second-order type with discrete-time dynamics is investigated to solve the corresponding consensus issues. Under fixed directed topology, in order to achieve general second-order consensus for the systems, a model-free Q-learning method is proposed, which can derive the coupling gains matrix without any information from the system dynamics. Moreover, applying the obtained coupling gains matrix, this general second-order multiagent systems can achieve consensus. Then, for undirected graphs, a similar corollary is obtained for this system to achieve general second-order consensus by means of the Q-learning method. Finally, the correctness of the new method is confirmed by several simulation examples. [ABSTRACT FROM AUTHOR]

This article proposes a $Q$ -learning (QL)-based algorithm for global consensus of saturated discrete-time multiagent systems (DTMASs) via output feedback. According to the low-gain feedback (LGF) theory, control inputs of the saturated DTMASs can avoid the saturation by utilizing the control policies with LGF matrices, which were computed from the modified algebraic Riccati equation (MARE) by requiring the information of system dynamics in most previous works. However, in this article, we first find the lower bound on the real part of Laplacian matrices’ nonzero eigenvalues of directed network topologies. Then, we define a test control input and propose a $Q$ -function to derive a QL Bellman equation, which plays an essential part of the QL algorithm. Subsequently, different from the previous works, the output-feedback gain (OFG) matrix of this article can be obtained by limited iterations of the QL algorithm without requiring the information of agent dynamics and network topologies of the saturated DTMASs. Furthermore, the saturated DTMASs can achieve global consensus rather than the semiglobal consensus of the previous results. Finally, the effectiveness of the QL algorithm is confirmed via two simulations. [ABSTRACT FROM AUTHOR]

In this article, we propose two model-free algorithms using state or output feedback for saturated discrete-time multiagent systems (SDTMASs) to attain global containment control. In most previous works, the control input can avoid saturation by utilizing the low gain feedback (LGF) method whereas requiring the knowledge of agent dynamics, and SDTMASs just can attain semi-global containment control. Distinct with the previous works, first, based on the $Q$ -learning (QL) technique, this article defines a $Q$ -function and deduces the corresponding QL Bellman equation, which is the most important part of the QL algorithm. Then, in order to solve the QL Bellman equation, we propose two iterative model-free algorithms using state and output feedback, and the LGF matrix can be acquired from that solution directly. Furthermore, under the state and output feedback control protocols with the feedback matrices obtained from the proposed model-free algorithms, the SDTMASs can achieve global containment control instead of semi-global containment control. Finally, we present some simulations to confirm the validity of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This essay considers the bipartite consensus of matrix-weighted second-order multi-agent systems with structurally unbalanced antagonistic interactions networks. Owing to the influence of matrix-weights, bipartite consensus and cluster bipartite consensus can also be reached, which is different from the existing works on signed networks. With the assistance of Lyapunov stability and matrix-valued Gauge transformation, a condition to achieve bipartite consensus is established. Moreover, a relatively straightforward algebraic graph condition for reaching cluster bipartite consensus is attained. Finally, simulation examples are supplied to illustrate the obtained results. • The bipartite consensus of MASs is investigated for structurally unbalanced matrix-weighted signed networks. • The MASs can be reached bipartite consensus and cluster bipartite consensus. • All the clusters can be obtained by designing matrix weights. [ABSTRACT FROM AUTHOR]

The containment control problem in fractional-order multiagent systems over a directed graph is studied in this article. Two distributed control protocols with or without time delays are designed by utilizing the sampled position and velocity data. Then, based on the knowledge of the matrix theory and Laplace transform, some necessary and sufficient conditions to reach containment are derived. For the protocol with time delays, similar sufficient and necessary conditions are obtained. Finally, some simulation examples are designed to verify that the theorems are correct. [ABSTRACT FROM AUTHOR]

This article refocuses on the global coordination of networked systems with input saturation and external disturbances. With the help of a novel backstepping approach, a multihop relay control algorithm subject to a group of modified heterogenous saturation functions is constructed, in which the number of the hop is equal to the order of the networked system. It is proved that these modified heterogenous saturation functions can develop a global unsaturated control algorithm for each agent. Then, some sufficient and necessary conditions are provided for the global consensus of the connected networked systems with input saturation in the absence of external disturbances. In the presence of the input saturation and external disturbances, a sufficient condition irrelevant to the interactive network topology information is proposed for the global swarm of connected networked systems. Finally, numerical simulations are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In the absence of assuming that all agents know the system matrix of the external system, for heterogeneous linear multiagent systems (MASs), this article resolves the cooperative regulation problem in the presence of communication constraints. Based on the mild assumption on the digraph, two novel adaptive protocols are presented to solve the cooperative output regulation problem (ORP) via state feedback and measurement output feedback subject to snatchy and asynchronous information exchange between agents, unknown time-varying delays, and probable information losses. Finally, some simulations are offered to demonstrate the validity of our results about the problem. [ABSTRACT FROM AUTHOR]

This article studies the consensus of hybrid second-order multiagent systems (MASs), where the hybrid MAS is constituted by the continuous-time second-order (CTSO) and discrete-time second-order (DTSO) dynamic agents. First, a hybrid consensus algorithm is proposed, where a sample-data control is considered in the CTSO subsystems. Under the proposed hybrid consensus algorithm, the convergence of the hybrid second-order MAS matrix is analyzed. Second, a sufficient and necessary condition is proposed, which indicates that the controller parameters, such as coupling gains and the sampling interval, and eigenvalues of network topology have a significant impact on the system consensus. Finally, several simulation examples are presented to prove the validity of the results. [ABSTRACT FROM AUTHOR]

This paper studies the consensus in fractional-order multiagent systems over directed graph via sampled-data control method. A distributed control protocol using the sampled position and velocity data is designed. By virtue of the Mittag-Leffler function, Laplace transform, and matrix theory, some necessary and sufficient conditions associated with the sampling period, the fractional order, the coupling strengths, and the network structure to obtain consensus of the systems are obtained. Then, some detailed discussions are presented about how to select the sampling period and how to design the coupling strengths to attain the consensus of the systems, respectively. Lastly, some numerical simulation results are illustrated to reflect the availability of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This work presents a new algorithm for flocking with a virtual leader by introducing a new sampling scenario, so‐called multi‐rate sampling. In the multi‐rate sampling, the period of receiving data from different sources is different, but the updating time for all individuals is the same. Here, the authors assume that the period of receiving data from neighbour agents is T, and that from the virtual leader is an integer multiple of it, that is, mT. An upper bound for period T is attained from the upper bound of the energy function that guarantees the neighbouring network to be connected and collision to be avoided between agents. Also, an upper bound on m, which ensures the velocity of informed and uninformed agents to tend the virtual leader's velocity, is derived. The convergence analysis demonstrates that whatever the acquiring period of the virtual leader's information mT is further, then the convergence rate of the group's velocity to the virtual leader's velocity will be greater. Finally, to show the validity of the results, they present a simulation. [ABSTRACT FROM AUTHOR]

In this article, an event-triggered method is proposed to solve the consensus of the second-order hybrid multiagent systems (MASs), which contain discrete-time and continuous-time individuals. First, we give a selection criteria of the coupling gains, the eigenvalues of communication topology, and the event-triggered sampling interval to guarantee the hybrid consensus, which have an impact on system stability, due to the interaction and co-existence of discrete-time and continuous-time individuals. Second, the hybrid second-order consensus under the event-triggered strategy is proven, where the agents communicate with their neighbors and update their controllers only at the triggered instants. Finally, we give some simulation examples to prove the validity of the main results. [ABSTRACT FROM AUTHOR]

The observability of discrete‐time multi‐agent systems (MASs) with switching topology under the framework of leadership coordinated control is studied. Based on the switched control system theory, some algebraic properties on observability of discrete‐time MASs with switching topology are given. Moreover, on the basis of the eigenvalues and eigenvectors of the system matrices, an effective algebraic characterisation on the observability of discrete‐time MASs is established based on fixed topology. The observability of some special topological graphs is also studied. Finally, numerical example and simulations are given. [ABSTRACT FROM AUTHOR]

This brief focuses on the consensus problem of multi-agent systems (MASs) consisting of friends and enemies in a matrix-weight-based signed topological network. To highlight the effects of matrix coupling, we analyze the integrator model in a competitive-cooperative coexistence network. Unlike scalar-weight-based topological networks, the phenomenon of clustering in matrix-weight-based networks naturally exists, which means the important role of matrix coupling in convergence. Hence, different form existing results, depending on matrix coupling, the research shows bipartite consensus can be achieved in an unbalanced situation. Algebraic conditions are proposed for achieving a bipartite consensus and our results on structural unbalanced graph are shown to be more universality. Finally, some simulation results are given to vindicate the analysis. [ABSTRACT FROM AUTHOR]

In this article, the consensus problem for the delayed fractional-order multiagent system (FOMAS) under directed graph is addressed by intermittent sampled-data control. First, an intermittent sampled-data control protocol with input time delay is proposed. By virtue of Laplace transform and stability theory, some necessary and sufficient conditions depending on the order, input time delay, sampling period, communication width, coupling strengths, and network structure are presented for the delayed FOMASs to reach consensus. Moreover, due to the relationship about the input time delay, communication width, and sampling period, four cases are carefully discussed to find that the sampling period has bounds for a given network with known input time delay and communication width to obtain consensus. Finally, some simulation examples are shown to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a second-order consensus for multiagent systems with a directed communication topology is studied. A novel consensus strategy is first proposed, where a periodic intermittent control strategy only with casual sampled position data is used, which not only decreases the operating time and the update rates of conditioners for every individual but also responds effectively to the case of missing velocity information. A necessary and sufficient consensus condition based on the coupling gains, the sampling period, the communication width, and the spectrum of the Laplacian matrix is established to reach the consensus, and the right intervals of the sampling period are given. Furthermore, a delay-induced consensus protocol is designed, and a necessary and sufficient condition is also given, by which the sampling period and the communication width can easily be chosen to achieve the consensus. At last, some simulation examples are given to verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the controllability problem is addressed for a two-time-scale discrete-time system with multiple agents. First, the system is described by a singularly perturbed difference equation expressed on fast timescale. Then, to eliminate the singular perturbation parameter, by using the iterative method and approximate approach, the two-time-scale system is separated into slow and fast subsystems. Subsequently, some sufficient and/or necessary conditions of controllability for the systems are derived by using matrix theory. Moreover, under three special network topologies, the necessary criteria for controllability are proposed via graph theory. Finally, we give a simulation example to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

The leaderless consensus of fractional-order multi-agent systems (FOMASs) by intermittence sampled data control method is investigated in this brief, for which a distributed intermittence sampled data control protocol is presented to reduce the updating rate and working time of controllers. Subsequently, the Laplace transform and the stability theory are utilized to derive some necessary and sufficient consensus criteria that show the relations among the fractional order, sampling period, communication width, coupling strengths, and network topology. What is more, it can be discovered that both the communication width and sampling period have the lower and upper bounds for given networks to attain leaderless consensus. Finally, a numerical simulation example is presented to prove the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the controllability of multi‐agent systems with second‐order dynamic under discrete‐time model, which evolve on two time scales. The authors first characterise the systems by difference equations with a singular perturbation parameter. Then, in order to get rid of the singular perturbation parameter, they split the systems into a slow subsystem and fast subsystem based on the iterative method and approximate approach. Moreover, according to matrix theory, they deduce a lot of necessary and/or sufficient controllability criteria of the systems. In particular, a second‐order controllability criterion only depending on the eigenvalues of matrices is proposed, which is more easy‐to‐use and efficient. A simulation example is lastly given to clarify the validity of all theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem for directed positive multiagent systems with nonlinear control input. The directed topology is supposed to be strongly connected. For the case of sector input nonlinearities, the non-negative global consensus conditions are presented by using a novel analysis method which directly considers the nonlinear input, and the feedback matrices are obtained with convex optimization method by solving the quadratic matrix inequalities subject to non-negative constraints. For the case of saturation-type sector input nonlinearities, the global consensus and local consensus results are analyzed, respectively. With the properties of Metzler matrix, the non-negative consensus results are further extended to the strongly connected and balanced positive multiagent systems subject to (saturation-type) sector input nonlinearities and parameter uncertainties. The results are simplified, and the feedback matrices can be given by solving iterative linear matrix inequality with non-negative constraints. Two simulation examples and a practical electrical circuit model are finally carried out to verify the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper investigates the joint effect of quantization, sampled data, and general Markovian interaction links on consensus networks with a leader under directed graphs. The diversity of edges formed by all the followers and the leader is also considered. Each agent in the network possesses continuous-time general linear dynamics. Each agent’s state is measured only at sampling time instants, which is encoded before transmission. Subsequently, the encoded state is transmitted through noiseless digital communication links with Markovian switching rates. For this problem, a sufficient condition is derived to guarantee the convergence of the encoded states, based on which a necessary and sufficient condition is obtained to achieve consensus tracking in the mean-square sense. In addition, two sufficient conditions on coupling gain, one of which is fully distributed, are provided by proposing an optimal linear quadratic regulator-based gain matrix to ensure consensus tracking and then, the analysis of consensus region is presented. Finally, a numerical example is presented for illustrating the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

, The authors study the semi‐global edge‐consensus of linear discrete‐time multi‐agent systems subject to edge state positive constraint and input saturation. By virtue of the positive system theory and low‐gain feedback method, the distributed control protocols for undirected and directed networks are designed to guarantee the non‐negative edge‐consensus with input saturation. Then, sufficient conditions, which can guarantee the edge‐consensus together with keeping the positive edge state constraint and avoiding the input saturation, are provided. Finally, two examples are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the authors propose a new algorithm for the flocking problem of multi‐agent systems with the dynamic virtual leader under the sampled‐data frameworks. A necessary time‐varying condition is derived on the sampling period for preserving connectivity of the network and avoiding collision among agents. Then, defining a new energy function, it is proved that using a connectivity‐preserving potential function and under the sampling period which satisfies the necessary condition, an asymptotic flocking motion is achievable. Under the proposed sampled‐data flocking algorithm, the connectivity preservation of the network and collision avoidance among agents are guaranteed as well as the velocity convergence of all agents to that of the virtual leader is ensured. Moreover, employing the upper bound of the energy function, they specify an upper bound of the sampling period which could satisfy the time‐varying necessary condition. Finally, they present a numerical simulation to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a self-triggered algorithm for leader-following consensus of general linear multi-agent systems with input time delay is proposed. It is shown that the leader-following consensus can be reached asymptotically and the Zeno-behaviour of triggering time sequences can be excluded. Under this algorithm, the next exact triggering time instant of each agent can be computed by the local information at the previous triggering time instant. Continuous communication, monitoring of measurement error and updating of controller input are thus avoided. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the controllability for an interconnected two-time-scale second-order multi-agent system. Firstly, to eliminate the singular perturbation parameter, we separate the multi-agent system into slow subsystem and fast subsystem by using singular perturbation methods. Then, based on matrix theory, some necessary and/or sufficient criteria are derived for second-order controllability of two-time-scale multi-agent systems with multiple leaders. Moreover, we propose some easy-to-use second-order controllability criteria determined only by eigenvalues of system matrices. Lastly, the effectiveness of the proposed theoretical results is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

Abstract Since many practical physical phenomena can be depicted more accurately and suitablely by fractional-order models, this work addresses the event-triggered consensus tracking for the fractional-order multi-agent systems (FOMASs) governed by general linear models. Firstly, a distributed event-triggered control algorithm relied on state feedback is derived. Then, according to the Laplace transform, the Mittag-Leffler function, the comparison test of improper integral, and the technique of inequality, some consensus criteria are obtained to ensure all followers can track a dynamic leader and Zeno behavior can be avoided. Lastly, some numerical simulation results are provided to verify the effectiveness of the event-triggered method. [ABSTRACT FROM AUTHOR]

This study addresses the group controllability of continuous‐time multi‐agent systems. The problem is investigated in the leaderless framework where the whole group is consisted of a number of dynamic agents with autonomous capability, which can complete the large‐scale complex task through local interaction and can be divided into some subgroups. This study concentrates on the group controllability problems of continuous‐time multi‐agent systems, gives the general definition of the group controllability, and establishes group controllability criteria. Sufficient and necessary conditions are derived for the group controllability of continuous‐time multi‐agent systems. Finally, the numerical example and simulations are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this brief, we investigate the consensus problem of nonlinear multiagent systems by means of general Lyapunov functions. That is, by constructing general Lyapunov functions, such as polynomial Lyapunov functions beyond quadratic forms, a sufficient condition is established for achieving global consensus. Compared with the existing consensus criteria deduced by quadratic Lyapunov functions, our consensus criterion is less conservative and can be applicable for more systems. In particular, for polynomial systems and even certain classes of nonpolynomial systems, our consensus criterion can be formulated based on polynomial Lyapunov functions, which can be calculated by using the sum-of-squares (SOS) programming tools such as SOSTOOLS. Finally, two simulation examples are given to illustrate the effectiveness of our proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates a class of heterogeneous swarming systems with periodically intermittent control. It is assumed that agents in the network are nonidentical and potential functions are heterogeneous. Each agent is assumed to obtain information from the leader and the neighbors only on a series of periodically time intervals. The dynamics of the swarm members are affected by inter-individual interactions and the environment. In addition, we consider the first-order integrator system with a class of attraction/repulsion functions. Some sufficient conditions are provided to guarantee exponential stability of the whole system. Although the information from the leader agent and the neighbors is not continuous, all follower agents can track the leader agent in certain error range. A numerical example is shown to illustrate the validity of the above theoretical result. [ABSTRACT FROM AUTHOR]

This paper deals with the low-gain output feedback cooperative control for discrete-time linear multi-agent systems subject to actuator saturation. Based on the algebraic Riccati equations, semi-global exponential consensus is demonstrated for multi-agent system networks with a switching topology that is known or unknown to the agents. The combinational measurements are utilized to design the state observer. The estimated combinational states are used for controller design and Lyapunov stability analysis. The theoretical results are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This study aims to investigate containment control of linear multi‐agent systems with input saturation on switching topologies. For such a multi‐agent system, both state feedback and output feedback containment control protocols are proposed via a novel low‐gain feedback approach. Consequently, the authors show that, under the assumption that the switching networks are jointly connected, semi‐global state feedback and output feedback containment control of the multi‐agent system can be attained. The effectiveness of the proposed algorithms is illustrated via numerical examples. [ABSTRACT FROM AUTHOR]