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• Distributed optimization problems of consensus are examined by a frequency-domain analysis approach. • An optimized distributed protocol is proposed such that the nonuniform time-delay FDMSs with SF have better consensus performance. • The double-integral dynamics of delayed FDMSs with SF is considered. This paper addresses distributed optimization problems concerning consensus in delayed fractional-order double-integrator multi-agent systems (FDMSs). To start with, an optimized distributed protocol with state-fractional-order-derivative feedback (SF) is presented for delayed FDMSs. Then, the consensus problems are studied for the two kinds of delayed FDMSs with SF in the presence of symmetric time-delays over undirected network topology and asymmetric time-delays over directed network topology. Next, by the means of graph theory, matrix theory and frequency-domain analysis method, the sufficient conditions to guarantee consensus of delayed FDMSs with SF are derived. Compared to the traditional distributed protocol without SF, the proposed distributed optimization protocol with SF are taken into account to enable better consensus performance in delayed FDMSs with SF. Finally, numerical experiments are carried out to verify the feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the privacy-preserving-based bipartite consensus control problem is investigated for a class of discrete-time nonlinear multi-agent systems (MASs). The classical bipartite consensus control implementation relies on the explicit information exchange between agents, which will lead to the possible leakage of agents' private information, especially the initial states. Therefore, to prevent data disclosure to neighbors inside the MASs and the outside eavesdroppers, the data is encrypted by means of Paillier encryption scheme during information transmission. This means each agent first sends the relative data in the form of ciphertext to its neighbors for further encryption process, and then restores the control protocol based on the returned encrypted information from the neighbors. Since homomorphic encryption only works for integers, the data must be quantized before encryption, and it will inevitably result in the quantization error. On the other hand, for the purpose of saving communication resources, both decentralized and distributed event-triggered schemes are also proposed. Resorting to the Lyapunov stability theory and algebraic graph theory, sufficient conditions are derived ensuring that the MASs subject to a confidential communication agreement can achieve the bounded bipartite consensus. Two numerical examples are presented to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the distributed specified-time group consensus control with hard settling-time constraint and milder communication topology constraint. To this end, we propose two distributed control schemes by employing a motion planning approach for the single- and double-integrator systems. Compared with the most existing works over undirected communication topologies, the underlying topology of each group is required to be directed graphs in our proposed distributed controllers. Furthermore, the root vertex of one group is allowed to belong to the other group. The convergence analysis is performed via the algebraic graph theory and matrix theory. The results show that the agents in the same group can reach consensus within any prespecified settling-time instead of a conservative upper bound of the settling-time. Moreover, the designed specified-time group consensus protocols do not require continuous information exchange. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper mainly studies the group consensus problem of the heterogeneous multi-agent systems with cooperative and competitive interactions and their strength among the agents. And both event-triggered mechanism and pinning control method are considered based on the system's topology with connected components. Besides, the novel fully distributed event-triggered conditions which only contain the local information for each agent are designed. Then, some sufficient conditions and the corresponding pinning control strategies are obtained via using algebraic graph theory and Lyapunov stability theorem, which can guarantee the system to reach multiple group consensus. In addition, Zeno-behavior for each agent is strictly excluded by utilizing time-correlation function. Finally, several simulations illustrate that our findings and the proposed methods are effective. Moreover, the results show that the convergence rate of the system will increase with the appropriate change of the cooperative or competitive interaction or their strength. [ABSTRACT FROM AUTHOR]

Highlights This paper studies the consensus problems for the two types of double-integrator fractional-order multi-agent system (DIFOMAS) with nonuniform time-delays: the DIFOMAS with symmetric time delays over undirected topology, and the DIFOMAS with asymmetric time delays over directed topology. The main contributions of this paper are as follows: • Consider the double-integrator fractional-order dynamics. • Consider the nonuniform time-delays, which contain up to n(n-1) different values when the DIFOMAS consists of n agents. • Consider the dynamics of each agent containing two state-variable with different fractional orders. • Obtain the two kinds of the upper bound of time-delays about Theorems 1 and 2 and the corollaries of Theorems 1 and 2. Abstract This paper addresses the distributed consensus control for a double-integrator fractional-order multi-agent system (DIFOMAS) with nonuniform time-delays. A general model of the DIFOMAS is introduced by such case: the dynamic model of each agent contains two state variables with different fractional orders. The consensus conditions on the two kinds of network topology and the nonuniform time-delays can be obtained by using the generic model: the DIFOMAS with symmetric time-delays over undirected topology, and the DIFOMAS with asymmetric time-delays over directed topology. With the help of matrix theory, Laplace transform and graph theory, two kinds of upper bounds of time-delays are derived to ensure the DIFOMAS with nonuniform time-delays can reach consensus. Finally, some numerical simulations with different parameters are offered to illustrate the feasibility and effectivity of the results derived. [ABSTRACT FROM AUTHOR]

• An optimization problem about the state mean of multi-agent systems with impulsive noise based on MCC derived from information theoretic learning is investigated in this paper, where the half-quadratic(HQ) strategy is used to simplify the solving process of the optimization problem. • A problem interfered by impulsive noise on the states of multi-agent systems is studied in this paper, where the adverse effect of impulsive noise on the states is eliminated by the MCC algorithm. • An event-triggered consensus problem of discrete-time multi-agent systems with random impulsive noise is addressed in this paper, where an event-triggering condition is derived for the system to achieve consensus. An event-triggered consensus problem of discrete-time multi-agent systems with impulsive noise under directed switching topology is investigated in this paper, where the control input of each agent is determined by its own state information and the state information of its neighbors that may be corrupted by impulsive noise. Firstly, to reduce the adverse effect of impulsive noise on consensus performance of the discrete-time multi-agent systems, maximum correntropy criterion (MCC) derived from information theoretic learning is introduced to calculate the communication weights among the agents, and an event-triggered strategy is adopted to drive the state variables of each agent to eventually converge to a same value. Secondly, the condition to guarantee consensus of the discrete-time multi-agent systems is derived by graph theory and Lyapunov stability theorem. Finally, the effectiveness of the theory is verified by several numerical simulations. [ABSTRACT FROM AUTHOR]

In order to bring the theoretical results into harmony or agreement with the reality, this paper copes with the leader-following mean square consensus issue for a class of nonlinear stochastic multi-agent systems with randomly occurring nonlinearities (RONs) and randomly occurring uncertainties (ROUs) under impulse time windows (ITWs). As a majorizing preconfigured mechanism of the windows, the configuration named periodically variable impulse time windows (PVITWs) is put forward. It not only ensures the periodic-based layout of impulse time window (ITW), but also allows the position and width of the window to be arbitrarily adjustable, so that the preset of ITW is more suitable for applications. Based on the Lyapunov stability theory and graph theory, the corresponding sufficient mean square consensus criteria are given. Finally, the feasibility of theoretical analysis is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this contribution, we aim to examine the scaled consensus problem for heterogeneous multi-agent systems, which comprise two kinds of agents: the agents with first-order dynamics and the agents with second-order dynamics. The scaled consensus here means that the ratios between the states of the agents asymptotically approach specified constants instead of the same value. Firstly, appropriate distributed control protocols are designed for first-order and second-order networked agents, respectively. Particularly, the effects of switching communication networks and time-varying delays on model performance are investigated in this paper. Secondly, an augmented system approach based on algebraic graph theory and non-negative matrix theory is adopted to solve the proposed scaled consensus problem. Finally, a sufficient criterion is established to certify the scaled consensus performance of mixed agents. The correctness of the theoretical result is demonstrated through several simulation examples. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of group consensus for a novel network model, which possesses a two-layer structure and consists of multiple interactive agents. Agents in the network are divided into several different groups according to hybrid interactions, then two neighboring agents can belong to the same group, different groups but in the same layer or different layers. Correspondingly, three kinds of relationships exist between neighboring agents in the network. Furthermore, consider that only agents in the first layer are pinned by virtual leaders, then based on the graph theory, Lyapunov function method, and optimization technique, some criteria for realizing group consensus of the network under fixed topology and switching topologies are established, which mainly depend on the topology and time intervals of the switching signal. It is found out that when the group consensus is achieved, the agents in the first layer follow the leaders asymptotically, while the agents in the second layer converge to opposite states of the leaders. Finally, a detailed numerical example is given for illustration. [ABSTRACT FROM AUTHOR]

The paper addresses a distributed containment issue for a stochastic nonlinear strict-feedback multi-agent system. In combination with the graph theory and neural networks technique, an adaptive neural containment protocol is developed within the traditional backstepping framework. Such a containment protocol allows one to extend some existing results to the case that multiple followers are confined to stochastic nonlinear dynamics. Furthermore, with the help of the quartic Lyapunov function, it is proved that all the signals in the resulting closed-loop system remain bounded in probability and the containment error converges to a small neighborhood of the origin in the sense of mean square by a suitable choice of parameters. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

In this paper, formation control problem for multiple uncertain nonlinear second-order agents in the presence of heterogeneous communication delays is addressed. A continuous repulsive vector is incorporated into agents' velocity to ensure collision avoidance, whose time derivative is approximated via a finite-time robust integral of the sign of the error (RISE)-like observer. Using adaptive neural control scheme, unknown model dynamics, external disturbances, RISE estimation error, and the time-delays among agents are robustly addressed. The sufficient conditions on the stability of the overall system and collision avoidance are derived using Lyapunov–Krasovskii functionals and algebraic graph theory, and it is proven that the formation tracking error converges to a small neighborhood of zero. Numerical simulation results are also given to illustrate the effectiveness of our proposed methods. [ABSTRACT FROM AUTHOR]

This paper focuses on studying the group consensus tracking issue of continuous-time second-order multi-agent systems (MASs) under directed fixed topology. A new protocol is introduced under the assumption that all the subgroups satisfy the in-degree balanced condition. For MASs with two subgroups, we first establish the relationship between the positive stability of matrix H and the connectedness of the topology graph. Then, we prove that MASs can achieve group consensus tracking if the system parameters satisfy some inequalities and matrix H is positive stable. Moreover, our paper extends the results for MASs with two subgroups to multiple χ -group consensus tracking. Especially, for a special graph with acyclic partition, a necessary and sufficient condition of χ -group consensus tracking is established. Finally, simulation examples are given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, the consensus for second-order heterogeneous multi-agent system is investigated. The heterogeneous system consists of linear and nonlinear second-order agents, where the nonlinear agents are still with different structures. First, the consensus of the system with and without a static leader is discussed, respectively. Then, we consider a general case where the inputs of linear second-order agents are bounded by virtue of the limitation of the actuators. Effective control protocols to achieve consensus are presented for these cases. Based on graph theory and Lyapunov stability theory, sufficient conditions are established for the consensus of heterogeneous system, where the communication topology is undirected and connected. Finally, several numerical examples are presented to verify the validity of the developed method. [ABSTRACT FROM AUTHOR]

For multi-agent systems, significantly adding to the complexity of dynamical behaviors are intrinsic nonlinearity and stochastic noises due to environmental uncertainties. This paper deals with the mean square bounded consensus problem of multi-agent systems with intrinsic nonlinear dynamics, where each agent is affected by stochastic noises. Considering the impact of the former behaviors of nonlinear agents, we put forward a novel type of integral distributed delay protocol which is formed as a weighted sum of historical information exchange over all time interval [ t − τ , t ] . Compared with the previous work, the protocol expression of this paper is more general and includes many traditional protocols as its special cases. Based on a Lyapunov-based approach, together with results from matrix theory and algebraic graph theory, sufficient conditions are derived for the mean square bounded consensus. Simulation examples with nonlinear even chaotic agents illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The cooperative exponential synchronization of multi-agent chaotic delayed neural networks (DNNs) with switching topology, stochastic disturbance and impulsive disturbance is investigated in this paper. Based on the Lyapunov stability theory, algebraic graph theory, matrix theory and the helpful stochastic Halanay inequality technique, some sufficient conditions are presented to guarantee the cooperative exponential synchronization for multi-agent chaotic DNNs with switching topology. Compared with the existing works about synchronization (or consensus) of multi-agent systems, the proposed method in this paper can provide a more general framework for the cooperative synchronization of nonlinear multi-agent systems with or without time delays, stochastic and impulsive disturbances. The famous master–slave (drive-response) synchronization of chaotic DNNs is a special case of this paper, and therefore the derived results can also be favorable for practical application in secure communication. Simulation results finally verify the effectiveness of the proposed synchronization control algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of consensus for the multi-agent systems with uncertain perturbations. A novel adaptive–impulsive protocol is designed for reaching the consensus. Particularly, this protocol is only imposed on a small fraction of agents to pin the whole system to a prescribed value. Two consensus criteria are established in cases whether the underlying graph of the multi-agent system is strongly connected or not. Two numerical examples are given to demonstrate the effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

This paper considers the containment control problem for leader-following multi-agent systems in the presence of dynamically switching topologies with communication delays. Two types of control algorithms are proposed for containment control with first-order dynamics and second-order dynamics. By applying modern control theory and algebraic graph theory, the stabilities of two containment control algorithms are analyzed on Lyapunov–Krasovskii method. Moreover, some sufficient conditions are provided through further researching the connected portion of multi-agent systems, which can ensure that the containment control can be achieved asymptotically when communication topologies are jointly-connected. Finally, some simulation examples are provided to demonstrate the effectiveness of two proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the leaderless consensus problem of multi-agent systems with jointly connected topologies and nonlinear dynamics is considered, in which the nonlinear dynamics are assumed to be non-identical and unknown. The unknown nonlinear dynamics existing in the systems are assumed to be linearly parameterized, and an adaptive design method for leaderless multi-agent systems is presented. By just using the relative position information between each agent and its neighbors, a distributed adaptive consensus control algorithm for the considered systems is proposed, in which the network graphs are jointly connected. Both the global uniform asymptotical stability and the global uniform asymptotical parameter convergence analysis of the adaptive control algorithm are carried out by using adaptive control theory, Lyapunov theory and algebraic graph theory. Finally, an example is given to illustrate the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a decentralized event triggered cooperative control design for uncertain multi-agent systems under limited communication resources. A local estimator is employed by each agent to generate self-state estimates. The estimated states are directly used in the consensus control design, and the estimator parameters are used in the event condition design. Once an event is triggered, the local estimator is repeatedly reset to its corresponding real state values, such that it can stabilize the uncertain dynamical systems without knowing the exact system model parameters. A theorem for this triggering condition is developed to provide stable thresholds that are robust to model uncertainties and guarantee the asymptotical stability by exploiting the M-matrix, algebraic graph theory and the Lyapunov method. It is rigorously proved that the overall system will achieve the consensus and has no zeno behavior under the introduced triggering condition. Simulation results are provided to show the effectiveness of the proposed decentralized event-triggered cooperative control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the problem of robust consensus for fractional multi-agent systems with external disturbances is investigated over a directed fixed interaction graph. Based on Mittag-Leffler stability theory and the inequality techniques, both linear and nonlinear systems are considered. Firstly, for fractional linear multi-agent systems, it is shown that consensus can be achieved asymptotically in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a small region determined by the bound of disturbances. Secondly, for fractional nonlinear multi-agent systems, a pinning control input is proposed such that robust consensus can be realized. Finally, the numerical simulations are given to verify the correctness of the presented theories. [ABSTRACT FROM AUTHOR]

This paper investigates group consensus of a class of heterogeneous multi-agent systems with input saturation via pinning scheme, in where the heterogeneous multi-agent system is composed of first-order agents and second-order agents. Firstly, based on the fact that the control input of partial first-order integrator agents could be bounded due to the limitation of actuators, a class of control protocols including partial first-order integrator agents with input saturation is proposed to solve the group consensus problem of heterogeneous multi-agent systems. Secondly, to guarantee the states of agents in the same group can converge to one specified consensus state, the group consensus problem of heterogeneous multi-agent systems with some pinned agents who can be first-order or second-order agents is discussed. Then a class of new control protocols with pinning scheme is proposed. By using LaSalle Invariance Principle, matrix theory, algebraic graph theory and Lyapunov stability theory, the rigorous proofs are given and the corresponding sufficient group conditions are also obtained. Finally, simulation results are also provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Time-varying group formation control problems for second-order multi-agent systems with directed topologies are investigated. Firstly, a time-varying group formation control protocol is constructed using local relative positions and velocities of each agent and its neighbors. Then based on graph theory, nonsingular transformations are applied to the closed-loop multi-agent systems. Sufficient conditions for second-order multi-agent systems to achieve time-varying group formation are further presented together with the time-varying group formation feasibility constraints. Explicit expressions of the subgroup formation reference functions are derived to describe the macroscopic movement of the time-varying subgroup formations. Moreover, by solving an algebraic Riccati equation, an approach to design the time-varying group formation protocol is proposed. Finally, a numerical example with three subgroups is provided to demonstrate the effectiveness of the obtained results. In contrast to the traditional complete formation, where only one formation is realized by the multi-agent system, in the group formation discussed in the current paper, agents are classified into subgroups and each subgroup is required to form a specified time-varying sub-formation via inter-subgroup and intra-subgroup interactions. [ABSTRACT FROM AUTHOR]

In this paper, the recent developments of distributed coordination control problems are summarized in a graph-theory-based framework. Distributed coordination has attracted tremendous attention in control and robot communities because of its potential applications in the past decade. The graph is used to describe the interconnections among agents, and different distributed coordination control problems, such as consensus, formation control, rendezvous, alignment, swarming, flocking, containment control and circumnavigation control, are adopted to this description by considering different cooperative objects. Therefore it is natural to study the distributed coordination control problems via graph theory, and the graph-theory-based results on consensus, formation control, and some closely related issues, i.e., rendezvous/alignment, swarming/flocking, containment control and circumnavigation control, are reviewed, and provide a cohesive overview in the coordination control problems, in system modeling, control law designs and analysis, and structure transformation. Finally, towards the practical applications, some potential directions possibly deserving investigation in distributed coordination control are discussed. [ABSTRACT FROM AUTHOR]

In this paper, an interventional consensus problem is formulated mathematically with signed graph theory and dynamical system theory. The interaction network associated with a multi-agent system is modeled by a signed graph (called coopetition network in sequel) and the dynamics of each agent is described by a high order differential equation with a nonlinear unknown time-varying disturbance. Then a distributed interaction law is designed for each agent to drive all agents belonging to two competitive subgroups to reach a bipartite consensus on a reference signal, which is generated by an exogenous system (called leader in sequel). Simultaneously, some neural network (NN) based adaptive estimators are proposed to estimate the nonlinear disturbances in the agent dynamics. The convergence of the bipartite consensus is analyzed by using a Lyapunov function method. Finally, some simulation results are presented to demonstrate the formation of the bipartite consensus. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of second-order impulsive consensus for multi-agent systems where each agent can be modeled as an identical nonlinear oscillator. Several fundamental consensus criteria are delivered based on algebraic graph theory and stability theory of impulsive differential equations by designing the suitable impulsive control protocols. Sufficient conditions are given to guarantee the consensus of the networked nonlinear oscillators. Finally, simulation results are presented to validate the effectiveness of theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics group consensus problem of heterogenous multi-agent systems with time delays, in which agents’ dynamics are modeled by single integrators and double integrators. To achieve group consensus, a class of dynamics group consensus protocols is proposed for heterogenous multi-agent systems with input time delays, which can also be used to solve group consensus for heterogenous multi-agent systems without input time delays. By using frequency-domain analysis method and matrix theory, some sufficient group consensus conditions, which are dependent on the input delays and the control parameters, are obtained for heterogenous multi-agent systems under directed and undirected communication topologies with and without input time delays, respectively. Simulation results are also provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, consensus problem of general nonlinear multi-agent systems with communication failures is studied based on a distributed consensus algorithm. Under the assumption that the communication graphs are strongly connected, we derive some sufficient consensus criterion for both cases fixed and switched topologies using the relative measured output states of each agent. Moreover, the case that there is a leader in the communication graph is also explicitly investigated. Finally, simulation examples are presented to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate group consensus problems for continuous-time multi-agent systems with time delays, where the agents׳ dynamics are controlled based on information from their neighbors at some discrete time instants. By utilizing nonnegative matrix theory and graph theory, the case with fixed topology and time-invariant delays is first considered, then the general case with switching topologies and time-varying delays is discussed. Some group consensus criteria are obtained in both cases, it is also shown that the agents in nonzero in-degree groups finally converge to the convex hull of those in zero in-degree groups. Simulation examples are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a group consensus problem is investigated for the heterogeneous agents that are governed by the Euler-Lagrange system and the double-integrator system, respectively, and the parameters of the Euler-Lagrange system are uncertain. To achieve group consensus, a novel group consensus protocol and a time-varying estimator of the uncertain parameters are proposed. By combining algebraic graph theory with the Barbalat lemma, several effective sufficient conditions are obtained. It is found that the time-delay group consensus can be achieved provided that the inner coupling matrices are equal in the different sub-networks. Besides, the switching topologies between homogeneous agents are also considered, with the help of the Barbalat-like lemma, and some relevant results are also obtained. Finally, these theoretical results are demonstrated by the numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: In many real-world multi-agent systems, the intrinsic dynamics of velocity for each agent is usually nonlinear dynamic rather than static. Moreover, it is often difficult to obtain the continuous velocity information of multi-agent systems. To overcome the above essential difficulties, this paper aims at investigating the second-order consensus problem of multi-agents systems with nonlinear dynamics by using impulsive control signal protocol. In detail, by using the impulsive signals from agents and virtual leaders, several impulsive control protocols are designed for reaching the second-order consensus of multi-agent systems with fixed or switching topologies. The theoretical analysis is also given to guarantee the second-order consensus based on algebraic graph theory and stability theory of impulsive differential equations. Finally, two typical examples are used to validate the above developed theoretical results. [Copyright &y& Elsevier]