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This paper studies the consensus problem of a new multi-agent system via multi-task, multi-control mechanism and multi-consensus strategy. Firstly, two multi-task algorithms are proposed, which can reasonably select some agent nodes with better performance to form the multi-agent system according to different tasks. Secondly, a multi-control protocol designed in this paper integrates continuous control mechanism, impulsive control mechanism and hybrid control mechanism, which has strong applicability and efficiency. Thirdly, a multi-consensus strategy is designed, and it can be converted into "average consensus strategy", "leader-following consensus strategy" and "hybrid consensus strategy" through different parameter settings, which greatly broadens the application field of the multi-agent system. We construct a dynamic model for the proposed multi-agent system, analyze it by using matrix measure and Lyapunov stability theory, and obtain the theorems that enable it to achieve multiple consensus. Finally, the efficiency and practicability of our theories are verified through several simulation experiments. We further carry out some comparative analysis with some relevant papers, and obtain the superiority of our theories in multiple indicators. [ABSTRACT FROM AUTHOR]

The Nash equilibrium seeking over networks of N players has been studied under the assumption that the network is static and strongly connected or switching and every time strongly connected. In this paper, we further consider the case where the network is jointly strongly connected. Since a jointly strongly connected network can be disconnected at any time instant, the existing approach cannot handle such a case. Like the literature, assuming the pseudogradient dynamics has a globally exponentially stable Nash equilibrium, we first establish a distributed estimator for actions of all players over jointly strongly connected networks. Then we compose the pseudogradient dynamics with the distributed estimator to obtain an extended gradient system with N + 1 subsystems. Under the assumption that the pseudogradient of the game is strongly monotone and Lipschitz continuous, we show that, starting from any initial condition, the state of every subsystem of the extended gradient system will exponentially converge to the Nash equilibrium of the game concerned. [ABSTRACT FROM AUTHOR]

• 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]

This paper is concerned with consensus for fractional-order multi-agent systems by observer-type output feedback with positive constraint depicted by general linear model. First, an observer-based protocol is presented and the sufficient conditions for the consensus for fractional-order multi-agent systems with positive constraint are derived. Then, the simplified conditions without utilizing the detailed topology of the graph are given. In order to simplify the process of the solution of the feedback gain matrix and the observer gain matrix, the linear programming approach is used. When the system matrix is strictly Metzler, semidefinite programming approach is adopted. Finally, some illustration examples are presented as the verification of the obtained methods. [ABSTRACT FROM AUTHOR]

In this paper, the consensus of fractional-order multi-agent systems is studied. By utilizing the unique properties of fractional-order calculus, namely hereditary and infinite memory, a new design scheme of the event-triggered pinning impulsive control strategy is proposed. Compared with the fixed pinning technique, the pinning agents here can be variable at each impulsive instant based on the considered two pinning rules (i.e., selecting randomly and according to the distances of error states). With the introduced rules, sufficient conditions are derived for consensus of systems, and the Zeno behavior is also excluded. Finally, our results show that the distance-ordered pinning can be achieved faster than the one with randomly pinning selection, and the inner impulsive gain of the impulsive controller can not be too large. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus of a multiagent system (MAS) under binary-valued communication with directed topology. An improved two-time-scale algorithm that alternates between control and estimation is proposed. Compared with the existing two-time-scale algorithm for the undirected topology case, we relax the conditions on the algorithm parameters, thereby providing more choices for practical implementations. The asymptotic property of the algorithm is analyzed by analyzing the convergence of the explicit closed-loop solution. To reduce the effect of binary communication on the consensus value for a single-sample path, the selection method for obtaining suitable parameters is given. To demonstrate their effectiveness, the selection method and algorithm are applied to the reputation management of a public welfare platform. [ABSTRACT FROM AUTHOR]

The problem of event-triggered guaranteed cost consensus for nonlinear multi-agent systems with time delay and uncertain parameters is solved in this paper. First, a distributed event-triggered strategy is presented, by which control protocol is updated only at the triggering time instants, leading to significant saving of communication resources. Second, based on the Lyapunov method and the proposed event-triggered strategy, some criteria are obtained to ensure that guaranteed cost consensus can be achieved. Moreover, it is proved that the Zeno behavior is excluded under the proposed event-triggered scheme. Third, an algorithm is given to design suitable control gains in terms of linear matrix inequalities. Finally, the validity of the proposed results in this paper is verified via numerical simulation. [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 this paper, the distributed event-triggered control (ETC) problems for nonlinear stochastic multi-agent systems (MASs) with external disturbance and time-delay are discussed. The leader-following input-to-state actual exponential mean-square consensus (EMSC) criteria are established in networks containing a directed spanning tree. By devising appropriate Lyapunov–Krasovskii function, sufficient conditions for the model to achieve leader-following input-to-state actual EMSC are obtained. The control gain matrix is designed to realize the controller. The lower bounds of interexecution times are given to show that the Zeno-behavior will not appear. Besides, the validity of theoretical analyses is verified by simulation. [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]

Highlights • This paper studies the consensus problem of discrete-time heterogeneous multi-agent systems with random link failures and switching topologies. • The properties of the infinite products of time-varying random row-stochastic matrices and graph theory are explored to analyze this problem. • A sufficient condition that only depends on the topology structures is obtained. Abstract In this paper, we consider the issue of consensus among the agents with heterogeneous dynamics under random link failures that obey Bernoulli distribution. The heterogeneous multi-agent systems (MASs) are composed of hybrid dynamic agents including first-order dynamic agents and second-order dynamic agents, and the communication topologies are assumed to be directed and time-varying. The failure control protocol is designed by randomly utilizing the previous one- or two-step states information sent by the neighbors. A criterion for the heterogeneous consensus is established by constructing augmented systems with nonnegative random coefficient matrices for the switching topologies. With the help of graph theory and stochastic matrix theory, a sufficient condition related to switching topologies is established to ensure the realization of heterogeneous consensus. Numerical examples are finally provided to validate the theoretical result. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the consensus of multi-agent systems with faults and mismatches under switched topologies using a delta operator method. Since faults and mismatches can result in failure of the consensus even for a fixed topology with a spanning tree, how to reach a consensus is a complicated and challenging problem under such circumstances especially when part topologies have no spanning tree. Although some works studied the influence of faults and mismatches on the consensus, there is little work on reaching a consensus for the multi-agent systems with faults and mismatches. In this paper, we introduce the delta operator to unify the consensus analysis for continuous, discrete, or sampled systems under one framework. We develop the theories on the delta operator systems first and then apply theories of the delta operator systems to the consensus problems. By converting the consensus problems into stability problems, we investigate and prove consensus and the associated conditions for systems 1) without any fault, 2) with a known fault, and 3) with unknown faults, under switching topologies with matching or mismatching coefficients. Numerical examples are provided and validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of event-triggered consensus control for high-order multi-agent systems with arbitrary switching topologies. To achieve this goal, a novel model partitioning approach is proposed, where the high-order error systems are partitioned into stable subsystems and unstable subsystems through coordinate transformations. By analyzing the unstable subsystems under arbitrary switching, an appropriate controller can be designed to guarantee the subsystems stable. Then the controller gain of the multi-agent systems can be derived through inverse transformations. The designed controller can guarantee the error state convergence under each topology within any time interval, which further ensures the consensus of high-order multi-agent systems under arbitrary switching topologies. Finally, a numerical example is provided to illustrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates consensus of linear multi-agent systems (MASs) with exogenous disturbances and intermittent communication. Based on a disturbance-observer method, both distributed state feedback and output feedback intermittent consensus protocols are proposed by using estimated disturbance and local relative information. And the consensus conditions are obtained by using Lyapunov stability theory. Finally, two numerical simulation examples are given to illustrate the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem of multi-agent systems with intermittent communications under sampled-data control. A novel approach called sampling time unit (STU) approach is proposed to study such system. In such approach, the work time is described by finite number of sampling time units and the rest time is describe by several average time units. The lengths of work time and rest time depend on the convergence or divergence property of each time unit. Based on the STU approach, the stabilization property at transition instants can be derived, which can compensate the divergence during rest time to some extents. The designed control scheme can tolerate a relatively large rest time. Based on the STU approach, a corresponding sampling-dependent time-varying Lyapunov function (SDTVLF) is utilized to describe the system state and derive the computable conditions for the overall consensus with maximum admissible rest time. Finally, a numerical example with two cases is provided to illustrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the event-triggered leader-follower consensus problem of linear multi-agent systems with disturbances over the directed graph. By using relative output information of the neighboring agents, we develop a novel class of distributed extended state observers. With the estimated values of tracking error and coupled states of the leader's input and disturbances, event-triggered protocols are designed to solve the leader-follower consensus problem. The proposed protocols update intermittently and can suppress disturbances actively. Subsequently, we prove the systems don't exhibit Zeno behavior. Furthermore, both the input of leader and disturbances are considered as unmodeled and not available to any follower. Finally, a simulation example is provided to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the consensus problem is investigated for a class of nonlinear multi-agent systems in lower triangular form through dynamic output feedback control. Each agent can only access to the uncertain relative output information from other agents under directed communication. The presence of unknown measurement sensitivities causes the relative output can not be used to construct the observer for each agent directly. For the sake of overcoming this difficulty, a dual-domination gain method is applied to dominate the nonlinear terms and the unknown measurement sensitivities. Then, a new dynamic output feedback consensus prtocol is presented to drive the multi-agent systems to consensus. The upper bound of the unknown measurements sensitivities is also given. At last, we provide two numerical simulation examples to verify the effectiveness of our proposed methods. [ABSTRACT FROM AUTHOR]

This paper considers an observer-based consensus problem of linear multi-agent systems with intermittent communication. An observer-based protocol with both continuous and sampled data is proposed. Consensus criteria and protocol design are obtained by matrix theory. Compared with the previous protocol, it is shown that our protocol can solve the consensus problem with lower communication time rate especially when the time interval without communication is sufficiently short. Finally, several examples are provided to show the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem of second-order multi-agent systems by means of the event-triggered approach. A novel protocol, which relaxes the mutual requirement on the velocity measurements of nodes, is proposed under the general directed topology. The proposed law is further extended to the case of changing coupling gains, that is, the node/edge-based scheme. It suggests that the variable coupling weights merely enhance or weaken the communication capacity among the nodes, while do not essentially change the structure of sensing graph. It hence gives some insight into the balance between performance index and configuration budget. Moreover, compared with the infinite precision computation algorithm, our quantization-based triggering rule is concretely designed to explore mild consensus criteria. Finally, numerical examples are presented to support the effectiveness of the proposed cooperation rules. [ABSTRACT FROM AUTHOR]

In this paper, the observer-based leader-following consensus problem for multi-agent systems with input saturation is studied under fixed and switching topology. Firstly, based on the measurable output information of systems, we construct an auxiliary observation system to estimate the real state information of systems. At the same time, the centralized event-triggered control is considered in the fixed and switching topology, and the Lyapunov function and Cauchy's convergence criterion are used to prove that the consensus of systems can be achieved. Secondly, the sufficient conditions of the event-triggered function are given, and it is proved that the constructed centralized event-triggered function can exclude the Zeno behavior. Then, the group case is considered in the fixed topology, and it is emphasized that the group event-triggered mechanism has the idea of event-triggered and decentralized control. Finally, the validity and feasibility of the theoretical results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following and leaderless consensus problem of high-order multi-agent systems on directed graphs are discussed. The delayed sampled outputs are only available data, observer-based output feedback controllers are presented. By constructing appropriate Lyapunov-Krasovskii function and auxiliary integral function to deal with the delayed sampled-data, sufficient conditions are given to ensure the global exponential consensus of the considered systems. We also obtain the upper bounds of the allowable delay and sampling period. Finally, we give the simulation examples to validate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate the global finite-time event-triggered consensus problem for a class of second-order multi-agent systems with the power of positive odd rational number and quantized control inputs under directed network topology. Under an appropriate assumption, a novel finite-time event-triggered consensus protocol is proposed to reduce the communication burden from the controller to the actuator. Based on the backstepping method, a synthetic trigger function is derived, and it is proven theoretically that the Zeno behavior is avoided for each agent under this trigger condition. Moreover, to avoid the chattering phenomenon caused by unknown input disturbances, the hysteretic quantizers are incorporated to quantize the input signals. It is shown that the proposed finite-time event-triggered consensus protocol enables the local neighbor position error, and the velocity error between any two agents converges toward a small range of the origin in a finite time. Finally, the proposed method is validated through a numerical example. [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]

In this paper, the consensus of fractional-order multi-agent systems with general linear models is investigated , where the fractional-order α satisfies 0 < α ≤ n for any given natural number n . A distributed observer-type protocol is proposed. By applying the fractional-order stability theory, properties of the Kronecker product, Mittag-Leffler function and Laplace transform, a sufficient condition is obtained under the assumption that each agent is stabilizable and detectable. Finally, a numerical simulation is presented to illustrate the usefulness of the theoretical result, which shows that the result obtained in this paper generalizes and improves some existing results in literature. [ABSTRACT FROM AUTHOR]

This paper discusses the continuous-time consensus problems for directed multi-agent networks under certain coupling or control. Since agents are driven not only by their neighbors' states but also by their derivatives in many realistic situations, dynamical networks described by singular systems are appropriate to study. Consensus problems for such multi-agent networks are considered when the agents communicate in the presence or absence of time delays. The maximum tolerated time-delay is obtained when the multi-agent network asymptotically reaches consensus. The results of this paper indicate that such multi-agent networks can achieve consensus with a demanding convergent speed through agents' interactions. Numerical examples are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, several consensus problems are studied for fractional-order double-integrator multi-agent systems, where the order of fractional derivative belongs to (0, 1). Both continuous-time and sampled-data based consensus protocols are proposed for absolute and relative damping cases, respectively. For the continuous-time protocols, consensus is achieved by using the connection between integer-order and fractional-order multi-agent systems. For the sampled-data based protocols, convergence analysis is provided by using the Hermite–Biehler theorem, which is used to deal with the stability of a polynomial with complex coefficients. It is shown that the consensus value is a function of the initial conditions for the absolute damping case, while the consensus value is related to the initial conditions and the time for the relative damping case. In addition, some examples are provided to validate the correctness of the main theorems. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the adaptive consensus problem of multi-agent nonlinear systems with odd impulsive sequence. To reduce the required information transmitted among the nodes, the distributed impulsive control protocol is designed. Considering the unknown system parameters in real system, the adaptive control technique is also used and some novel sufficient consensus conditions are derived to achieve the consensus of multi-agent nonlinear systems. The proposed odd impulsive control can obtain larger control region than the common impulsive consensus method with fixed impulsive instants, which is more flexible and reliable in practical application. Finally, two simulations are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the consensus problem of multi-agent systems (MASs) described by linear dynamic models. In order to avoid using the global information and reduce communication burden, the distributed adaptive event-based control approach is presented. Some novel triggering functions and control protocols are designed. The obtained results show that consensus can be achieved only with local information and communicating with neighbors continually is avoided as well. In addition, the Zeno-behavior for the concerned closed-loop system is excluded. Finally, a numerical example is provided to validate the availability of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the consensus problem of first-order multi-agent systems with unknown communication delay. Given unstable agent dynamics and directed network topology, consensus conditions upon two kinds of communication delays are provided. When the relative information is affected by delay, an allowable delay bound for consensus is obtained; if delay influences neighbors’ transmitted information, sufficient consensus condition admitting any large yet bounded delay is acquired. It is observed in particular that when the network topology is undirected, the delay is allowed to be time-varying. Finally, two numerical examples are carried out to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper examines the robust consensus problem of nonlinear multi-agent systems via a resilient controller subject to switching topology, wherein the effect of uncertainty in the form of additive perturbations and a randomly varying communication delay is considered in the control design. In particular, a directed graph is used to describe the interaction topology of the addressed multi-agent system and a stochastic variable obeying the Bernoulli distributed white sequences is incorporated to represent the randomness of delay. By utilizing the Lyapunov’s direct method and some matrix operations, a sufficient condition for mean-square asymptotic consensus of the addressed system is derived. Subsequently, the explicit characterization of the resilient control gain is obtained by means of linear matrix inequalities that can be effectively solved by using the ideas of convex optimization. An academic example is eventually presented to illustrate the significance and potency of the proposed control design strategy. [ABSTRACT FROM AUTHOR]

In this paper, we study the distributed optimization problem of multi-agent systems with delayed sampled-data, where the interconnected topology is directed, weighted-balanced and strongly connected, and also local cost functions are strongly convex with globally Lipschitz gradients. Based on synchronous and asynchronous sampled-data, we construct two respective algorithms. Our main results, sufficient conditions for the convergence to an optimal solution, are obtained under assumption that all design parameters are chosen properly. We also present one example to validate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a distributed event-triggered algorithm was proposed to solve a convex quadratic optimization problem of multi-agent systems under undirected and connected topologies. The event-triggered condition of each agent just requires its own state value and the state values of its neighbors at the triggering time, and hence the continuous communication and calculation are not required. Moreover, the minimum event-triggered interval is bounded by the sampling time and the Zeno behavior is therefore naturally avoided. The result is also extended to the networks with undirected and switching topologies. Numerical simulations show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Event-triggered scheme for multi-agent system is motivated by the network systems with limited communication and energy resources. In our paper, the event-triggered consensus problem of multi-agent system with heterogeneous matching uncertainties is considered. An event-based distributed adaptive controller and a novel event-triggered rule without continuous communication among agents are proposed, with which the consensus errors are uniformly bounded and all the agents could converge to an adjustable small bounded set exponentially. Meanwhile, the Zeno behavior is excluded with the designed control strategy. Finally, numerical examples are given to illustrate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper studies the consensus of second-order continuous-time multi-agent systems with quantized interaction. For static consensus, a hybrid impulsive protocol is proposed using the quantized relative position information. We prove that for any quantizer accuracy, the multi-agent systems can reach consensus if impulsive intervals are less than a given value. For dynamical consensus, an impulsive protocol is presented using both the quantized relative position and velocity information. It is shown that for any given impulsive interval, the multi-agent system can achieve consensus by selecting appropriate control gains and sufficiently small quantizer accuracy. The simulation results are given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time event-triggered consensus control problem for multi-agent systems with nonlinear uncertainties. The fixed-time consensus protocols are presented based on event-triggered strategies which can significantly reduce energy consumption and the frequency of the controller updates. Both the centralized and the distributed consensus control strategies are considered. It is proved that under the proposed event-triggered consensus control strategies the Zeno behavior is avoided. Compared with the finite-time consensus, the fixed-time consensus can be achieved within a fixed settling time with arbitrary initial states of the agents. Finally, two examples are presented to show the effectiveness of the fixed-time event-triggered consensus protocols. [ABSTRACT FROM AUTHOR]

The paper investigates second-order consensus problem of nonlinear multi-agent systems with mixed time-delays and intermittent communications, where the mixed time-delays are composed of discrete and distributed delays, and each agent is assumed to obtain the relatively completely intermittent information of neighboring agents due to communication constraints. A new kind of distributed control protocol is designed based on the adaptive intermittent control ideas, some novel criteria are derived in matrix inequalities form by resorting to the generalized Halanay inequality. It is proved that second-order consensus can be reached if communication duration is larger than a threshold value under the strongly connected and balanced topology, and the relationship between the delays and communication duration over each control period is sought out. Finally, two simulation examples are provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the consensus problem for continuous time linear multi-agent systems with directed communication topology. An estimation error dynamic is proposed to design the reduced-order observer for dealing with unknown coefficient matrices. To guarantee the consensus, control protocols based on the reduced-order observer are designed to utilize the relative outputs of neighboring agents whose communication topology contains a directed spanning tree. Then the algorithms are extended to the model reference consensus case, where the case of zero control input for reference node is not assumed. Numerical examples are given to illustrate the effectiveness of proposed approaches. [ABSTRACT FROM AUTHOR]

This paper focuses on the event-triggered distributed subgradient algorithms for solving a class of convex optimization problems based on first-order discrete-time multi-agent systems over undirected networks. The communication process of the whole network is controlled by a set of trigger conditions monitored by each agent. The trigger condition and event-triggered distributed subgradient optimization algorithm for each agent are completely decentralized and just rest with each agent's and its neighboring agents’ individual states at the event-triggered sequence of themselves as well as each agent's local objective function. At each time instant, each agent updates its state by employing its own objective function and the states collected from itself and its neighboring agents at their separate event-triggered time instants. A sufficient condition for ensuring the consensus and reaching the optimization solution is established under the condition that the undirected network topology is connected and the design parameters are properly designed. Theoretical analysis shows that the event-triggered distributed subgradient algorithm is capable of steering the whole network of agents asymptotically converge to an optimal solution of the convex optimization problem. Simulation results validate effectiveness of the introduced algorithm and demonstrate feasibility of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem of second-order multi-agent systems with constant time-delay, fixed topology and impulsive algorithm based on periodic sampling. First, by theory of impulsive differential equations, it is proved that the consensus is achieved if and only if some matrix has a simple 1 eigenvalue and all the other eigenvalues are in the unit circle. Meanwhile, the consensus state of the system is obtained, which indicates that the positions and the velocities of all agents reach, respectively, a constant state and zero. Hence we say a static consensus is achieved for multiple second-order agents. Then, by stability of polynomials, we establish a necessary and sufficient condition from the perspective of topology and protocol parameters, which provides the range of allowable time-delay and the choice of impulse period. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem of large-scale multi-agent systems (MASs) with a directed communication topology, especially for the MAS whose topology contains small strongly connected components. A sufficient and necessary consensus criterion is proposed through the combination of two methods. Firstly, a communication searching algorithm is utilized to make sure that each agent obtains the local topology information of strongly connected component where it is located. Secondly, a state-linear-transformation decomposes the consensus problem into a group of stability problems based on the strongly connected components. The corresponding consensus criterion reduces the computational complexity. Moreover, according to the consensus criterion, a distributed design procedure of gain matrices is proposed based on the homotopy method. [ABSTRACT FROM AUTHOR]

In this paper, the sampled containment control scheme is proposed to study leader-following consensus problem in second-order systems. Compared to existing investigations, we develop the containment control to the sampled-data case for sake of the movements of the agents and the limited capacities of the communication. Furthermore, it is noted that the proposed algorithm is discussed for nonlinear dynamics which is much more challenging rather than linear ones. By using the LMIs and Lyapunov method, some useful sufficient conditions are presented. Finally the numerical examples are included to validate the effectiveness of proposed algorithms. [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, a class of consensus protocol for detail-balanced networks of agents with general Lipschitz-type nonlinear dynamics and external disturbances is investigated. To guarantee asymptotic consensus in such a multi-agent system, several distributed controllers are constructed based only on the relative state information of neighboring agents. By appropriately constructing Lyapunov function and using tools from M-matrix theory, some sufficient conditions for achieving distributed consensus are provided. Finally, two examples and simulations are given to illustrate the effectiveness of the obtained theoretical result. [ABSTRACT FROM AUTHOR]

This paper studies the self-triggered control consensus problem of general linear multi-agent systems(MASs). A novel self-triggered control strategy based on output feedback is proposed for centralized and distributed cases, respectively. In consideration of the states of agents that are not available, a state observer is adopted. A dynamic observer-based control law is employed to improve the transient response. Under this triggering strategy, both the estimated states of MASs and the states of controller are updated at triggering time. The next triggering time is predetermined at the last triggering instant. Moreover, the asymptotic consensus of MASs can be guaranteed. Finally, the effectiveness of the proposed control strategy is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

Consensus can be achieved under various topologies for multi-agent systems. Then, which one is the optimal? In this paper, we consider the problem of optimal topology for consensus of heterogeneous multi-agent systems. We assume that the system consists of a leader and several followers with heterogeneous dynamics. Firstly, we define a quadratic cost function composed of consensus error and control effort for the heterogeneous multi-agent system. Secondly, by using linear-quadratic regulator theory and matrix theory, we prove that the optimal position topology and the optimal velocity topology are star graphs. Finally, simulations are carried out to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate distributed optimal control of a multi-agent consensus problem in an obstacle-laden environment. A new optimal control protocol is proposed which can let the multi-agent system reach consensus as well as avoid obstacles with a reasonable control effort. The penalty function designed to achieve obstacle avoidance capability is constructed from an inverse optimal control perspective. The asymptotic stability and optimality of the consensus algorithm are proven. In addition, the control law of each agent only requires local information from the neighbors. Finally, simulations are presented to illustrate the effectiveness of the proposed methods. [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, the consensus problem for a class of heterogeneous multi-agent systems with input saturation is investigated. The heterogeneous multi-agent system is composed of first-order agents and second-order agents. We consider that only a few first-order agents are restrained and their control input must be bounded. Firstly, a consensus control protocol under leaderless network is proposed. By applying the graph theory and LaSalle invariance principle, the protocol is proved feasible. Secondly, the consensus problem of heterogeneous multi-agent systems is discussed with a static leader and an active leader, respectively. Particularly, when the velocity of the active leader cannot be obtained in real time, a new neighbour-based consensus control protocol based on distributed observers and auxiliary systems is developed. Some sufficient conditions for consensus are established under fixed undirected connected topology. Finally, some examples were presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the robust consensus problem of fractional-order linear multi-agent systems with positive real uncertainty where the fractional-order α satisfies 0 < α < 2 . For multi-agent systems with fixed undirected topology, a distributed protocol is proposed based on the information of second-order neighbors. Then, new LMI-based sufficient conditions for robust consensus of fractional-order multi-agent systems are obtained and the feedback matrix is also determined accordingly. Finally, numerical simulation examples are presented to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the consensus problem of third-order nonlinear multi-agent systems with a fixed communication topology. A consensus protocol is proposed for solving such a problem. By a transformation, the consensus problem is converted to a stability problem, then sufficient consensus criteria are obtained by proposing a novel Lyapunov function. It is shown that consensus can be achieved for a sufficiently large feedback gain, provided that certain quadratic inequalities with respect to two parameters are satisfied. Finally, the effectiveness of the theoretical results is demonstrated through an example. [ABSTRACT FROM AUTHOR]