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• A novel distributed control protocol is constructed, in which only the past sampled position data of neighbors are utilized. • The necessary and sufficient criteria depending on the order, coupling gains, sampling period, and communication topology, are established to attain consensus for the systems. • An explicit guide about how to select the coupling gains to have a large upper bound and a big tolerance interval of sampling period for a given system under undirected communication graph. In this paper, the consensus of fractional-order multi-agent systems with the order α satisfying α ∈ (0 , 1 ] is investigated. A novel distributed control protocol is constructed, in which only the past sampled position data of neighbors are utilized. Then, based on Laplace transform, Mittag-Leffler function, and matrix theory, necessary and sufficient criteria depending on the order, coupling gains, sampling period, and communication topology, are established to attain consensus for the systems. Meanwhile, the intervals of coupling gains and sampling period associated with the maximum eigenvalue of Laplacian matrix over an undirected graph are presented to attain consensus. Finally, the availability of theoretical results is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

• The leader-following bipartite consensus of multi-agent systems with matched uncertainty is studied. • A nonlinear function is added to the control protocol to suppress the influence of matched uncertainty. • The event-triggered mechanisms are designed for each edge and the leader. • The control protocols and event-triggered conditions in this paper are fully distributed. • The state feedback and output feedback control protocol are proposed. The leader-following bipartite consensus of multi-agent systems (MASs) with matched uncertainty is investigated by using the fully distributed asynchronous edge-based event-triggered mechanism. Firstly, event-triggered mechanisms are constructed for each edge and the leader to decrease the consumption of system resources. The state feedback and output feedback control protocols are proposed, which do not depend on the global values of the communication graph. Secondly, sufficient conditions for the bipartite consensus of MASs are obtained by Lyapunov stability theory. Thirdly, the feasibility of the proposed event-triggered mechanisms is further verified by exclusion of Zeno phenomenon. Finally, the effectiveness of control protocol is illustrated by simulation. [ABSTRACT FROM AUTHOR]

In this paper, a resilient distributed consensus algorithm is proposed based on multi-agent system to defend against the Byzantine attack. Two attack scenarios including node attack and edge attack are considered and the differences between them are described, in which the edge attack scenario is seldom considered before. The assumption for a network under g -local attacks is relaxed from (2 g + 1) -robust directed graph to (g + 1) -robust one based on a novel filtering method. The convergence and optimality are guaranteed by theoretical analysis, which ensures all the agents without attack can make an agreement and converge to a certain range. The simulation results show that for the two attack scenarios, the proposed algorithm can converge to the optimal solution of the compensation problem and the original problem, respectively. The proposed algorithm is more effective and has faster convergence speed compared with the contrast one. [ABSTRACT FROM AUTHOR]

The consensus problem for a multi-agent system (MAS) is investigated in this paper via a sliding mode control mechanism subject to stochastic DoS attack, which may occur on each transmission channel independently and randomly according to the Bernoulli distribution. A distributed dynamic event-triggered strategy is implemented on the communication path among agents, where dynamic parameters are introduced to adjust the threshold of event-triggered condition. After that, a distributed sliding mode controller is proposed for ensuring the stochastic consensus of the MAS. Meantime, a minimization problem is solved to obtain the correct controller gain matrix. At last, a numerical example is shown to demonstrate the presented results. [ABSTRACT FROM AUTHOR]

This paper studies a distributed average tracking problem of uncertain multiagent systems over directed graphs. The basic idea is to establish an appropriate reference model by introducing an adaptive control scheme. The output of the reference model is the average of multiple time-varying reference signals. This implies that the reference model partially solves the problem of distributed average tracking of directed graphs. Moreover, an appropriate control law is designed to make the output of the multiagent system with uncertain parameters approaches the average of the reference signals from the reference model. The feasibility of the proposed scheme is theoretically proved and the effectiveness of the scheme is verified through a simulation example. [ABSTRACT FROM AUTHOR]

This paper focuses on the issues of non-fragile event-triggered consensus problem for nonlinear multiagent systems (MASs) with external disturbance subjected to randomly occurring packet losses and periodic Denial of Service (DoS) attacks. Under connected communication topology, each agent exchanges information with its neighbors. In the presence of packet losses and DoS attacks, an event-triggered mechanism is designed to decide when to communicate the current sampled-data. Randomness is solved by using Bernoulli distribution in a stochastic way and the external disturbance is handled by using H ∞ performance. A sufficient condition is derived in terms of linear matrix inequalities (LMIs) by introducing time-varying Lyapunov–Krasovskii Functional (LKF), ensuring mean square consensus for the resulting closed-loop systems. Finally, to show the effectiveness and applicability of proposed control scheme, two numerical simulations are presented. [ABSTRACT FROM AUTHOR]

This paper proposes two kinds of distributed disturbance observer (DO) based consensus control laws for linear multi-agent systems (MAS) with mismatched disturbances. For a linear MAS with mismatched disturbances generated by exosystems, we design relative information based distributed DOs for each agent to obtain information of disturbances. The first method is to utilise the information of disturbances obtained by the distributed DO as a feedforward term to reject influence of exogenous disturbances for consensus results, where the gain matrix of the feedforward term is obtained via solving a matrix equation. The second method is to design an internal model based dynamic compensator to reject influence of exogenous disturbances, where the dynamic compensator is also updated by the distributed DO. The leaderless and leader-follower consensus are both considered in this paper, and rigorous proof of consensus results is also given. Finally, some numerical simulations verify effectiveness of the proposed consensus control laws. [ABSTRACT FROM AUTHOR]

In this paper, we study the cooperative consensus control problem of mixed-order (also called hybrid-order) multi-agent mechanical systems (MMSs) under the condition of unmeasurable state, unknown disturbance and constrained control input. Here, the controlled mixed-order MMSs are consisted of the mechanical agents having heterogeneous nonlinear dynamics and even non-identical orders, which means that the agents can be of different types and their states to be synchronized can be not exactly the same. In order to achieve the ultimate synchronization of all mixed-order followers, we present a novel distributed adaptive tracking control protocol based on the state and disturbance observations. Wherein, a distributed state observer is used to estimate the followers' and their neighbors' unmeasurable states. And, a novel estimated-state-based disturbance observer (DOB) is proposed to reduce the effect of unknown lumped disturbance for the mixed-order MMSs. The proposed control protocol and observers are fully distributed and can be calculated for each follower locally. Lyapunov theory is used for proving the stability of the proposed control algorithm and the convergence of the cooperative tracking errors. A practical cooperative longitudinal landing control example of unmanned aerial vehicles (UAVs) is given to illustrate the effectiveness of the presented control protocol. [ABSTRACT FROM AUTHOR]

This paper is concerned with the secure bipartite consensus of second-order multi-agent systems under denial-of-service (DoS) attacks. The communication network is an antagonistic network, in which there is cooperative or competitive relationship between neighboring agents. Meanwhile, information cannot be transmitted when the system is attacked. A novel event-triggered control algorithm based on sampled data is proposed to save limited resources and exclude the Zeno behavior. By applying the convergence of monotone sequences, graph theory as well as the discrete-time Lyapunov function method, some sufficient conditions on threshold parameters, frequency and duration of DoS attacks, and sampling period are derived to ensure the bipartite consensus under DoS attacks. Finally, the correctness and advantages of theoretical results are demonstrated by a numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, a distributed control architecture is presented for addressing the cooperative perimeter surveillance of rectangular areas for multi-agent system whose dynamics is described by double integrator models subject to exogenous bounded disturbances. In particular, a novel methodology to generate proper state trajectories of a swarm of agents is provided and then exploited as references for the underlying model predictive controllers bank. Specifically, the swarm is first driven along the perimeter of a rectangular strip and next imposed to enter a given containment region while remaining simultaneously outside a forbidden region around a prescribed target. Steady-state conditions are analyzed and sufficient conditions derived in terms of the control law parameters. Simulation results put in light the main properties of the control architecture that is designed to adequately switch between two different distributed algorithms in order to guarantee constraints satisfaction within the capturing region despite any disturbance realization. [ABSTRACT FROM AUTHOR]

This paper studies practical consensus problems for continuous-time multiagent systems with heterophilous dynamics. Agents in the network tend to cease communication when they are close enough to each other inspired by the heterophily principle in social and opinion dynamics. We propose two types of state constraints on dynamical agents, in which the hard constraint refers to exogenous restrictions that rule the entire evolution of the agent behavior and the soft constraint turns out to be endogenous and only the ultimate equilibria of the agents are restricted. Sufficient conditions have been established to achieve practical consensus for both types of constrained systems. Numerical simulations show that the practical consensus time grows logarithmically, revealing a rapid convergence with respect to disagreement of initial conditions. [ABSTRACT FROM AUTHOR]

This paper is concerned with event-triggered secure consensus for a class of linear multi-agent systems (MASs) under denial-of-service (DoS) attacks. Different from some existing methods, a multi-sensor multi-rate (MSMR) sampling mechanism is introduced to sample system states of agents. A class of multi-rate observer is devised to deal with some problems involved, such as the asynchrony and the incompleteness of several state sub-vectors, caused by the MSMR sampling mechanism. By using the partially updated state information of each agent, a novel multi-rate event-triggered mechanism is proposed, in which the continuous monitoring of the combined measurement information is avoided. Then, an event-based distributed secure consensus control protocol is presented against DoS attacks for the MAS under a directed communication topology. By taking into account the information on the duration and frequency of the DoS attacks, a sufficient condition is established to design suitable control protocols such that consensus can be achieved. Finally, a numerical example is provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we address the distributed convex optimization problems for multi-agent systems. In our research, it is assumed that each agent in the multi-agent system could merely interact with its neighbors via a directed graph and is available to its own cost function. We then utilize the push-sum distributed dual averaging (PS-DDA) algorithm to tackle with the distributed optimization problem. However, we consider that there exist subgradient delays in PS-DDA algorithm. The proof of the main result which shows that the PS-DDA algorithm with subgradient delays converges and the error possesses sublinear growth of a rate O (τ 2 T − 0.5) , where T denotes the total amount of iterations, is detailed presented in this paper. Finally, a numerical example is simulated to show the performance of the algorithm we study in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the scaled consensus of resource-limited multi-agent systems with second-order integrator dynamics and undirected topologies is investigated. In order to reduce bandwidth and computation requirements, a scaled consensus protocol based on periodic edge-event driven control is proposed. It is proven that all the agents could converge to a scaled consensus state while the interaction topology is connected. Moreover, a self-triggered scheme is proposed so as to further reduce communication times between agents. Notably, the event-detecting period is introduced so that Zeno behavior could be excluded in our model. Finally, simulations are given to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of localizing and circumnavigating an unknown stationary target by multiple autonomous agents using bearing-only measurements is studied. We assume that all agents are anonymous in the sense that they are indistinguishable from each other, and each agent is not permitted to exchange its local measurements or state information. A novel collision avoidance mechanism is proposed to ensure collision-free system evolution, and a distributed control algorithm is developed to steer the group of agents to circumnavigate the target at a desired distance with any prescribed angular spaced formation. Global finite-time stability of the system is rigorously derived. The performance of the proposed algorithms is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper deals with the event-triggered collaborative control problem of multiagent systems (MASs) under denial-of-service (DoS) attacks. For large-scale MASs, it is difficult to implement fully distributed collaborative control by tuning the coupling strengths of all edges due to the limitation of computing resources in practical applications. To overcome this difficulty, an edge-pinning-based adaptive strategy for coupling strengths is established, under which only the coupling strengths of partial edges are tuned instead of all ones. Under this strategy, the edge-pinning-based resilient distributed event-triggered synchronous and asynchronous adaptive laws are designed, both of which ensure the implementation of security consensus against DoS attacks and the elimination of Zeno behavior. It should be pointed out that the designed two resilient consensus strategies are fully distributed. Additionally, under these event-triggered strategies, the updating of control protocols and the monitoring of triggering functions do not require continuous communications, thus reducing the communication burden among agents. Finally, simulations conducted on a network composed by six aircrafts are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of multi-objective time-varying formation control in cyber–physical systems (CPSs) with saturated constraints and malicious agents. By incorporating the concept of multi-agent systems and employing objective weight allocation method, the problem is reformulated as the seeking for the Nash equilibrium solution in a time-varying non-cooperative game. To evaluate the trustworthiness of agent behavior, we propose an adaptive weight learning algorithm based on reinforcement learning. Furthermore, we develop a novel smooth saturation control strategy and a predefined time controller to design a distributed resilient algorithm for CPSs with both known and unknown parameters. Additionally, we apply the designed algorithm to the resilient distributed multi-objective time-varying formation control problem of unmanned aerial vehicles (UAVs) to verify its effectiveness. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time cluster optimization problem of first-order multi-agent systems (MASs) under directed detail-balanced networks, in which the optimization objective is a linear combination of local objective functions. Two piecewise distributed control protocols are proposed to solve the optimization problem with time-invariant and time-varying objective functions, respectively. Under the two proposed piecewise control protocols, the fixed-time cluster optimization problem can be solved on the basis of maintaining the cluster consensus unchanged. Furthermore, the initial states of all the agents need not be restricted to the minimum of their local cost functions. Finally, we provide two examples to illustrate the effectiveness of the proposed control protocols. [ABSTRACT FROM AUTHOR]

This paper deals with the privacy-preserving average consensus problem for continuous-time multi-agent network systems (MANSs) based on the event-triggered strategy. A novel event-triggered privacy-preserving consensus algorithm is designed to achieve the average consensus of MANSs while avoiding the disclosure of the agents' initial states. Different from the approaches incorporating stochastic noises, an output mask function in the proposed algorithm is developed to make initial state of each agent indiscernible by the others. Particularly, under the output mask function, all agents can exactly tend to the average value of initial states rather than the mean square value. Under the proposed algorithm, detailed theoretical proof about average consensus and privacy of the MANSs are conducted. Moreover, the proposed algorithm is extended to nonlinear continuous-time MANSs, and the corresponding results are also derived. A numerical simulation eventually is performed to demonstrate the validity of our results. [ABSTRACT FROM AUTHOR]

This paper considers a nonsmooth constrained distributed convex optimization over multi-agent systems. Each agent in the multi-agent system only has access to the information of its objective function and constraint, and cooperatively minimizes the global objective function, which is composed of the sum of local objective functions. A novel continuous-time algorithm is proposed to solve the distributed optimization problem and effectively characterize the appropriate gain of the penalty function. It should be noted that the proposed algorithm is based on an adaptive strategy to avoid introducing the primal-dual variables and estimating the related exact penalty parameters. Additional, it is demonstrated that the state solution of the proposed algorithm achieves consensus and converges to an optimal solution of the optimization problem. Finally, numerical simulations are given and the proposed algorithm is applied to solve the optimal placement problem and energy consumption problem. [ABSTRACT FROM AUTHOR]

In this paper, the distributed optimization problem is investigated by employing a continuous-time multi-agent system. The objective of agents is to cooperatively minimize the sum of local objective functions subject to a convex set. Unlike most of the existing works on distributed convex optimization, here we consider the case where the objective function is pseudoconvex. In order to solve this problem, we propose a continuous-time distributed project gradient algorithm. When running the presented algorithm, each agent uses only its own objective function and its own state information and the relative state information between itself and its adjacent agents to update its state value. The communication topology is represented by a time-varying digraph. Under mild assumptions on the graph and the objective function, it shows that the multi-agent system asymptotically reaches consensus and the consensus state is the solution to the optimization problem. Finally, several simulations are carried out to verify the correctness of our theoretical achievements. [ABSTRACT FROM AUTHOR]

In this paper, the impulsive average-consensus problem of first-order multi-agent systems with dynamically changing topologies is investigated. Continuous-time dynamics and impulsive protocols are both subjected to effects from nonuniform time-varying communication delays. By utilizing Razumikhin techniques and time-varying Lyapunov function method, some impulse-delay-dependent sufficient criteria for the average-consensus of multi-agent systems are derived. In addition, the discrete-time connection digraph is designed in terms of linear matrix inequalities for given impulsive sequences and some programming skills are used to make the discrete-time topology meet the needs of the actual environment. Numerical simulations are given to illustrate the effectiveness and validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the positive consensus for a class of multi-agent systems (MASs) with average dwell time (ADT) switching. First, sufficient and necessary conditions are derived for preserving the positivity of the closed-loop MASs. Second, the performance analysis of the consensus error system is accomplished by using the multiple Lyapunov functions (MLFs) approach, and an ADT switching technique designs the corresponding controlled switching signal. Then, both leaderless and leader-following positive consensus are achieved. Furthermore, to reduce the computational complexity, a novel leader-following positive consensus criterion is derived in the form of linear programming (LP). Finally, simulation examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem for a class of nonlinear multi-agent systems with asymmetric time-varying output constraints and completely unknown non-identical control directions. Firstly, in order to deal with the problem of asymmetric time-varying output constraints, the original output-constrained multi-agent systems are transformed into new unconstrained multi-agent systems by constructing the state transformation for each agent. Secondly, the emergence of multiple Nussbaum-type function terms is avoided by introducing novel sliding-mode-esque auxiliary variables and consensus estimate variables, which allows the control directions to be completely unknown non-identical. Thirdly, a novel control strategy is proposed by combining novel variables with state transformation method for the first time, which makes the design of distributed consensus protocol more concise. Through Lyapunov stability analysis, the proposed distributed protocol ensures that the output constraints are never violated and the consensus can be achieved asymptotically. Finally, a practical simulation example is given to demonstrate the effectiveness of the proposed distributed consensus protocol. [ABSTRACT FROM AUTHOR]

This paper deals with the leaderless consensus controller design for nonlinear multi-agent systems (MASs) subject to the input saturation nonlinearity by using an event-triggered (ET) mechanism. An adaptive ET scheme has been established with variable threshold parameter for attaining an efficient control bandwidth. Linear parameter varying (LPV) formulation and region of stability investigation for dealing with the inherent nonlinearity and input saturation, respectively, are focused in the study. A consensus controller design condition has been formulated to ensure the regional stability, to determine the consensus protocol gains, to choose the parameters of ET mechanism, and to select an appropriate adaptation law for ET control. Elimination of Zeno behavior, based on nonlinearity bounds, for the adaptive ET mechanism has been ensured through a rigorous analysis. In contrast to excising methods, a directed communication topology, adaptive ET mechanism, and removal of Zeno behavior as well as elimination of the windup effect of saturation have been considered in our work. A simulation study has been provided for six robotic agents and comparison results with the existing method are revealed. [ABSTRACT FROM AUTHOR]

• A novel finite-time sliding mode manifold is developed, which removes the need for the fractional-order signum function and reduces the computational burden. • An adaptive distributed finite-time controller is proposed by combining artificial potential function with sliding mode technique. • The presented controller is capable of achieve finite-time consensus, connectivity preservation, and event-triggered transmission simultaneously. In this paper, we consider the robust finite-time consensus problem for second-order multi-agent systems (MASs) with limited sensing range and weak communication ability. As a stepping stone, a novel distributed finite-time sliding mode manifold is developed for MASs. Then, by combining artificial potential function technique with the presented sliding mode manifold, a robust distributed control scheme is proposed to enable the finite-time consensus of MASs while preserving the prescribed communication connectivity. Furthermore, the sampling frequency and implementation burden of the proposed controller can be reduced with resort to the event-triggered methodology. Finally, numerical examples are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the distributed optimization problems with linear coupling constraint of general homogeneous and heterogeneous linear multi-agent systems under weighted-balanced and strongly connected digraphs. In order to control all agents converge to the optimal output, we propose distributed control laws, therein, the optimal output can make the global cost function reach minimum. Then we guarantee the convergence of the proposed algorithms by the properties of Laplacian matrix and Lyapunov stability theorem. Furthermore, we extend the result of heterogeneous linear multi-agent system to the case that dynamics of agents are subject to external disturbances, and prove that the algorithm designed by internal model principle can make all agents reach the optimal output exactly. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms. [ABSTRACT FROM AUTHOR]

• Second-order MAS is utilized in distributed optimization problems with triggers. • The communication schemes of the proposed distributed algorithms contain two categories of triggers, the event-triggered communication and the time-triggered communication. • The criteria about the selection of controller parameters and the trigger conditions are derived to ensure that the algorithms converge to the optimal solution. This paper deals with the large category of convex optimization problems on the framework of second-order multi-agent systems, where each distinct agent is assigned with a local objective function, and the overall optimization problem is defined as minimizing the sum of all the local objective functions. To solve this problem, two distributed optimization algorithms are proposed, namely, a time-triggered algorithm and an event-triggered algorithm, to make all agents converge to the optimal solution of the optimization problem cooperatively. The main advantage of our algorithms is to remove unnecessary communications, and hence reduce communication costs and energy consumptions in real-time applications. Moreover, in the proposed algorithms, each agent uses only the position information from its neighbors. With the design of the Lyapunov function, the criteria about the controller parameters are derived to ensure the algorithms converge to the optimal solution. Finally, numerical examples are given to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Abstract This paper considers solving a class of optimization problems over a network of agents, in which the cost function is expressed as the sum of individual objectives of the agents. The underlying communication graph is assumed to be undirected and connected. A distributed algorithm in which agents employ time-varying and heterogeneous step-sizes is proposed by combining consensus of multi-agent systems with gradient tracking technique. The algorithm not only drives the agents' iterates to a global and consensual minimizer but also finds the optimal value of the cost function. When the individual objectives are convex and smooth, we prove that the algorithm converges at a rate of O (1 / t) if the homogeneous step-size does not exceed some upper bound, and it accelerates to O (1/ t) if the homogeneous step-size is sufficiently small. When at least one of the individual objectives is strongly convex and all are smooth, we prove that the algorithm converges at a linear rate of O (λt) with 0 < λ < 1 even though the step-sizes are time-varying and heterogeneous. Two numerical examples are provided to demonstrate the efficiency of the proposed algorithm and to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract: Repeated practice is one of the most effective methods in improving the performance of coordination control tasks for groups of individuals, such as marching band, soldier (tank or warcraft) formation, and unmanned aerial vehicle flying queue. The key objective of this paper is to give a theoretical explanation for this observed behavior by considering a class of coordination learning problems for groups of mobile agents. To be specific, the agents are considered to preserve the desired relative formations between each other through a learning process, for which iterative rules are applied to construct distributed algorithms based on the relative information between each agent and its neighbors. Convergence results are derived by combining the graph theory based method and the Lyapunov analysis, which can address coordination learning problems for multi-agent systems both with and without a reference as the prior knowledge. In addition, numerical simulation results are provided to demonstrate the coordination learning performance for groups of mobile agents. [Copyright &y& Elsevier]