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This paper designs event-triggered delay compensation and disturbance attenuation control algorithms for multi-agent systems. First, through predictor-based model reduction method, an unknown large input delay can be compensated and delay-free dynamics is obtained. Based on the transformed systems, predictive descriptor observers are proposed to obtain estimated system states and sensor faults. Then, an event-triggered fault-tolerant algorithm is designed to save energy resources for communication among the agents while attenuating the disturbances. Moreover, it is validated that the systems do not exhibit Zeno behaviour using the designed event-triggering sequence. Numerical simulations are conducted to demonstrate the effectiveness of designed algorithms. [ABSTRACT FROM AUTHOR]

This paper focuses on the distributed resource allocation problem of a second-order multi-agent system with external disturbances. The global network resource equality constraint is considered. A distributed algorithm with an exponential convergence rate is proposed based on an internal model for a known bounded disturbance. By using the active disturbance approach to design a reduced-order extended state observer, the proposed algorithm is modified to reject an unknown external disturbance. Moreover, exponential convergence is achieved through the Lyapunov theory when the disturbance is constant. When the differential of the disturbance is bounded, by adjusting the control parameter of the observer, the proposed algorithm converges to an arbitrarily small neighbourhood of the optimal solution. Finally, our simulation results demonstrate the effectiveness of our proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the problem of fixed-time consensus tracking control is investigated for multi-agent networks with input uncertain dynamics under the undirected graph. First, a nonsingular terminal sliding mode manifold is proposed, with which the convergence time is globally bounded irrelevant to initial states. Then, with the aid of the observer method and sliding mode technique, the distributed nonsingular controller is designed for the underlying system to ensure that the consensus tracking errors go into sliding mode manifold and converge to origin within a desired time. Finally, examples are presented to verify the validity of the new control strategy. [ABSTRACT FROM AUTHOR]

In this paper, a class of multi-agent flocking control algorithms are contrived, which can specify communication networking, inter-agent distance and position-pattern subgrouping for second-order particle multi-agent systems, by embedding Olfati-Saber's algorithm with what we call the topological specification matrices/vectors. In other words, by equipping Olfati-Saber's algorithms with more weighting factors, the steady-state formation behaviours in a concerned multi-agent system can be manoeuvered while collision-free flocking is induced. More specifically, we create novel collective potential functions with the topological specification matrices/vectors to evaluate multi-agent dynamics and achieve the expected steady-state features in terms of graph connectivity, distance keeping, position-pattern-related subgrouping and obstacle avoidance. Moreover, formation convergence can be improved by integral specification of position difference. Numerical simulations well demonstrate effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider the distributed smooth optimisation problem of multi-agent systems over undirected connected communication topologies. The objective is to minimise the global objective function, which is the sum of local private objective functions, by exchanging and computing local information among each agent or with its neighbourhoods. To avoid continuous communication among agents and reducing communication overheads, we propose an event-triggered distributed optimisation algorithm based on a proportional-integral control strategy. We first show that the developed algorithm does not exhibit Zeno behaviour. Then, it is shown that the proposed algorithm exponentially converges to an exact global minimiser under the restricted secant inequality condition. This condition admits a more general class of the global objective function since it does not require the convexity of the global objective function and the global minimisers are not required to be unique. Theoretical results are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed optimisation problem over a multi-agent network, where the objective function is described by a sum of all the local objectives of agents. The target of agents is to collectively reach an optimal solution while minimising the global objective function. Under the assumption that the information exchange among agents is depicted by a sequence of time-varying undirected graphs, a distributed optimisation algorithm with uncoordinated time-varying step-sizes is presented, which signifies that the step-sizes of agents are not always uniform per iteration. In light of some reasonable assumptions, this paper fully conducts an explicit analysis for the convergence rate of the optimisation method. A striking feature is that the algorithm has a geometric convergence rate even if the step-sizes are time-varying and uncoordinated. Simulation results on two numerical experiments in power systems show effectiveness and performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates distributed connectivity-preserving consensus problems of networked multi-agent systems with limited communication ranges. Compared with existing literature, a main contribution of this paper is to present a new nonlinear transformation approach of consensus errors for preserving the initial interaction patterns of multi-agent systems. Both the consensus and the connectivity preservation can be achieved by using one transformed error function. Based on the proposed nonlinear error transformation, we derive distributed connectivity-preserving consensus algorithms for single-integrator dynamics, double-integrator dynamics and second-order nonlinear systems. The asymptotic stability of consensus errors and the connectivity preservation among agents are established through Lyapunov stability analysis. [ABSTRACT FROM PUBLISHER]

This paper investigates the data-driven consensus tracking problem for heterogeneous multi-agent systems. All of the heterogeneous dynamics, disturbances and measurement noises are considered for the output tracking consensus of nonlinear multi-agent network under a data-driven scheme. A dynamic linearisation method is introduced to deal with the nonlinear nonaffine structures of the agents and a heterogeneous linear data model for the agent is obtained due to the heterogeneous dynamics of the agent itself. On this basis, a distributed model-free adaptive predictive control (DMFAPC) algorithm is constructed by the use of consensus errors and the robustness analysis is conducted in the presence of disturbances. Further, the results are modified by using measured outputs to replace the system outputs, and thus a measured output-based DMFAPC is presented to deal with the omnipresent measurement noises in practical applications. The two proposed DMFAPC methods are data driven since no mechanistic model information is required wherein. And thus, no unmodelled dynamics affects the consensus performance. Instead, they can improve the control performance by utilising additional predictive information. The two proposed DMFAPC methods are verified using numerical simulations. [ABSTRACT FROM AUTHOR]

This paper discusses a convex optimisation problem with a common set of constraints in the framework of multi-agent systems. Each agent only exchanges information with its neighbours and collaboratively searches for the optimal solution of the global function. To this addressed problem, a distributed multi-step subgradient projection algorithm is developed, where an adaptive event-triggering protocol is designed to govern the information exchange. It is disclosed that the state of each agent representing the estimate of the optimal solution asymptotically converges to one of the optimal solutions under suitably chosen stepsizes and momentum parameters. Simulation results verify that the proposed algorithm has better convergence performance than the standard event-triggered subgradient projection algorithm. In addition, the communication frequency between agents can be effectively reduced to save communication resource consumption. [ABSTRACT FROM AUTHOR]

This paper proposes a class of distributed event-triggered algorithms that solve the average consensus problem in multi-agent systems. By designing events such that a specifically chosen Lyapunov function is monotonically decreasing, event-triggered algorithms succeed in reducing communications among agents while still ensuring that the entire system converges to the desired state. However, depending on the chosen Lyapunov function the transient behaviours can be very different. Moreover, performance requirements also vary from application to application. Consequently, we are instead interested in considering a class of Lyapunov functions such that each Lyapunov function produces a different event-triggered coordination algorithm to solve the multi-agent average consensus problem. The proposed class of algorithms all guarantee exponential convergence of the resulting system and exclusion of Zeno behaviours. This allows us to easily implement different algorithms that all guarantee correctness to meet varying performance needs. We show that our findings can be applied to the practical clock synchronisation problem in wireless sensor networks (WSNs) and further corroborate their effectiveness with simulation results. [ABSTRACT FROM AUTHOR]

In the presence of probabilistic communication networks between agents, the convergence analysis of max-consensus algorithm (MCA) is addressed in this paper. It is considered that at each iteration of MCA, all agents share their measurements with adjacent agents via local communication networks which is applicable in many multi-agent systems (MASs). It is assumed that the communication networks have Bernoulli dropouts, i.e. the information exchanged between agents may be lost with Bernoulli distribution. In the proposed method, the information topology of MAS is modelled as a dynamic graph with the Bernoulli adjacency matrix. It is proved that in the presence of Bernoulli dropouts and under non-restrictive assumptions concerning the MAS features and communication topology, the MCA converges with a probability one in the finite time. Furthermore, the upper bounds are provided by means of deterministic and probabilistic expressions for the expectation and dispersion of convergence time, respectively. It is shown that the proposed upper bounds are asymptotic, i.e. there are specific conditions of MAS in which the convergence time of MCA tends to the proposed upper bounds. The convergence accuracy of MCA is discussed in terms of probabilistic equations. The validity of the proposed theorems is illustrated by means of simulation results. [ABSTRACT FROM AUTHOR]

Social networking sites (SNSs) make it possible to connect people and they can communicate with others. Due to the lack of privacy mechanisms, the users in SNSs are vulnerable to some kinds of attacks. Security and privacy issues have become critically important with the fast expansion of SNSs. Most network applications such as pervasive computing, grid computing and P2P networks can be viewed as multi-agent systems which are open, anonymous and dynamic in nature. Moreover, most of the existing reputation trust models (RTMs) do not depend on any clustering structures. The clustering structures are used to effectively calculate the trustworthiness of the network nodes. In this paper, a novel cosine similarity-based clustering and dynamic reputation trust aware key generation (CSBC-DRT) scheme is proposed. For better faced clustering, a cosine similarity measure is estimated for all the nodes on the network. Based on the similarity measure among the nodes, the network nodes are clustered into disjoint groups. The RTM is built in this proposed scheme. Here, an improved MD5 algorithm is explored for key generation and key verification. After the key verification, the trusted measures such as reputation value, positive edge and negative edge values are computed to formulate the trusted network. The proposed scheme performs better than the existing RTM, which provides trusted communication in social networks. [ABSTRACT FROM PUBLISHER]

This paper considers a multi-agent system with multiple leader agents. All the agents have bounded inputs. Any two agents can communicate only if they are within a fixed distance of each other. Leaders are special agents which generate trajectories autonomously based upon certain objectives. The follower agents must partition into groups such that agents in each group track exactly one leader. Given a particular partition and the resulting information exchange topology, every follower in each group must converge onto their leader's trajectory in min–max time. A special directed spanning tree is selected in each group. Each follower agent in this tree pursues its tail agent using a time-optimal feedback policy. These local feedback laws achieve global min–max time consensus tracking for any general information graph. Further, a decentralised algorithm is proposed to partition the agents so that consensus tracking for all the groups is accomplished in the shortest possible time. [ABSTRACT FROM AUTHOR]

In this paper, the distributed convex optimisation problem of the multi-agent system over an undirected network is investigated, in which the local objective function of each agent is only known by itself. To reduce the communication consumption between agents, a state-based dynamic event-triggered algorithm with positive minimum inter-event time (MIET) is provided, where the aperiodic information communication only occurs at some discrete triggering time instants. Moreover, the sampling control technology is combined into the previous event-triggered algorithm for verifying the event-triggered condition at every sampling time, instead of continuous access. Finally, several numerical simulations are presented for illustrating and verifying the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we address the resilient group consensus of multi-agent networks in the presence of structured and unstructured Byzantine faults. In the case of structured Byzantine faults that feed different but structured values to the network, it is shown that non-faulty nodes can achieve group consensus without using any fault tolerant algorithm. Necessary and sufficient conditions on the network are derived so that the conventional consensus algorithm leads to group consensus values in the range determined by the initial values of the non-faulty nodes. In the presence of unstructured Byzantine faults, two fault tolerant algorithms are proposed to overcome the highly disruptive behaviour. Subsequently, convergence analysis of these algorithms is carried out by exploiting the robustness properties of the network. Finally, theoretical results are illustrated with several simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, the consensus-based approach for the economic dispatch problem in microgrid via distributed event-triggered control is considered. Its basic principle is to utilise the consensus of the multi-agent systems consisting of generators and loads, which will work cooperatively such that the optimal incremental cost and optimal power output could be obtained to solve the economic dispatch problem. The consensus analysis of the proposed systems focused on the following two physical scenarios: (i) containing the power balance constraint but without generation limit; (ii) the power balance constraint and with generation limit. The corresponding effective distributed event-triggered controller is designed respectively to avoid the continuous communication between the agents, the state updating of each agent depending on its own state and its neighbouring agents at their last triggering time. Compared with the centralised event-triggered mechanism, the proposed distributed scheme could reduce the frequency of information exchange between the agent and its neighbours and save the bandwidth and energy. Simulation indicates the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the mechanism of the human–computer game is investigated with the help of multi-agent systems (MASs) and reinforcement learning (RL). The game is formulated as a bipartite consensus problem while the interactions among humans and computers are modelled as a multi-agent system over a coopetition network. The coopetition network associated with the multi-agent system is represented by a signed graph, where positive/negative edges denote cooperative/competitive interactions. We assume the decision mechanism of the agents are model free and each agent has to make a distributed decision by learning the input and output data from himself/itself and his/its neighbours. The individual decision is developed with the neighbours' state information and a performance index function. A policy iteration (PI) algorithm is proposed to solve the Hamilton-Jacobi-Bellman equation and obtain the optimal decision strategy. Furthermore, an actor-critic neural network is adopted to approximate the performance index and the optimal decision strategy in an online manner. The simulation results are finally given to validate the proposed reinforcement learning approach. [ABSTRACT FROM AUTHOR]

This paper considers distributed multi-objective optimisation problems with time-varying cost functions for network-connected multi-agent systems over switching graphs. The scalarisation approach is used to convert the problem into a weighted-sum objective. Fixed-time consensus algorithms are developed for each agent to estimate the global variables and drive all local copies of the decision vector to a consensus. The algorithm with fixed gains is first proposed, where some global information is required to choose the gains. Then, an adaptive algorithm is presented to eliminate the use of global information. The convergence of those algorithms to the Pareto solutions is established via Lyapunov theory for connected graphs. In the case of disconnected graphs, the convergence to the subsets of the Pareto fronts is studied. Simulation results are provided to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The objective of this paper is to design distributed control algorithms for a multi-agent system such that a rigid formation can be achieved asymptotically and the agents can finally move with a desired velocity. In particular, it is assumed that the formation is not necessarily minimally rigid, and the desired velocity is available to only a subset of the agents. Estimators are constructed for the agents to estimate the desired velocity, which are further used to design the control inputs of the agents. The proposed control algorithms consist of a formation acquisition term which depends on a potential function and the rigidity matrix, and a velocity estimation term. To deal with non-minimal rigidity, the centre manifold theorem is exploited to prove the stability of the resulting system. Simulation results are also provided to show the effectiveness of the proposed control algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the stationary average consensus problem for second-order discrete-time multi-agent systems (SDMAS). A stationary consensus problem is to find a control algorithm that brings the state of a group of agents to a common constant value which is called the collective decision. We introduce the concept of stationary average consensus of SDMAS and propose a consensus algorithm. Based on the polynomial stability and the graph theory, we obtain two necessary and sufficient conditions of stationary average consensus of SDMAS. The last theorem provides an algebraic criterion of stationary average consensus, and can help us to determine the parameters in the consensus algorithm. Furthermore, in this consensus algorithm, only the states of the agents are transferred among the agents. Therefore, this algorithm can not only solve the stationary average consensus problem but also reduce the amount of transferred data. A numerical example is provided to illustrate the efficiency of our results. [ABSTRACT FROM AUTHOR]

This paper investigates the consensusability of multi-agent systems via observer with limited communication data. A novel algorithm to determine the parameters of quantizer and encoder is provided. The observer-based consensusability with unlimited bandwidth and observer-based consensusability with communication data rate are discussed separately. Finally, a simulation is given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, an optimal Sliding-Mode Control (SMC) technique based on Projection Recurrent Neural Network (PRNN) is proposed to solve the tracking consensus for the robotic multi-agent system. Based on a connection topology between the leader and agents and relative degree of the system, the sliding surfaces are defined in terms of the error signals. Then, a performance index is defined to realise the exponential reaching law and minimum control effort. By considering the actuator limits, a constrained Quadratic Programming (QP) problem is derived. The solution of the QP is calculated using PRNN, which is developed based on Variational Inequality (VI) problem. The structure of PRNN is composed of a dynamic and an algebraic equation, in which a projection operator acts as an activation function. The convergence analysis of PRNN as a numerical optimiser has been performed using Lyapunov theorem. Moreover, the sufficient conditions are derived for ensuring the robust stability of the closed-loop system. The performance of the proposed algorithm has been investigated by applying it to a robotic multi-agent system and has been compared with an adaptive backstepping SMC. [ABSTRACT FROM AUTHOR]

For an uncontrollable system, adding leaders and adjusting edge weights are two methods to improve controllability. In this paper, the controllability of multi-agent systems under directed topologies is studied, especially on the leader selection problem and the weight adjustment problem. For a multi-agent system, necessary and sufficient algebraic conditions for controllability with fewest leaders are proposed. To improve controllability by adjusting edge weights, the system is supposed to be structurally controllable, which holds if and only if the communication topology contains a spanning tree. It is also proved that the number of the fewest edges needed to be assigned on new weights equals the rank deficiency of controllability matrix. In addition, a leader selection algorithm and a weight adjustment algorithm are presented. Simulation examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the admissible consensus problem for heterogeneous descriptor multi-agent systems. Based on algebra, graph and descriptor system theory, the necessary and sufficient conditions are proposed for heterogeneous descriptor multi-agent systems achieving admissible consensus. The provided conditions depend on not only the structure properties of each agent dynamics but also the topologies within the descriptor multi-agent systems. Moreover, an algorithm is given to design the novel consensus protocol. A numerical example demonstrates the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive fuzzy iterative learning control scheme is proposed for coordination problems ofMth order (M≥ 2) distributed multi-agent systems. Every follower agent has a higher order integrator with unknown nonlinear dynamics and input disturbance. The dynamics of the leader are a higher order nonlinear systems and only available to a portion of the follower agents. With distributed initial state learning, the unified distributed protocols combined time-domain and iteration-domain adaptive laws guarantee that the follower agents track the leader uniformly on [0,T]. Then, the proposed algorithm extends to achieve the formation control. A numerical example and a multiple robotic system are provided to demonstrate the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the decentralised event-triggered consensus problem for multi-agent systems with Lagrangian dynamics under undirected graphs. First, a distributed, leaderless, and event-triggered consensus control algorithm is presented based on the definition of generalised positions and velocities for all agents. There is only one triggering function for both the generalised positions and velocities and no Zeno behaviour exhibited under the proposed consensus strategy. Second, an adaptive event-triggered consensus control algorithm is proposed for such multi-agent systems with unknown constant parameters. Third, based on sliding-mode method, an event-triggered consensus control algorithm is considered for the case with external disturbance. Finally, simulation results are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an energy-based control methodology is proposed to satisfy the Reynolds three rules in a flock of multiple agents. First, a control law is provided that is directly derived from the passivity theorem. In the next step, the Number of Neighbours Alignment/Repulsion algorithm is introduced for a flock of agents which loses the cohesion ability and uniformly joint connectivity condition. With this method, each agent tries to follow the agents which escape its neighbourhood by considering the velocity of escape time and number of neighbours. It is mathematically proved that the motion of multiple agents converges to a rigid and uncrowded flock if the group is jointly connected just for an instant. Moreover, the conditions for collision avoidance are guaranteed during the entire process. Finally, simulation results are presented to show the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper focuses on the resource allocation problem(RAP) with constraints under a fixed general directed topology by using the distributed sub-gradient algorithm with event-triggered scheme in multi-agent systems, where each agent owns a cost function and its state value is bounded. The distributed sub-gradient algorithm aims to minimise the total cost by a distributed manner while achieving an optimal solution. Unlike centralised methods, the triggering condition and algorithm for each agent are fully decentralised. At each instant of time, each agent updates its state by employing the states which are collected from itself and its neighbouring agents at their last triggering time. In order to illustrate the effectiveness of the proposed sub-gradient algorithm with event-triggered control law, one simulation example is presented before the conclusion. [ABSTRACT FROM AUTHOR]

This article discusses the issue of robust adaptive neural network (NN) consensus tracking control for nonlinear strict-feedback multi-agent systems with quantised input. By combining the neural network approach with robust techniques, a novel switching function is introduced to guarantee the tracking performance of this system. To estimate the unmeasured state, an NN-based adaptive state observer is developed. Based on backstepping dynamic surface control algorithms, a robust output feedback controller is constructed to guarantee that all signals in the closed-loop system remain globally uniformly ultimately bounded. Finally, numerical simulations are carried out to demonstrate the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]

For third-order multi-agent system with time delay based on fixed undirected networks, a theoretical condition is given first that ensures the system to asymptotically converge. Then, to simplify the communication complexity of the multi-agent consensus, a simple yet efficient algorithm is proposed termed the nearest neighbour principle (NNP). NNP leverages partial second-order and third-order neighbour information to largely reduce communication costs and thus contributing to the acceleration of convergence speed. Compared with classical third-order consensus algorithms, the simulation results show that NNP can not only urge the system to achieve consensus but also reduce its convergence time and communication cost. [ABSTRACT FROM AUTHOR]

This paper presents a consensus-based stochastic subgradient algorithm for multi-agent networks to minimise multiple convex but not necessarily differential objective functions, subject to an intersection set of multiple closed convex constraint sets. Compared with the existing results an alternative subgradient algorithm is first introduced based on two level subgradient iterations, where the first level is to minimise the component functions, and the second to enforce the iterates not oscillate from the constraint set wildly. In addition, a distributed consensus-based type of the proposed subgradient algorithm is constructed within the framework of multi-agent networks for the case when the iteration index of local objective functions and local constraint sets is not homologous. Detailed convergence analysis of the proposed algorithms is established using matrix theories and super-martingale convergence theorem. In addition, a pre-step convergence factor is obtained in this study to characterise the distance between the iterations and the optimal set, while some existing literatures only present a convergence work. Simulation results are given to demonstrate the effectiveness of the developed theoretical results. [ABSTRACT FROM AUTHOR]

An adaptive gain scheduling technique is investigated to discuss distributed time-varying formation (TVF) control problems for general linear time-invariant multi-agent systems (LTI-MASs), where two types of topologies are considered: (1) the interaction topology is undirected and connected, and (2) the interaction topology is directed. Two fully distributed adaptive TVF control protocols are, respectively proposed, which both assign a time-varying coupling weight to each node in the interaction topology. Two algorithms to design the constructed protocols are presented under the undirected and directed interaction topologies, respectively. A feasible TVF set is provided. The stabilities of two algorithms are, respectively proved based on the Lyapunov functional theory. For both undirected and directed interaction topologies, general LTI-MASs can achieve the given TVF using the designed fully distributed adaptive formation protocol without any global information about the interaction topology when the TVF satisfies the feasible set. Finally, theoretical results are illustrated with numerical simulation examples. [ABSTRACT FROM AUTHOR]

We consider several basic consensus problems in multi-agent systems with switching interconnection graphs, where the connections between any two agents are assumed bidirectional for notation simplicity. When the switching interconnection graphs are always connected, it has been shown in the literature that the Laplacian-based algorithm always achieves the average consensus. We first extend the discussion to the case where disconnected interconnection graphs are involved, by showing that the average consensus is still achieved if the dwell time ratio between connected graphs and disconnected ones satisfies a specified condition. Next, we consider the case where there is no connected graph but the combination of a set of graphs is connected, and propose two switching strategies for achieving the average consensus. Several numerical examples are provided to show the algorithms. [ABSTRACT FROM PUBLISHER]

We address the problem of reaching resilient consensus among a set of agents in the presence of faulty nodes (attacked or noisy). We propose general algorithms, i.e., receiving as inputs a consensus algorithm, the network topology, the initial states, and the number of maximum allowed faulty nodes. These algorithms let the agents identify the set of attacked nodes and correct the consensus value by ignoring the faulty nodes. We prove that if the number of faulty nodes is below the maximum allowed, then each non-faulty agent detects them without false positives. If the inputted discrete-time consensus algorithm has polynomial-time complexity O (C) , then the proposed correction algorithms have polynomial-time complexity O (C n f) (and O (C n) for the detection of faulty nodes), for n nodes, and f maximum allowed faulty nodes. Finally, we show the effectiveness of the algorithms through simulation, pointing out attacking scenarios dealt with our methods, where the state-of-the-art underperformed. [ABSTRACT FROM AUTHOR]

In this study, we investigate the distributed convex optimisation problem of the multi-agent system over an undirected network, in which the global objective function is the sum of all the local cost functions and the local cost function of each agent is only known by itself. In order to save the computation and communication resources, the above optimisation problem is addressed by designing two zero-gradient-sum algorithms with state-based dynamic event-triggered mechanism, where the information communication only occurs at some discrete triggering time instants. The Zeno behaviour of the above event-triggered control scheme is excluded by the existence of the positive minimum inter-event time (MIET). The convergence is proved based on the Lyapunov method. Finally, we illustrate and evaluate the effectiveness of the proposed event-triggered algorithms through numerical experiments on simulated. [ABSTRACT FROM AUTHOR]

Stationary average-tracking problems of unmatched constant reference signals are investigated for first-order multi-agent systems, and an integral-type average-tracking algorithm with delayed-state feedback is constructed. With identical communication delays and different introduced self-delays, sufficient conditions are obtained for the agents converging to the average-value of unmatched reference signals asymptotically by using the frequency-domain analysis method. To our delight, introducing delayed-state feedback improves the robustness to communication delay and unmatched reference signals. Simulation results show the effectiveness of our proposed algorithm. [ABSTRACT FROM AUTHOR]

A distributed adaptive containment control scheme is developed for a class of discrete-time multi-agent systems (MASs) under directed graphs. Each agent's model is described by nonlinear dynamics with unknown parameters that are nonlinearly coupled with the states. To deal with the uncertainties, a criterion function with weighted factor is adopted. By minimising the criterion function, a projection algorithm for each agent is designed to estimate the unknown parameters. Using the estimated parameters, an adaptive controller with only local information is designed for each agent to achieve containment control of MASs. Under the proposed distributed adaptive containment control scheme, it is guaranteed that all the leaders can finally track their reference signals and all the states of followers asymptotically converge to the convex hull formed by leaders (i.e. the convex hull formed by the reference signals). Finally, two simulation examples are given to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

To deal with the consensus problem of general first-order multi-agent systems with intermittent communication, a persistent-hold consensus algorithm is designed by introducing the hold control after the usual intermittent control. Under the fixed topology, consensus convergence conditions are obtained based on matrix theory and graph theory for the agents under our proposed persistent-hold strategy, and the results show that our proposed strategy has less conservative converging conditions than the usual intermittent control. Besides, consensus convergence conditions are also obtained for the agents under the switching topologies. Numerical simulations show the correctness of theoretical results. [ABSTRACT FROM AUTHOR]

We study a continuous-time surplus-based algorithm for multi-agent average consensus, and derive a tight upper bound on the key parameter included in this algorithm that ensures convergence over strongly connected and balanced digraphs. We specialise the upper bound result to undirected (connected) graphs and unweighted cyclic digraphs; in particular, for undirected graphs the algorithm converges for arbitrary positive values of the parameter, and for cyclic digraphs the upper bound on the parameter depends only on the number of agents and may be easily calculated. Moreover, it is suggested through extensive simulation that, for the same number of agents, the upper bound for cyclic digraphs be smaller than that for other strongly connected and possibly unbalanced digraphs; this implies that as long as the parameter satisfies the upper bound for cyclic digraphs, this parameter can work for other digraphs. [ABSTRACT FROM AUTHOR]

Here, we developed a two-dimensional multi-agent random walk algorithm. In our algorithm, agents interact with each other and change their directional rules by locally detecting moving directions of other agents. In addition to that, we introduced modulation effects in which agents controlled rule-intervals depending on number of local other agents. We show that modulation effects which introduce global ambiguity play a crucial role in establishing optimal random walk by checking the slope value (μ), depending on the density of agents. We set a modulation-added model and non-modulation model. The latter is control model. In case of non-modulation model, the slope values (μ) highly depend on the density of agents. However, in case of modulation-added model, the slope values (μ) are flexible and independent of the density of agents. [ABSTRACT FROM AUTHOR]

The event-based broadcasting containment control problem for both first-order and second-order multi-agent systems under directed topology is investigated. Based on certain event, each agent decides when to transmit its current states to its neighbours and the agents’ distributed control algorithms are based on these sampled state measurements, which can significantly decrease the number of the controllers’ updates. All the agents are divided into two groups, namely, the leaders and the followers. The formation control is introduced. The leaders exchange their information to converge to a formation. The followers utilise the information from both their leader neighbours and their follower neighbours and are driven to the convex hull of the leaders using the proposed control algorithms. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM PUBLISHER]

We consider a linear algorithm to achieve formation control in a group of agents which are driven by second-order dynamics and affected by two rationally independent delays. One of the delays is in the position and the other in the velocity information channels. These delays are taken as constant and uniform throughout the system. The communication topology is assumed to be directed and fixed. The formation is attained by adding a supplementary control term to the stabilising consensus protocol. In preparation for the formation control logic, we first study the stability of the consensus, using the recent cluster treatment of characteristic roots (CTCR) paradigm. This effort results in a unique depiction of the non-conservative stability boundaries in the domain of the delays. However, CTCR requires the knowledge of the potential stability switching loci exhaustively within this domain. The creation of these loci is done in a new surrogate coordinate system, called the ‘spectral delay space (SDS)’. The relative stability is also investigated, which has to do with the speed of reaching consensus. This step leads to a paradoxical control design concept, called the ‘delay scheduling’, which highlights the fact that the group behaviour may be enhanced by increasing the delays. These steps lead to a control strategy to establish a desired group formation that guarantees spacing among the agents. Example case studies are presented to validate the underlying analytical derivations. [ABSTRACT FROM AUTHOR]