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Minimum circle circumnavigation is proposed in this paper, which is of special value in target monitoring, capturing and/or attacking. With this new pattern, our goal is to steer one agent to enclose multiple targets along a safe and minimum circular orbit with the desired tangential speed. This is achieved by a control protocol with dynamic compensators, which is also capable of avoiding collision between the agent and the multiple targets during the whole operational process. The control protocol is further extended to the scenarios of multiple agents circulating a group of targets by adding a coordination mechanism into the tangential velocity term, which allows the agents to distribute evenly on each expected circular orbit with the same or different radius. Simulations results illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper makes further generalisations based on the application of edge-based state decomposition methods on average consensus. The edge-based state decomposition method is a privacy-preserving technique that leverages the number of neighbours to decompose node information, effectively safeguarding the privacy of nodes in average consensus, even in the absence of reliable neighbours. Building upon this method, our research expands its applicability to bipartite consensus and scale consensus. In bipartite consensus, the method can also accurately achieve consensus while guaranteeing privacy. In contrast, scale consensus effectively protects the privacy of the final consistency result. In addition, this paper refines the privacy proofs for different enemies. Finally, the simulation results presented at the end of the paper validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the problem of practical finite-time coordinated path following control of a multi-agent system in an uncertain Euler flow field is studied. The coordinated path following control system is decoupled into a path following sub-system and a coordinated formation sub-system. The uncertain Euler flow field is estimated by constructing an extended state observer. By embedding the extended state observer into the design of the finite-time controllers for both sub-systems, practical finite-time stability of the coordinated path following control system is proved. Simulation results are provided for validating the feasibility and effectiveness of the control method. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem of the multi-agent system by means of the sliding mode control (SMC) approach. For each agent, the component-based weighted try-once-discard protocol is used for scheduling the transmission of error signals via communication network to the controller. Only one node with the greatest difference at each moment can send its information through the network to the controller. Then, taking the protocol's impact into account, a token-dependent sliding mode controller is designed. Both the asymptotic stability of the closed-loop error system and the reachability of the specified sliding surface are achieved. In addition, by utilising the optimised solving algorithm, the controller gains are attained. Eventually, a simulation example proves the effectiveness of the suggested SMC approach. [ABSTRACT FROM AUTHOR]

For a multi-agent system (MAS) with a directed weighted chain graph, this article studies the effect of adding reverse edges on its convergence rate. The introduction of weights leads to our research being more complex and challenging. Firstly, for the case of one reverse edge, there are two completely opposite conclusions about the effect of adding one reverse edge on the convergence rate under certain conditions, which is dependent on whether the end node of the reverse edge is the root node of the chain graph or not. Subsequently, we discuss the relative positions of two reverse edges in three cases and obtain the convergence rate of the whole network is determined by the ranges, the relative positions of these two reverse edges, and the sizes and distribution of weights in the directed weighted graph. Moreover, as the number of reverse edges increases, we overcome the complex relationships among multiple reverse edges and establish similar theories. Finally, some numerical examples are given to illustrate our main theorems. Our results generalise the results from unweighted directed graph to a weighted directed graph. [ABSTRACT FROM AUTHOR]

In this paper, the problem of circle formation of multi-agent system in a plane is investigated. Inspired by the idea of decouple design, we decompose the overall control objective into two sub-goals, the first one is circle forming that agents need to move to a circle with a desired radius and centred on a predefined target, and the second one is space adjustment that each agent form and maintain a desired relative position with its neighbours. Since the completion of the second objective requires information from neighbouring agents, a distributed event-triggered controller is proposed to save communication resources and reduce the number of controller updates, which consists of two parts corresponding to two sub-goals. Furthermore, it is proved that there exists no Zeno behaviour under the proposed control laws. Finally, a numerical simulation verifies the effectiveness of the distributed event-triggered circle formation controller proposed in this paper. [ABSTRACT FROM AUTHOR]

The consensus control problem of multi-agent systems (MASs) has received an increasing research interest with ever-developing consensus theory. Before it can be widely applied to actual engineering, the consensus theory needs to be improved by addressing some practical problems. One of the key problems is how to ensure the desirable performance of each agent as well as the entire MAS when confronted with faults, which is referred to as the fault-tolerant consensus control (FTCC) issue. In this survey, we review the classic and recent results in the context of FTCC from two aspects, namely, physical security and logical security. In addition, we provide the latest results on FTCC where the physical and logical security are considered simultaneously in a framework. Finally, we outline several potential future research topics on the FTCC issue. [ABSTRACT FROM AUTHOR]

This study considers the consensus tracking problem for second-order multi-agent systems subject to channel fading. In order to reduce the network burden, an event-triggered strategy is introduced to lessen the frequency of information transmission between agents, based on which an event-triggered sliding mode controller is designed. Meanwhile, considering that the transmission among followers will be affected by channel fading, the statistical characteristic of channel fading is integrated into the measurement function of consensus tracking errors. Both the reachability and stability of the multi-agent system are analysed theoretically, and it is also proved that the event triggering strategy can exclude Zeno behaviour. Finally, a simulation example is provided. [ABSTRACT FROM AUTHOR]

This paper addresses an event-triggered distributed convex optimisation problem over networks with time-varying delays. The communication between agents is triggered by conditions monitored by nodes. The proposed triggering condition is decentralised and does not require continuous communications among agents to calculate the threshold. By constructing a new Lyapunov–Krasovskii function, the optimisation problem is solved, and the explicit sufficient condition for the maximum admissible time delay is derived. Moreover, the Zeno behaviour of the closed-loop system is excluded. Finally, a simulation example is provided to verify the results obtained in this paper. [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 the consensus tracking problem of second-order multi-agent systems. The key feature in this work is that the state transmission among followers may be subject to channel fading. In order to cope with the adverse factor, this work introduces the statistical information of channel fading into the measure function on the consensus tracking errors. Meanwhile, a feasible distributed sliding mode controller is designed by means of the received fading states. And then, both the reachability and the stability of sliding mode dynamics are analysed, under which the consensus tracking for followers to the leader is attained. Finally, a numerical simulation example is provided for verifying the proposed sliding mode control scheme. [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]

The robust output formation problems are considered for uncertain multi-agent systems. The dynamic of each agent is constructed by a nominal system combined with uncertainties and external disturbances. Based on the interaction topology among agents, a robust time-invariant formation controller is proposed. The designed controller consists of two parts: a nominal output feedback formation controller and a robust compensator. The nominal controller is designed to achieve the desired output formation, and the robust compensator is introduced to restrain the influence of the uncertainties and disturbances. An output formation feasible condition is proposed, and it is proven that the output formation error can be made arbitrarily small. Finally, a simulation example is provided to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the second-order leader-following consensus of coupled nonlinear agents with intermittent control is investigated. A subset of followers is pinned while it is assumed that the underlying digraph contains a directed spanning tree with the leader node as the root. By using multiple Lyapunov functions method and algebraic graph theory, it is proved that second-order consensus is guaranteed by choosing the control and rest durations appropriately in each time interval. This result provides high flexibility in control gain design, allowing multiple switching with different gains in arbitrarily-chosen time intervals. As a result, it not only encompasses many existing intermittent control schemes but can also manage practical situations, such as recovery from occasional control failures. Numerical simulations are also given to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the iterative learning control is introduced to solve the consensus tracking problem of a multi-agent system with random noises and measurement range limitation. A distributed learning control algorithm is proposed for all agents by utilising its nearest neighbour measured information from previous iterations. With the help of the stochastic approximation technique, we first establish the consensus convergence of the input sequences in almost sure sense for fixed topology as the iteration number increases. Then, we extend the results to switching topologies case which is dynamically changing along the time axis. Illustrative simulations verify the effectiveness of the proposed algorithms. [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]

In this paper, the leader-following consensus problem of the fractional-order nonlinear multi-agent systems via event-triggered control is considered. An effective event-triggered controller is designed and then generalised exponential consensus of the controlled multi-agent systems is studied in the sense of Mittag-Leffler stability of fractional-order systems. The event-triggering function design is dependent on the parameter of the system structure and the minimum inter-event interval can be flexibly adjusted with different fractional-order α. With the event-triggered control scheme, the consensus condition is obtained and the convergence rate of the system is estimated. Numerical simulation indicates the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The consensus problem of a class of fractional-order linear multi-agent systems with distributed control containing input time-delay is investigated. By adopting the frequency domain analysis and generalised Nyquist criterion for the fractional-order time-delay systems, the delay-dependent consensus condition is obtained. Then, we are interested in finding the maximum time-delay tolerance and give an exact formula for calculating the maximum time-delay to maintain the system is consensusable. As illustrated by the numerical examples, the proposed theoretical results work effectively and accurately. [ABSTRACT FROM AUTHOR]

This paper studies a leader-following consensus problem of continuous-time double-integrator multi-agent systems with measurement noises and time-varying communication delays under directed topology. By utilising the neighbour position and velocity information, which are delayed and disturbed by measurement noises whose intensities are considered a function related to the neighbour position and velocity of agents, a distributed consensus protocol is presented, sufficient conditions of the tracking consensus in the sense of mean square are derived. Finally, the effectiveness of the proposed consensus protocol is proved by some simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the event-triggered consensus control for a general linear multi-agent system with model uncertainties and external disturbances. A consensus protocol is proposed using the local state information at asynchronous event-triggering time instants, where each agent determines when to perform sampling and control updating using the designed event-triggered condition. Then the robust consensus condition and the feedback matrix design method are derived to make the uncertain multi-agent system reach consensus with a desired disturbance attenuation ability. Furthermore, it is demonstrated that the Zeno behaviour will never occur by giving the lower bound of inter-event time intervals. Finally, a simulation example is given to verify the obtained theoretical results, with the comparison simulation conducted by using the periodic triggering strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of multi-target localisation and circumnavigation by a multi-agent system in two-dimensional space, where each target's bearing measurement can be obtained by at least one agent. Both stationary and slowly-moving targets are considered. An estimator is designed to estimate the target position; then a distributed estimation algorithm is designed for each agent to cooperatively estimate the centroid of multi-target; and finally, based on the first two steps, a circumnavigation controller is devised to guarantee that each agent circumnavigates all targets around the multi-target centroid with a desired radius. The convergence of the estimation algorithm and the stability of the circumnavigation controller are proved. A numerical simulation is provided to verify the correctness of the conclusion and the effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation. [ABSTRACT FROM PUBLISHER]

This paper studies the distributed event-triggered output consensus problem of heterogeneous multiagent system with general linear dynamics under an undirected connected graph. With the state-dependent triggering function, we design a novel distributed event-triggered output consensus controller for each agent to reach consensus with zero final consensus error. This strategy has several distinguishing features, including the fact that individual agent does not require continuous, or even periodic, communication with their neighbours to update the controller or monitor the triggering condition, and all parameters required by its implementation can be locally determined by the agent. We also prove that events cannot be triggered infinitely in finite time (i.e. no Zeno behaviour). Furthermore, the simulation examples are given to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

The consensus problem of feedforward nonlinear systems under an undirected network with a time-varying communication delay is studied. In order to solve this problem, new consensus controller with an additional design parameter that can eliminate the effect of a feedforward nonlinearity and a time-varying communication delay on the consensus problem is proposed. Also, it is proved that if an upper bound of time-varying delay is known, the proposed consensus controller can always solve the consensus problem of multi-agent systems even in the presence of feedforward nonlinearity and an arbitrarily large communication delay. A numerical example is given to illustrate the validness of the proposed approach. [ABSTRACT FROM AUTHOR]

The consensus problem of fractional-order multi-agent systems is studied in this paper. To achieve consensus, a fractional-order observer-type consensus protocol based on relative output measurements is proposed and its stability is also certified theoretically. The notion of consensus region for fractional-order dynamic is introduced and analysed. A multistep consensus protocol design procedure is presented for given consensus region. Several numerical simulations are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper investigates the finite-time consensus problem for second-order multi-agent systems with unknown velocities and disturbances. By introducing the second-order sliding mode observer, two novel distributed finite-time protocols with only relative position measurements are proposed for the both cases with known and unknown boundaries of disturbances. On the basis of Lyapunov stability theorem and homogeneous theory, it is proved that the consensus can be achieved in finite time. Simulation examples are provided to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the consensus issue for multi-agent systems with fixed directed interaction topology, and each agent is supposed to have nonlinear dynamics. By introducing the event-triggered mechanism into intermittent control, suitable consensus protocols are provided, which can save communication resources and reduce the number of control updates. Based on the Lyapunov functional method and stability analysis for switching systems, both centralised and decentralised event-triggered strategies for consensus are proposed. Furthermore, the proof of Zeno behaviour being excluded is given. Finally, some numerical examples are shown to demonstrate the effectiveness of the theoretical results. [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]

In this paper, a leader-following coordination problem of heterogeneous multi-agent systems is considered under switching topologies where each agent is subject to some local (unbounded) disturbances. While these unknown disturbances may disrupt the performance of agents, a disturbance observer-based approach is employed to estimate and reject them. Varying communication topologies are also taken into consideration, and their byproduct difficulties are overcome by using common Lyapunov function techniques. According to the available information in difference cases, two disturbance observer-based protocols are proposed to solve this problem. Their effectiveness is verified by simulations. [ABSTRACT FROM PUBLISHER]