Multi-agent Consensus Problem Research Articles

Distributed Dynamic Event-Triggered Consensus Control for Multiagent Systems With Guaranteed Performance and Positive Inter-Event Times

This paper addresses the distributed consensus issue of linear multiagent systems (MASs) subject to disturbances. First, a fully distributed adaptive control law is established for each agent, removing the assumption that global information should be known prior. Additionally, unlike existing consensus studies, the restrictions on continual communication among agents and constant controller updates are eliminated through the designed state observers and event-triggered conditions (ETCs). Moreover, an innovative event-triggered condition (ETC) is created that, via the inclusion of a dynamic parameter, captures mixed triggering and time-varying thresholds as special cases. Particularly, distinct from some dwell time methods that enforce inter-event time (IET) greater than zero at the expense of asymptotic stability, positive inter-event times (IETs) and asymptotic stability can be guaranteed simultaneously by the suggested event-triggered conditions (ETCs) in the absence of disturbances. Furthermore, positive minimum inter-event times (MIETs) can be maintained even in the presence of disturbances, which indicates the robustness of the proposed event-triggered mechanism (ETM). It is shown that the suggested technique performs disturbances suppression for all agents in a completely distributed manner while omitting Zeno behavior. Finally, a simulation example demonstrates the suggested scheme’s efficacy. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The multiagent consensus problem is considered in this paper, which can be applied to some practical systems, e.g., the unmanned aerial vehicles formation problems, as the control objective in these applications can be converted into the consensus problem of MASs. Different from existing results, a novel ETM is proposed, reducing agents’ communication and preventing continuous controller updates. In addition, disturbances widely exist in engineering. The proposed method ensures that the interval between two consecutive event triggers is greater than a small positive constant. Therefore, it is helpful for applying the proposed method in practical engineering. Finally, the established method is applied to a two-mass-spring control problem, and the effectiveness is illustrated. It is anticipated that the proposed approach can be extended to MASs with more realistic network-induced constraints and applied to more practical engineering systems.

Consensus Seeking in Large-Scale Multiagent Systems With Hierarchical Switching-Backbone Topology.

Recent developments in multiagent consensus problems have heightened the role of network topology when the agent number increases largely. The existing works assume that the convergence evolution typically proceeds over a peer-to-peer architecture where agents are treated equally and communicate directly with perceived one-hop neighbors, thus resulting in slower convergence speed. In this article, we first extract the backbone network topology to provide a hierarchical organization over the original multiagent system (MAS). Second, we introduce a geometric convergence method based on the constraint set (CS) under periodically extracted switching-backbone topologies. Finally, we derive a fully decentralized framework named hierarchical switching-backbone MAS (HSBMAS) that is designed to conduct agents converge to a common stable equilibrium. Provable connectivity and convergence guarantees of the framework are provided when the initial topology is connected. Extensive simulation results on different-type and varying-density topologies have shown the superiority of the proposed framework.

Event-Triggered Sliding Mode Neural Network Controller Design for Heterogeneous Multi-Agent Systems

A class of heterogeneous second-order multi-agent consensus problems is studied, in which an event-triggered method is used to improve the feasibility of the control protocol. The sliding mode control method is used to achieve the robustness of the system. A special type of general radial basis function neural network is applied to estimate the uncertainties. The event-triggered mechanism is introduced to reduce the update frequency of the controller and the communication frequency among the agents. Zeno behavior is avoided by ensuring a lower bound between two adjacent trigger instants. Finally, the simulation results are provided to demonstrate that the time evolution of consensus errors eventually approaches zero. The consensus of multi-agent systems is achieved.

Three-dimensional impact-angle-constrained cooperative guidance strategy against maneuvering target

In order to improve the multiple-missile cooperative attack capability and penetration capability, this paper investigates two three-dimensional impact-angle-constrained cooperative guidance strategies against maneuvering target for controllable thrust missiles. First, a three-dimensional nonlinear guidance model is established that does not assume small missile lead angles in the guidance process. Second, in the line-of-sight (LOS) direction of the cluster cooperative guidance strategy, the proposed guidance algorithm transforms the simultaneous attack problem into a second-order multiagent consensus problem, which effectively solves the practical problem of low guidance precision provoked by the time-to-go estimation. Then, by combining second-order sliding mode control (SMC) and nonsingular terminal SMC theory, the guidance algorithms in the normal and lateral directions to the LOS are designed, respectively, so that the multi-missile can accurately attack a maneuvering target while satisfying the impact angle constraints. Finally, by utilizing the second-order multiagent consensus tracking control in the leader-following cooperative guidance strategy, a novel leader-following time consistency algorithm is investigated to ensure that the leader and followers can attack the maneuvering target simultaneously. Moreover, the stability of the investigated guidance algorithms is proved mathematically. The effectiveness and superiority of the proposed cooperative guidance strategies are verified by numerical simulations.

Consensus of multiagent with interaction distortions via echo control

This paper studies the discrete-time multiagent consensus problem with kinds of diverse interaction distortions which are related to the states of agents, and a novel dual switching control strategy is proposed, named echo control, to make the system achieve state consensus. The main feature of the echo control strategy is that agents resend the information flows (received from neighbors) to the corresponding neighbor, just like the reflecting of sound waves. In other words, every individual under the echo control strategy is not only the sender and receiver of the information flows, but also the reflector of its neighbors’ messages. In this way, a negative feedback loop is constructed between every two agents, which is designed to ensure the stability of the multiagent system (MAS), and then the agents’ states will converge to a common value. The effectiveness of the echo control protocol is theoretically analyzed, and numerical simulations validate the correctness of the relevant results.

Multiagent Consensus Subject to Communication and Privacy Constraints

We consider a multi-agent consensus problem in the presence of adversarial agents. The adversaries are able to listen to the inter-agent communications and try to estimate the state of the agents. The agents have a limited bit-rate for communication and are required to quantize the transmitted signal in order to meet the bit-rate constraint of the communication channel. We propose a consensus protocol that is protected against the adversaries, i.e., the expected mean-square error of the adversary state estimate is lower bounded. In order to deal with the bit-rate constraint, we propose a dynamic quantization scheme that guarantees protected consensus.

Dynamic Quantized Consensus of General Linear Multiagent Systems Under Denial-of-Service Attacks

In this article, we study multiagent consensus problems under Denial-of-Service (DoS) attacks with data rate constraints. We first consider the leaderless consensus problem and after that we briefly present the analysis of leader–follower consensus. The dynamics of the agents take general forms modeled as homogeneous linear time-invariant systems. In our analysis, we derive lower bounds on the data rate for the multiagent systems to achieve leaderless and leader–follower consensus in the presence of DoS attacks, under which the issue of overflow of quantizer is prevented. The main contribution of the article is the characterization of the tradeoff between the tolerable DoS attack levels for leaderless and leader–follower consensus and the required data rates for the quantizers during the communication attempts among the agents. To mitigate the influence of DoS attacks, we employ dynamic quantization with zooming-in and zooming-out capabilities for avoiding quantizer saturation.

Consensus-based distributed fixed-time optimization for a class of resource allocation problems

A class of resource allocation problems with equality constraint are considered in this paper, such as economic dispatch problem in smart grid systems, which is essentially an optimization problem. Inspired by the Lagrange multiplier method, the resource allocation problem is transformed into a multi-agent consensus problem for large-scale networked distributed nodes. A consensus-based distributed fixed-time optimization algorithm is presented, where the information exchange network is depicted by a strongly connected and weight-balanced digraph. This type of communication network can ensure that the equality constraint always holds. Moreover, a new globally fixed-time stability theorem for nonlinear systems is first given in this paper. Based on this theorem and consensus theory, the optimal resource allocation scheme can be given in a fixed time. Finally, the application and comparison of the designed algorithm show that the algorithm can effectively solve the allocation problem of power resources such as economic dispatch.

Dynamic Event-triggered Control in Discrete-time Multi-agent Consensus over Directed Topologies

In this paper, we study the problem of multi-agent consensus in networks of discrete-time integrator agents with directed topologies. With the aim to reduce the frequency of interaction among agents for saving energy expenses, we develop three triggering-based protocols for strongly connected agent networks. Our common strategy is to use triggering protocols that take account of the state values received from neighbors in determining the event times. The first two protocols are event-triggering type, where the thresholds are state dependent so that when the agents are far from consensus, the events take place less frequently. The two protocols are called static and dynamic depending on the use of auxiliary variables in determining the thresholds. The third protocol is self-triggering type, where at each triggering time, an agent computes the time for its next transmission, which is communicated to its neighbors together with its state data. For these protocols, we present Lyapunov-based design methods, and demonstrate their efficacy through numerical examples.

Observer-based H∞ consensus for linear multi-agent systems subject to measurement outliers

The consensus problem has a crucial role in theoretical and practical aspects of interconnected systems, for instance in smart computing field. This paper is concerned with the observer-based H∞ consensus problem for a class of linear multi-agent systems subject to measurement outliers. In the addressed observer-based H∞ consensus problem, measurement outliers can affect the estimation accuracy and thus affect the consensus performance. To assuage the impact of measurement outliers, a control protocol based on an observer containing a saturation function with variable saturation limits is proposed. The purpose of this paper is to find a solution to the addressed H∞ consensus problem for a class of linear multi-agent systems subject to measurement outliers by designing an observer-based control protocol such that multi-agent systems can fulfill the H∞ consensus performance over a finite horizon. With the aid of Lyapunov theory, the sufficient condition is established to guarantee that the consensus error dynamic system satisfies the H∞ consensus performance. Then, the linear matrix inequality (LMI) approach is used to obtain the desired parameters of the observer-based control protocol. Finally, the effectiveness of the proposed control protocol is verified in a simulation environment. Aim: The purpose of this study is to find a solution to the addressed H∞ consensus problem for a class of linear multi-agent systems subject to measurement outliers. Methods: By choosing a suitable Lyapunov function, the sufficient condition is obtained, which can guarantee the consensus error dynamic system satisfying the given H∞ consensus performance. The LMI approach is employed to design the desired controller. With Matlab LMI toolbox, a numerical example was conducted to demonstrate the effectiveness of the proposed observer-based control protocol in the simulation environment. Results: A satisfactory consensus performance can be guaranteed for multi-agent systems subject to measurement outliers under the proposed observer-based control protocol. The constructed saturation function with variable saturation limits can mitigate the effect of measurement outliers by dynamically regulating saturation limits. Compared with the traditional observer-based control protocol, in this paper, the proposed observer-based control protocol shows robustness against measurement outliers. Conclusion: A solution to the addressed multi-agent consensus problem subject to measurement outliers was found by designing an observer-based consensus controller. The obtained results can be extended to sensor networks, neural networks, and nonlinear multi-agent systems.

Resilient self/event-triggered consensus based on ternary control

This paper considers the problem of multi-agent consensus in the presence of adversarial agents. Such adversaries may try to introduce undesired influence on the coordination of the regular agents and to even prevent them from reaching consensus. To our setting, we extend the so-called mean subsequence reduced algorithms with the aim to reduce the use of computation and communication resources of the agents. In particular, by employing self- and event-triggered communication, the frequencies of state updates as well as data transmissions are kept low. Moreover, the control inputs of the agents take the form of ternary signals, allowing them to further reduce the amount of information at each transmission. We will observe that in hostile environments with adversaries, the self-triggered approach can bring certain advantages over the event-triggered counterpart. Moreover, a novel switching scheme is introduced to mix the two protocols to further enhance the performance of the agents.

The Influence of Memory in Multi-Agent Consensus

Multi-agent consensus problems can often be seen as a sequence of autonomous and independent local choices between a finite set of decision options, with each local choice undertaken simultaneously, and with a shared goal of achieving a global consensus state. Being able to estimate probabilities for the different outcomes and to predict how long it takes for a consensus to be formed, if ever, are core issues for such protocols. Little attention has been given to protocols in which agents can remember past or outdated states. In this paper, we propose a framework to study what we call `memory consensus protocol'. We show that the employment of memory allows such processes to always converge, as well as, in some scenarios, such as cycles, converge faster. We provide a theoretical analysis of the probability of each option eventually winning such processes based on the initial opinions expressed by agents. Further, we perform experiments to investigate network topologies in which agents benefit from memory on the expected time needed for consensus.

Dynamic Resilient Network Games With Applications to Multiagent Consensus

A cyber security problem in a networked system formulated as a resilient graph problem based on a game-theoretic approach is considered. The connectivity of the underlying graph of the network system is reduced by an attacker who removes some of the edges whereas the defender attempts to recover them. Both players are subject to energy constraints so that their actions are restricted and cannot be performed continuously. For this two-stage game, which is played repeatedly over time, we characterize the optimal strategies for the attacker and the defender in terms of edge connectivity and the number of connected components of the graph. The resilient graph game is then applied to a multi-agent consensus problem. We study how the attacks and the recovery on the edges affect the consensus process. Finally, we also provide numerical simulation to illustrate the results.

Average Consensus by Graph Filtering: New Approach, Explicit Convergence Rate, and Optimal Design

This paper revisits the problem of multi-agent consensus from a graph signal processing perspective. Describing a consensus protocol as a graph spectrum filter, we present an effective new approach to the analysis and design of consensus protocols in the graph spectrum domain for the uncertain networks, which are difficult to handle by the existing time-domain methods. This novel approach has led to the following new results in this paper: 1) New necessary and sufficient conditions for both finite-time and asymptotic average consensus of multi-agent systems. 2) Direct link between the consensus convergence rate and the periodic consensus protocols. 3) Conversion of the fast consensus problem to the problem of polynomial design of graph spectrum filter. 4) A Lagrange polynomial interpolation method and a worst-case optimal interpolation method for the design of periodic consensus protocols for the MASs on uncertain graphs. 5) Explicit formulas for the convergence rate of the designed protocols. Several numerical examples are given to demonstrate the validity, effectiveness and advantages of these results.

Dynamic Quantized Consensus of General Linear Multi-agent Systems under Denial-of-Service Attacks

In this paper, we study a multi-agent consensus problem under Denial-of-Service (DoS) attacks with data rate constraints. We consider leaderless consensus under an undirected communication graph and assume that the graph is connected in the absence of DoS. The dynamics of the agents take general forms modeled as homogeneous linear time-invariant systems. In our analysis, we derive specific bounds on the data rate for the multi-agent system to achieve consensus even in the presence of DoS attacks. The main contribution of the paper is the characterization of the trade-off between the tolerable DoS attack level and the required data rates for the communication among the agents. To avoid quantizer saturation under DoS attacks, we employ dynamic quantization with zoom-in and zoom-out capabilities.

Dynamic Resilient Graph Games for State-Dependent Jamming Attacks Analysis on Multi-Agent Systems

A cybersecurity problem for a multi-agent consensus problem is investigated through a dynamic game formulation. Specifically, we consider a game repeatedly played between a jamming attacker and a defender. The attacker attempts to jam the links between a number of agents to delay their consensus. On the other hand, the defender tries to maintain the connection between agents by attempting to recover some of the jammed links with the goal of achieving faster consensus. In each game, the players decide which links to attack/recover and for how long to continue doing so based on a Lyapunov-like function representing the largest difference between the states of the agents. We analyze the subgame perfect equilibrium of the game and obtain an upper bound of the consensus time that is influenced by the strategies of the players. The results are illustrated with a numerical example.

An event‐triggered approach to quantized resilient consensus

SummaryWe consider an event‐triggered update scheme for the problem of multiagent consensus in the presence of faulty and malicious agents within the network. In particular, we focus on the case where the agents take integer (or quantized) values. To keep the regular agents from being affected by the behavior of faulty agents, algorithms of the mean subsequence reduced type are employed, where neighbors taking extreme values are ignored in the updates. Different from the real‐valued case, the quantized version requires the update rule to be randomized. We characterize the error bound on the achievable level of consensus among the agents as well as the necessary structure for the network in terms of the notion of robust graphs. We verify via a numerical example the effectiveness of the proposed algorithms.

Consensus of Multiagent Systems Via Asynchronous Cloud Communication

In this paper, we study a multiagent consensus problem in which agents are only able to communicate with each other intermittently through a cloud server. To reduce the amount of required communication, we develop a self-triggered algorithm that allows agents to communicate with the cloud only when necessary rather than at a fixed period. Unlike the vast majority of similar works that propose distributed event- and/or self-triggered control laws, this paper does not assume agents can be “listening” continuously. In other words, when an event is triggered by one agent, neighboring agents will not be aware of this until the next time they establish communication with the cloud themselves. Using a notion of “promises” about future control inputs, agents are able to keep track of higher quality estimates about their neighbors allowing them to stay disconnected from the cloud for longer periods of time while still guaranteeing a positive contribution to the global task. We prove that our self-triggered coordination algorithm guarantees that the system asymptotically reaches the set of desired states. Simulations illustrate our results.

Multi-agent Consensus Problem Based on Observer and Considered Lur’e Nonlinearity in Directed Topology

This paper studies the multi-agent systems consensus problem considering Lur’e-type nonlinearity under directed network. Compared with the conclusions of the existing undirected communication topology, the conclusions obtained have greatly reduced the communication topology requirements and are more general. This paper designs a control protocol based on the observer, which solves the problem that the system state information is unknown. By decomposition of a specific form of the Laplacin matrix, consensus problem is converted into stability problem for low-dimensional systems. In this paper, the method of solving the control protocol is given and proved by the piecewise Lyapunov function. The simulation results show that the designed control protocol can solve the consistency problem.

An Overview on Denial-of-Service Attacks in Control Systems: Attack Models and Security Analyses.

In this paper, we provide an overview of recent research efforts on networked control systems under denial-of-service attacks. Our goal is to discuss the utility of different attack modeling and analysis techniques proposed in the literature for addressing feedback control, state estimation, and multi-agent consensus problems in the face of jamming attacks in wireless channels and malicious packet drops in multi-hop networks. We discuss several modeling approaches that are employed for capturing the uncertainty in denial-of-service attack strategies. We give an outlook on deterministic constraint-based modeling ideas, game-theoretic and optimization-based techniques and probabilistic modeling approaches. A special emphasis is placed on tail-probability based failure models, which have been recently used for describing jamming attacks that affect signal to interference-plus-noise ratios of wireless channels as well as transmission failures on multi-hop networks due to packet-dropping attacks and non-malicious issues. We explain the use of attack models in the security analysis of networked systems. In addition to the modeling and analysis problems, a discussion is provided also on the recent developments concerning the design of attack-resilient control and communication protocols.