General Linear Multi-agent Systems Research Articles

Fault-Tolerant Periodic Event-Triggered Consensus Under Communication Delay and Multiple Attacks

This article proposes a resilient strategy for leaderless and leader–following consensus in general linear multiagent systems under simultaneous presence of false data injection and denial-of-service (DoS) attacks. To save energy, local control updates and communication between the neighboring agents are based on a distributed periodic event-triggered scheme. Sufficient conditions to guarantee the exponential mean square bounded consensus are derived as linear matrix inequality (LMI) conditions obtained from some delay-dependent Lyapunov–Krasovskii functionals. The proposed design framework computes the required consensus control gain based on a desired level of resilience to DoS. The guaranteed level of resilience in our proposed LMI-based method is less conservative (more realistic) compared to the existing analytical solutions. Two physical constraints, namely nonuniform time-varying communication delay and actuator faults, are also included in the problem formulation to enhance the practicability of the proposed solution. Simulations results demonstrate the effectiveness of the proposed framework in the presence of the considered cyberthreats and physical constraints.

Distributed Time-Varying Group Formation Tracking for Multiagent Systems With Switching Interaction Topologies via Adaptive Control Protocols

In this article, time-varying group formation (TVGF) tracking problems for general linear multiagent systems (GLMASs) with switching interaction topologies are investigated. Different from previous studies, a novel TVGF tracking approach is proposed, where all agents are divided into three types: the virtual leader, the group leader, and the follower. The virtual leader is designed to assign the trajectory of GLMASs. Subgroups can be interacted with each other by cooperation among group leaders such that the relative configuration between different groups can be adjusted simultaneously. The followers in each group can achieve time-varying subformations. Moreover, under the influence of external disturbances and switching topologies, based on the distributed observer, two different distributed adaptive control protocols are constructed without using any global information such as the eigenvalue of the Laplacian matrix related to the communication topologies, the upper boundness of the leader’s input, and so on. The algorithms to determine parameters of control protocols are also presented. Furthermore, the closed-loop stability of GLMASs is proven by the Lyapunov theory. Finally, numerical simulations are given to verify the effectiveness of theoretical results.

Output Consensus of General Linear Networked Multiagent Systems With Unknown Disturbances via Cloud Computing

For a general linear multiagent system (MAS) with multigroup suffering from disturbances, a cloud-based output consensus control scheme, including a cloud predictive control protocol and a disturbance observer, is proposed to achieve output consensus via cloud computing. In a cloud framework, agents in each group only send their own information to a corresponding cloud node, and cloud nodes transmit next control command for agents. Accordingly, the communication burden of an individual agent is reduced in each group. Moreover, the communication burden of each agent remains constant despite the scale of the network, and energy consumption is also reduced effectively from the perspective of one agent. In a cloud, delayed states of agents are reconstructed via delayed outputs received from a sensor, and a predictor is designed based on observed delay states. A cloud predictive control protocol is developed by dynamic variables and the predicted output to compensate for network delays from a cloud to an actuator, and a disturbance observer is presented based on predicted and local outputs. In theory, sufficient conditions for stability are presented and analyzed, and it is proved that the proposed cloud-based control scheme renders the MAS stable and to achieve output consensus. Finally, two simulations are presented to verify the proposed control scheme.

Observer-Based Output Feedback Event-Triggered Adaptive Control for Linear Multiagent Systems Under Switching Topologies.

The consensus problem of general linear multiagent systems (MASs) is studied under switching topologies by using observer-based event-triggered control method in this article. On the basis of the output information of agents, two kinds of novel event-triggered adaptive control schemes are designed to achieve the leaderless and leader-follower consensus problems, which do not need to utilize the global information of the communication networks. Finally, two simulation examples are introduced to show that the consensus error converges to zero and Zeno behavior is eliminated in MASs. Compared with the existing output feedback control research, one of the significant advantages of our methods is that the controller protocols and triggering mechanisms do not rely on any global information, are independent of the network scale, and are fully distributed ways.

Time-Varying Group Formation-Containment Tracking Control for General Linear Multiagent Systems With Unknown Inputs.

Time-varying group formation-containment tracking problems for general linear multiagent systems with unknown control input are investigated. Agents are classified into tracking leaders, formation leaders, and followers and assigned in groups. Tracking leaders with unknown control inputs provide unpredictable trajectories as macroscopic moving references. Formation leaders accomplish desired subformations while following the trails of tracking leaders. At the same time, followers converge into different convex hulls spanned by formation leaders. First, formation-containment tracking protocols are designed with neighboring relative information and effects of unknown input of tracking leaders. Then, the design of group division is analyzed by adjusting the properties in Laplacian matrices, which represent interaction relationships. An algorithm to determine the parameters in control protocols is proposed, and the formation tracking feasible constraint is presented. Next, it is proved that the general linear multiagent system can achieve time-varying group formation-containment control effectively with errors uniformly asymptotically converging to zero under designed protocols. Finally, a numerical simulation is given to verify the effectiveness of obtained theoretical results.

Leader-Following and Leaderless Consensus of Linear Multiagent Systems Under Directed Graphs by Double Dynamic Event-Triggered Mechanism

This article proposes a unified framework to investigate the leader-following and leaderless consensus problem of general linear multiagent systems under the directed communication topology only containing a spanning tree. To further reduce the use of resources for the control objective, an energy-saving control algorithm is introduced composed of double dynamic event-triggered mechanisms that work independently: one intends to control the communication of agents with their neighbors and the other to decide the update of controllers. It is shown that the control algorithm performs well compared to most existing control algorithms in terms of the communication cost between agents and the update cost of controllers. In addition, a new procedure to choose parameters is obtained by the developed Lyapunov stabilty method, with the potential of achieving less conservative parameters than related results. Finally, the effectiveness of the proposed control scheme is verified by numerical simulations.

Appointed-Time and Attack-Free Bipartite Synchronization of Generic Linear Multiagent Systems Over Directed Switching Networks

This article derives a solution to the appointed-time and attack-free bipartite synchronization problem for generic linear multiagent systems over directed switching networks accommodating cooperative and antagonistic interactions. Herein, appointed-time means that the settling time is independent of any parameters and is preappointed in advance. Attack-free requires that the communication channel is protected, which means that no state and observer information exchange is allowed, and only measured relative output information is available when designing protocols. Firstly, by virtue of Pontryagin’s maximum principle, a distributed appointed-time state-feedback protocol is developed for directed switching networks, which tackles the appointed-time bipartite synchronization problem from a motion-planning approach based on sampling measurements, but takes the risk of facing cyber attacks on information exchange channels. Then, to be free of network attacks, a sampling-based attack-free observer using relative output information is designed to observe bipartite synchronization errors at an appointed time. By combining the appointed-time state-feedback protocol with the sampling-based attack-free observer, an attack-free output-feedback protocol is developed without requiring the state or control input information. The attack-free appointed-time bipartite synchronization problem is thus resolved. Both the state-feedback and attack-free protocols show the ability of disturbance rejection to the nonidentical bounded disturbances. To our knowledge, it is the first time to solve the appointed-time and attack-free bipartite synchronization problem for generic linear multiagents based on state- and output-feedback information, respectively. Finally, simulations verify the effectiveness of the two protocols.

Fully Distributed Formation Control of General Linear Multiagent Systems Using a Novel Mixed Self- and Event-Triggered Strategy

In this study, the state formation control issue of general linear networked multi-agent systems (MASs) is considered. Combining self-triggered strategy with general event-triggered strategy, a novel fully distributed asynchronous mixed self- and event-triggered control strategy is proposed, which can make the MASs achieve the prescribed state formation structure. The control strategy proposed in this study does not depend on any global network information. Therefore, no matter how large scale of the network is, the control strategy is feasible. Meanwhile, the control strategy uses the sampled state information at triggering instants instead of the real-time state information, which efficiently eliminates continuous communication among agents. Different from the existing studies, the event-triggered detector starts to work if and only if the next self-triggering instant comes in the control strategy proposed in this article. Thus, the control strategy can save more communication resources between sensor and event-triggered detector within the same inter-event interval compared with the previous event-triggered strategies. In addition, the control strategy designs a exponential decay term in the triggering function to rule out the unexpected Zeno behavior and reduce the triggering number. Finally, the numerical simulation result of multi-robot formation is given, which demonstrates the feasibility and performance of the proposed control strategy.

Fully Distributed Fault-Tolerant Event-Triggered Control of Microgrids Under Directed Graphs

This paper proposes an event-triggered fault-tolerant (ETFT) control strategy for voltage restoration in microgrids (MGs). The presence of partial loss of effectiveness (PLOE) and bias faults in the actuators are considered. The proposed algorithm is independent of the global information related to the directed communication network and does not involve the boundaries of the fault factors. Each distributed generator (DG) only needs to know the relative information between its neighbors, which means that the algorithm is fully distributed. The boundary layer technique is used to construct smooth ETFT controllers, avoiding the undesirable chattering effect of discontinuous controllers. Furthermore, a novel consensus error prediction model is developed to eliminate the need for continuous communication between DGs. The proposed algorithm is not only applicable to the secondary voltage restoration of MGs but can also be extended to general linear multi-agent systems (MASs). Finally, the simulation results verify the effectiveness of the algorithm.

A Distributed Resource Allocation Algorithm for the General Linear Multiagent Systems

We study the distributed resource allocation problem for heterogeneous multiagent systems over an undirected graph, an essential issue in multiagent system coordinated control and complex network system control. The decision variable is subject to global equality and local convex set constraints, and the objective is smooth and convex. It aims to minimize the global objective function by exchanging neighboring information between agents. An adaptive distributed algorithm is designed using the distance function-based exact penalty function method. A state- and time-based triggering condition is designed to avoid continuous communication and reduce the communication burden. From a random initial state, the proposed algorithm asymptotically converges to the optimal value by means of LaSalle’s invariance principle. Finally, examples are provided to demonstrate the effectiveness of our algorithm.

Dynamic Event-Triggered Consensus of General Linear Multi-Agent Systems With Adaptive Strategy

Consensus of multi-agent systems (MASs) with general linear dynamics is investigated. In order to reduce communication frequency and avoid dependence on global information, adaptive event-triggered strategy is applied. A kind of dynamic event-triggered strategy, which is more flexible in giving event-trigger threshold, is proposed. An event-trigger condition based on continuous relative measurement is first designed. Then, the event-trigger condition is improved to only utilize event-triggered information. Sufficient criteria are derived to guarantee consensus. Moreover, it is proved that the designed event-trigger conditions can exclude Zeno behavior. Numerical simulation is performed to verify the effectiveness of the obtained results.

Event-triggered predictive control for linear discrete-time multi-agent systems

This paper considers the event-triggered predictive control(ETPC) problem for linear discrete-time multi-agent systems. To achieve accurate state estimation under event-triggered communication between agents, an event-triggered predictive control scheme as well as a novel class of triggering condition are proposed for synchronization of multi-agent systems with single-integrator dynamics, where the control input of each agent no longer remains constant but updates periodically within the time interval between two consecutive triggering instants. Then, the proposed scheme is extended to the general linear multi-agent systems. By comparing with the time-triggered control(TTC) method and the existing event-triggered control(ETC) methods, the control performance of the proposed ETPC scheme is almost the same as that of the TTC approach, and the communication payload between agents is reduced with much less triggering times than existing ETC methods. Finally, two numerical examples are given to verify the theoretical analysis and demonstrate the superiority of the proposed method comparing with some existing methods.

Seeking Tracking Consensus for General Linear Multiagent Systems With Fixed and Switching Signed Networks.

The existing studies for tracking consensus of multiagent systems (MASs) are all restricted to networks with only cooperative relationships among agents. Tracking consensus, however, requires beyond these traditional models due to the ubiquitous competition in many real-world MASs, such as biological systems and social systems. Taking into account this fact, this article aims to extend the dynamics of tracking consensus to signed networks containing both cooperative and competitive relationships among agents. A group of agents with general linear dynamics is considered. The cases of the fixed network as well as switching networks are analyzed, respectively. In the end, some algebraic conditions related to the network structure and the positive/negative edge weight are established to ensure the implementation of tracking consensus. Moreover, the single decoupling system is allowed to be strictly unstable in theory, and the upper bound of the eigenvalue modulus of the system matrix related to the system instability is given.

Affine Formation Control of General Linear Multi-Agent Systems with Delays

This paper studies affine formation control problem of general linear multi-agent systems (MASs) over undirected graph in the presence of time delays. Different delay conditions are considered and predictive observers are designed for the followers to predict the states in the future. Then, affine formation control laws are designed based on the predicted states, and sufficient conditions are derived to ensure the convergence of the formation errors. With an adaptive mechanism, the proposed control laws can be implemented without the usage of global information. Under the proposed protocols, the MASs can form a target formation shape and realize time-varying geometric transformations continuously. Finally, simulations are conducted to verify the effectiveness of the theoretical results.

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.

Distributed Fixed-Time Resource Allocation Algorithm for the General Linear Multi-Agent Systems

This brief focuses on the distributed resource allocation problem (RAP) for a general linear heterogeneous multi-agent system (MAS), in which each agent adopts different structure parameters. By means of multi-agent consensus approach and symbolic-function-based fixed-time control theory, an initialization-free distributed resource allocation algorithm is designed. Moreover, the equality constraint is solved based on the proportional-integral (PI) control idea and the output of all agents tracks to the optimal solution within fixed-time. Finally, we reveal the effectiveness and fast convergence performance of our proposed algorithm by a simulation example.

Observer-based event-triggered finite-time consensus for general linear leader-follower multi-agent systems

In this study, the event-triggered finite-time consensus problem of a class of general linear leader-follower multi-agent systems with unmeasurable states is investigated. First, an observer-based distributed event-triggered strategy is proposed in view of introducing an external dynamic threshold that is independent of the state variables. Second, the Lyapunov method and proposed event-triggered strategy are implemented as the control scheme to ensure that the tracking error can converge to the origin within a finite time under given conditions. Analytical findings indicate that the Zeno behavior can be avoided by selecting the appropriate parameters. Finally, a numerical simulation is implemented, and the results verify the effectiveness of the proposed method.

Fully distributed event-triggered secure consensus of general linear multi-agent systems under sequential scaling attacks

In this article, the secure consensus problem is studied for a general linear multi-agent system, where a fully distributed event-triggered scheme is introduced to increase the feasibility and improve the scalability of the control protocol. Firstly, an edge-based sequential scaling attack is formulated with constraints on the attack duration and the frequency, which includes multiplicative deception attacks and DoS attacks as a particular situation when the scaling factor is equal to 0. Then a fully distributed event-triggered control protocol is designed, in which the global information is no longer needed. Sufficient conditions related to triggering parameters, the scaling factor, the attack duration and attack frequency are derived ensuring the asymptotic consensus of MAS. Furthermore, the impact of the triggering parameters and the scaling factor on the attack duration and the attack frequency are also discussed. The Zeno behavior is proved not to happen. Finally, two simulation examples based on unmanned intelligent vehicles are conducted to verify the results.

Reliable Memory Sampled-Data Consensus of Multi-Agent Systems With Nonlinear Actuator Faults

This brief proposes a memory-based sampled-data consensus framework for general linear multi-agent systems (MAS) in the presence of a class of nonlinear actuator faults (NAF). To reduce state exchanges and preserve energy resources, communication between the neighboring agents are based on only samples of the states with variable sampling intervals. As two common constraints in the actuators, the bounded nonlinear partial loss of effectiveness and bias faults are both taken into account in the problem formulation. Sufficient conditions to guarantee consensus under the given circumstances are derived as linear matrix inequality (LMI) conditions. Different from existing Lyapunov-Krasovskii-based methods, the proposed design framework in this brief is based on a looped functional approach which reduces the conservation in designing the required consensus control gains. This less conservative approach allows a larger sampling interval as well as more severe actuator faults which together enhance the practicability of the proposed approach. Simulation results based on a tunnel diode circuit and a non-holonomic mobile robot MASs quantify the effectiveness of the proposed approach and the improved sampling intervals.

Fully distributed event-triggered bipartite formation tracking for multi-agent systems with multiple leaders and matched uncertainties

This paper investigates the bipartite time-varying output formation tracking issue for general linear multi-agent systems with multiple leaders and matched uncertainties. The outputs of followers are required to form two antagonistic prescribed time-varying subformations, one of which tracks the convex combination of the outputs of multiple leaders and the other tracks the symmetric convex combination. An independent asynchronous fully distributed event-triggered control protocol is formulated by using relative information between neighboring agents. It is shown that, with the formulated protocol, the bipartite time-varying output formation tracking can be achieved if the feasible formation condition is satisfied. The Zeno behavior is proved to be excluded. Then, we further construct a novel self-triggered control protocol to avoid continuous monitoring of estimate error. Since the protocol incorporates both event-triggered control and adaptive control, it efficiently avoids continuous communication among agents and can be implemented in a fully distributed manner. Moreover, it is noteworthy that in the case where relative information is available while absolute information is not, the protocol is applicable. Finally, the feasibility of the constructed protocols is verified by a numerical example.