Distributed Event-Triggered Adaptive Control for Consensus of Linear Multi-Agent Systems with External Disturbances

Human-in-the-Loop Consensus Control for Multiagent Systems With External Disturbances

In this article, the human-in-the-loop leader-follower consensus control problem is addressed for multiagent systems (MASs) with unknown external disturbances. A human operator is deployed to monitor the MASs' team by transmitting an execution signal to a nonautonomous leader in response to any hazard detected, with the control input of the leader unknown to all followers. For each follower, a full-order observer, in which the observer error dynamic system decouples the unknown disturbance input, is designed for asymptotic state estimation. Then, an interval observer is constructed for the consensus error dynamic system, where the unknown disturbances and control inputs of its neighbors and its disturbance are treated as unknown inputs (UIs). To process the UIs, a new asymptotic algebraic UI reconstruction (UIR) scheme is proposed based on the interval observer, and one of the significant features of the UIR is the capacity to decouple the control input of the follower. The subsequent human-in-the-loop asymptotic convergence consensus protocol is developed by applying an observer-based distributed control strategy. Finally, the proposed control scheme is validated through two simulation examples.

Adaptive penalty-based neurodynamic approach for nonsmooth interval-valued optimization problem

The complex and diverse practical background drives this paper to explore a new neurodynamic approach (NA) to solve nonsmooth interval-valued optimization problems (IVOPs) constrained by interval partial order and more general sets. On the one hand, to deal with the uncertainty of interval-valued information, the LU-optimality condition of IVOPs is established through a deterministic form. On the other hand, according to the penalty method and adaptive controller, the interval partial order constraint and set constraint are punished by one adaptive parameter, which is a key enabler for the feasibility of states while having a lower solution space dimension and avoiding estimating exact penalty parameters. Through nonsmooth analysis and Lyapunov theory, the proposed adaptive penalty-based neurodynamic approach (APNA) is proven to converge to an LU-solution of the considered IVOPs. Finally, the feasibility of the proposed APNA is illustrated by numerical simulations and an investment decision-making problem.

Adaptive Event-Triggered Consensus of Multi-Agent Systems in Sense of Asymptotic Convergence

In this paper, the asymptotic consensus control of multi-agent systems with general linear agent dynamics is investigated. A neighbor-based adaptive event-triggering strategy with a dynamic triggering threshold is proposed, which leads to a fully distributed control of the multi-agent system, depending only on the states of the neighboring agents at triggering moments. By using the Lyapunov method, we prove that the states of the agents converge asymptotically. In addition, the proposed event-triggering strategy is proven to exclude Zeno behavior. The numerical simulation results illustrate that the agent states achieve consensus in sense of asymptotic convergence. Furthermore, the proposed strategy is shown to be scalable in case of variable agent numbers.

Cooperative Differential Game-Based Distributed Optimal Synchronization Control of Heterogeneous Nonlinear Multiagent Systems

This article presents an online off-policy policy iteration (PI) algorithm using reinforcement learning (RL) to optimize the distributed synchronization problem for nonlinear multiagent systems (MASs). First, considering that not every follower can directly obtain the leader's information, a novel adaptive model-free observer based on neural networks (NNs) is designed. Moreover the feasibility of the observer is strictly proved. Subsequently, combined with the observer and follower dynamics, an augmented system and a distributed cooperative performance index with discount factors are established. On this basis, the optimal distributed cooperative synchronization problem changes into solving the numerical solution of the Hamilton-Jacobian-Bellman (HJB) equation. Finally, an online off-policy algorithm is proposed, which can be used to optimize the distributed synchronization problem of the MASs in real time based on measured data. In order to prove the stability and convergence of the online off-policy algorithm more conveniently, an offline on-policy algorithm whose stability and convergence are proved is given before the online off-policy algorithm is proposed. We give a novel mathematical analysis method for establishing the stability of the algorithm. The effectiveness of the theory is verified by simulation results.

Dynamic consensus of linear multi-agent system using self-triggered distributed model predictive control

This article discusses self-triggering algorithm using distributed model predictive control (DMPC) to achieve dynamic consensus in linear multi-agent systems (MASs). The iterative computations and communications required at each time step in traditional consensus algorithms cause escalation of the energy consumption and shorten the life span of the MAS. An attempt to solve this problem is made by proposing a sequential self-triggering consensus algorithm, where each agent computes its own triggering instants. A Laguerre based DMPC design is adopted that notably reduces the computational complexity of conventional DMPC. The proposed self-triggered DMPC algorithm optimizes the control input and triggering interval while guaranteeing the dynamic consensus of the agents. By virtue of the Laguerre function based control architecture, the additional computations owing to the self-triggered algorithm do not impose stress on the controller; yet reduce the load on communication resources. The equality constraint on the terminal state of the agents is utilized along with Lyapunov criteria to establish the closed loop stability of the MAS. The proposed scheme achieves a considerable drop in controller design computations as well as data transmissions among agents, and the same is established by comparing these traits of existing schemes while achieving comparable performance. The proposed algorithm is verified through simulation of platoon configuration of vehicles, each of which is modeled as a linear multi-input multi-output (MIMO) system.

Robust Output Regulation of Linear Uncertain Systems by Dynamic Event-Triggered Output Feedback Control

In this article, the robust output regulation problem of the linear uncertain system is investigated by the event-triggered control approach. Recently, the same problem is addressed by an event-triggered control law where the Zeno behavior may happen when time tends to infinity. In comparison, a class of event-triggered control laws is developed to achieve output regulation exactly, and meanwhile, explicitly exclude the Zeno behavior for all time. In particular, a dynamic triggering mechanism is first developed by introducing a dynamic changing variable with specific dynamics. Then, by the internal model principle, a class of dynamic output feedback control laws is designed. Later, a rigorous proof is provided to show that the tracking error of the system converges to zero asymptotically while prohibiting the Zeno behavior for all time. Finally, we give an example to illustrate our control approach.

Fully Distributed Event/Self-Triggered Bipartite Output Formation-Containment Tracking Control for Heterogeneous Multiagent Systems

This article considers the bipartite time-varying output formation-containment tracking control issue for general linear heterogeneous multiagent systems with multiple nonautonomous leaders, where the full states of agents are not available. Both cooperative interaction and antagonistic interaction between neighboring agents are taken into account. First, an observer is constructed using the output information to observe the state information. Then, based on the information between neighboring agents, an independent asynchronous fully distributed event-triggered bipartite compensator is put forward to estimate the convex hull spanned by the states of multiple leaders. Note that the compensator does not require to use of any global information. Subsequently, a formation-containment tracking control strategy based on the observer and compensator and an algorithm to determine its control parameters are given. The Zeno behavior is further proved to be excluded in any finite time. In addition, a novel self-triggered control strategy based only on the sampled information at triggering instants is also formulated, which avoids continuous communication among agents. Finally, a numerical example is given to validate the effectiveness and performance of the proposed control strategies.

Adaptive Time-Varying Formation Tracking Control for Multiagent Systems With Nonzero Leader Input by Intermittent Communications

The time-varying formation (TVF) tracking problem is studied for linear multiagent systems (MASs), where followers reach a preset TVF when tracking the leader's state. Followers are divided into the informed ones, which directly receive the leader's information, and uninformed ones. To alleviate communication requirements, trigger mechanisms are designed for the leader and all edges. Note that the designed trigger mechanisms enable the leader to send information intermittently and each follower to transmit information asynchronously when the corresponding trigger mechanism is satisfied. To address the TVF tracking problem, the node-event (for the leader) and (dynamic) edge-event triggered adaptive control strategy is proposed, which is fully distributed and has no relation to the system network's scale. Moreover, the MASs do not exhibit the Zeno behavior. Finally, a practice example is introduced to effectively illustrate the theoretical results.

Adaptive Event-Triggered Control Approach to the Cooperative Output Regulation of Heterogeneous Multiagent Systems Under Digraphs

The cooperative output regulation (COR) problem of heterogeneous linear multiagent systems under digraphs has been considered under the assumption that continuous communication between neighbors and continuous update of controllers. To get rid of this assumption, that is, to realize event-triggered communication between neighbors and discrete update of controllers, this article proposes the fully distributed event-triggered observers to estimate the matrix and the state for the exosystem, and the event-triggered controllers to solve the COR problem. Moreover, the Zeno behavior is excluded by proving that the interevent times of each agent are strictly greater than zero under the design triggering conditions. Finally, two examples are given to verify the effectiveness and advantages of the proposed methods.

Distributed Adaptive Nash Equilibrium Solution for Differential Graphical Games

This article investigates differential graphical games for linear multiagent systems with a leader on fixed communication graphs. The objective is to make each agent synchronize to the leader and, meanwhile, optimize a performance index, which depends on the control policies of its own and its neighbors. To this end, a distributed adaptive Nash equilibrium solution is proposed for the differential graphical games. This solution, in contrast to the existing ones, is not only Nash but also fully distributed in the sense that each agent only uses local information of its own and its immediate neighbors without using any global information of the communication graph. Moreover, the asymptotic stability and global Nash equilibrium properties are analyzed for the proposed distributed adaptive Nash equilibrium solution. As an illustrative example, the differential graphical game solution is applied to the microgrid secondary control problem to achieve fully distributed voltage synchronization with optimized performance.

Leader-Follower Asymptotic Consensus Control of Multiagent Systems: An Observer-Based Disturbance Reconstruction Approach

In this article, a leader-follower asymptotic consensus control strategy is developed for a class of linear multiagent systems (MASs) with unknown external disturbances and measurement noises. First, the preconditions, the minimum phase condition (MPC) and observer matching condition (OMC), are discussed in detail, and an equivalent result under these two preconditions is given. In this way, the corresponding results from Corless and Tu (1998) are improved. Meanwhile, a reduced-order observer is designed for a constructed augmented system to estimate the system states and noises of each agent. Next, with the help of a traditional interval observer, a novel unknown disturbance reconstruction method is developed, and the reconstruction can converge to the unknown disturbance asymptotically and decouple from the control input. The subsequent asymptotic consensus is accomplished by utilizing an observer-based control scheme, with its design satisfying the so-called separation principle. Finally, two simulation examples are given to verify the effectiveness and show the advantages of the proposed methods.

The Bipartite Edge-Based Event-Triggered Output Tracking of Heterogeneous Linear Multiagent Systems

This article focuses on the bipartite output tracking control for heterogeneous linear multiagent systems under the asynchronous edge-based event-triggered transmission mechanism. First, the distributed bipartite edge-based event-triggered compensator is established to estimate the state of the exosystem. The estimated state of the compensator is the same as the state of the exosystem in modulus and opposite in sign because of the existence of antagonistic communications. To be independent of the topology information, the adaptive compensator with an edge-based event-triggered mechanism is then established. And the observer is proposed to recover the unmeasurable system states. Then, the distributed control scheme based on the compensator and the observer is designed to address the bipartite output tracking problem. Moreover, the results in the signed fixed graph are extended to signed switching graphs. The Zeno behavior of each edge is ruled out. Finally, two numerical examples, one application example and one comparison example, are given to demonstrate the feasibility of the main theoretical findings.

Event-Triggered Distributed Average Tracking Control for Lipschitz-Type Nonlinear Multiagent Systems

This article investigates the event-triggered distributed average tracking (ETDAT) control problems for the Lipschitz-type nonlinear multiagent systems with bounded time-varying reference signals. By using the state-dependent gain design approach and event-triggered mechanism, two types of ETDAT algorithms called: 1) static and 2) adaptive-gain ETDAT algorithms are developed. It is the first time to introduce the event-triggered strategy into DAT control algorithms and investigate the ETDAT problem for multiagent systems with Lipschitz nonlinearities, which is more practical in real physical systems and can better meet the needs of practical engineering applications. Besides, the adaptive-gain ETDAT algorithms do not need any global information of the network topology and are fully distributed. Finally, a simulation example of the Watts-Strogatz small-world network is presented to illustrate the effectiveness of the adaptive-gain ETDAT algorithms.

Leader-Following Consensus of Heterogeneous Linear Multiagent Systems With Communication Time-Delays via Adaptive Distributed Observers

This article investigates the leader-following consensus problem of heterogeneous linear multiagent systems under switching and directed topologies. It is assumed that the communication between agents suffers from time-varying delays and only the neighboring agents of the leader are able to get access to the information of the leader agent, including its agent matrices. A key technical lemma on the input to state stability of time-delayed systems is first established with which the main results of this article can be obtained. An adaptive distributed observer, taking into consideration of communication time delays, is proposed for each follower to estimate the leader's system matrices and its state. Then, a distributed controller based on this adaptive observer is developed. We show that the resulting closed-loop multiagent system achieves the leader-following output consensus. Two examples are finally given to illustrate the effectiveness of the proposed controller.

Intelligent Event-Based Fuzzy Dynamic Positioning Control of Nonlinear Unmanned Marine Vehicles Under DoS Attack

This article addresses the dynamic positioning control problem of a nonlinear unmanned marine vehicle (UMV) system subject to network communication constraints and deny-of-service (DoS) attack, where the dynamics of UMV are described by a Takagi-Sugeno (T-S) fuzzy system (TSFS). In order to save limited communication resource, a new intelligent event-triggering mechanism is proposed, in which the event triggering threshold is optimized by a Q -learning algorithm. Then, a switched system approach is proposed to deal with the aperiodic DoS attack occurring in the communication channels. With a proper piecewise Lyapunov function, some sufficient conditions for global exponential stability (GES) of the closed-loop nonlinear UMV system are derived, and the corresponding observer and controller gains are designed via solving a set of matrix inequalities. A benchmark nonlinear UMV system is adopted as an example in simulation, and the simulation results validate the effectiveness of the proposed control method.

Distributed Bipartite Adaptive Event-Triggered Fault-Tolerant Consensus Tracking for Linear Multiagent Systems Under Actuator Faults

This article considers the distributed bipartite adaptive event-triggered fault-tolerant consensus tracking issue for linear multiagent systems in the presence of actuator faults based on the output feedback control protocol. Both time-varying additive and multiplicative actuator faults are taken into account in the meantime. And the upper/lower bounds of actuator faults are not required to be known. First, the state observer is designed to settle the occurrence of unmeasurable system states. Two kinds of event-triggered mechanisms are then developed to schedule the interagent communication and controller updates. Next, with the developed event-triggered mechanisms, a novel observer-based bipartite adaptive control strategy is proposed such that the fault-tolerant control problem can be addressed. Compared with some related works on this topic, our control scheme can achieve the intermittent communication and intermittent controller updates, and the more general actuator faults and network topology are considered. It is proved that the exclusion of Zeno behavior can be realized. Finally, three illustrative examples are given to demonstrate the feasibility of the main theoretical findings.

Leader-Following Consensus for a Class of Nonlinear Multiagent Systems Under Event-Triggered and Edge-Event Triggered Mechanisms

Considering that there are many systems with limited network bandwidth in practice, this article studies the leader-following consensus problem for a class of nonlinear multiagent systems (MASs). The purpose of this article is to reduce unnecessary information transmission between any pair of adjacent agents including the leader in the MASs through intermittent communication. The novel event-triggered and asynchronous edge-event triggered mechanisms are designed for the leader and all edges, respectively. The static and dynamic consensus protocols under these mechanisms are proposed to address the leader-following consensus problem for MASs with Lipschitz dynamics, and the systems will not exhibit Zeno behavior under these two control schemes. Note that the dynamic consensus protocol does not rely on any global values of MASs, it is a fully distributed way. Finally, a practice simulation example is introduced to illustrate the theoretical results obtained.

Hybrid Event-Triggered and Impulsive Control Strategy for Multiagent Systems With Switching Topologies

This article investigates the hybrid event-triggered and impulsive consensus problems for leaderless and leader-following multiagent systems (MASs) with switching topologies. Based on the state information of neighboring agents at event-triggered moments and impulsive instants, a hybrid event-triggered and impulsive control strategy (HETICS) is designed to reduce the communication frequency between neighboring agents and to ensure consensus of leaderless and leader-following MASs. By utilizing the Lyapunov direct method, some consensus criteria are obtained for leaderless and leader-following MASs with switching topologies. It is shown that the HETICS excludes the Zeno behavior. Several numerical examples and simulations are given to illustrate the effectiveness of the proposed consensus strategy and a comparison with previous consensus control methods is given.

Event-Triggered Robust Control for Output Consensus of Unknown Discrete-Time Multiagent Systems With Unmodeled Dynamics

This article investigates the event-triggered output consensus problem for a class of unknown heterogeneous discrete-time linear multiagent systems in the presence of unmodeled dynamics. The agents have individual nominal dynamics with unknown parameters, and the unmodeled dynamics are in the form of multiplicative perturbations. A novel design framework is developed based on an event-triggered internal reference model and a distributed model reference adaptive controller. To deal with the heterogeneity of the multiagent system, the event-triggered internal reference model is designed to generate a virtual reference signal for each agent with a dynamic event-triggering mechanism being adopted to reduce the communication burden between neighboring agents. To handle the unknown parameters and unmodeled dynamics, the robust model reference adaptive controller is then designed to follow the generated virtual reference signal. It is shown that if the unmodeled dynamics satisfy certain conditions, then the boundedness of all the signals and variables in the closed-loop system and convergence of consensus errors to a residual set are guaranteed. Moreover, the consensus errors will converge to zero asymptotically in the absence of unmodeled dynamics. Compared with existing related works, the proposed framework is able to deal with the agents with individual unknown nominal dynamics and unmodeled dynamics. Moreover, the proposed framework is fully distributed in the sense that no knowledge of any global information is needed. Finally, the performance of the proposed method is validated by examples.

Event-Based Tracking Consensus for Multiagent Systems With Volatile Control Gain

This work investigates the tracking consensus problem of multiagent systems over directed networks, where the control gains follow certain volatile patterns. Some event-based consensus protocols are formulated so as to reduce the redundant execution of control. By using an extended differential inequality with a time-dependent coefficient, criteria for tracking consensus under time- and state-dependent triggering conditions are constructed, respectively. It is proved that the time average of the control gain, together with the agent dynamics, network topology, and triggering conditions, governs the consensus despite the fluctuation of control gain. The derived theorem can be utilized to ensure consensus with intermittent strategies aiming to lessen the burden in communications, including aperiodic on-off control with periodic perturbation and pulse-modulated on-off control. Unlike existing works, the requirement of a positive lower bound of control ratios is removed and, thus, a wide range of control gain patterns is possible, signifying higher flexibility in intermittent policy design. Finally, numerical examples are provided to further illustrate the theoretical results.

Designing Event-Triggered Observers for Distributed Tracking Consensus of Higher-Order Multiagent Systems

In this article, the asymptotic tracking consensus problem of higher-order multiagent systems (MASs) with general directed communication graphs is addressed via designing event-triggered control strategies. One common assumption utilized in most existing results on such tracking consensus problem that the inherent dynamics of the leader are the same as those of the followers is removed in this article. In particular, two cases that the dynamics of the leader are subjected, respectively, to bounded input and unknown nonlinearity are considered. To do this, distributed event-triggered observers are first constructed to estimate the state information of the leader. Then, local event-triggered tracking control protocols are designed for each follower to complete the goal of tracking consensus. One distinguishing feature of the present distributed observers lies in the fact that they could avoid the continuous monitoring for the states of the neighbors' observer states. It is also worth pointing out that the present tracking consensus control strategies are fully distributed as no global information related to the directed communication graph is involved in designing the strategies. Two simulation examples are finally presented to verify the efficiency of the theoretical results.

Reset Observer-Based Zeno-Free Dynamic Event-Triggered Control Approach to Consensus of Multiagent Systems With Disturbances

In this article, we investigate the observer-based event-triggered consensus problem of multiagent systems with disturbances. A reset observer consisting of a linear observer and reset element is proposed, the reset element endows the reset observer the ability to improve transient estimation performance compared with traditional linear observers. A hybrid dynamic event-triggering mechanism (ETM) is proposed, in which an internal timer variable is introduced to enforce a lower bound for the triggering intervals such that Zeno-free triggering can be guaranteed even in the presence of disturbances. Then, in order to describe the closed-loop system with both flow dynamics and jump dynamics, a hybrid model is constructed, based on which the Lyapunov-based consensus analysis and dynamic ETM design results are presented. In contrast with linear observer-based consensus protocols and the existing dynamic ETMs, the system performance can be improved and continuous communication between neighboring agents is not needed. Finally, a simulation example is provided to show the effectiveness of the proposed methods.

Multi-agent collaborative control parameter prediction for intelligent precision loading

Due to the low adjustment accuracy of manual prediction, conventional programmable logic controller systems can easily lead to inaccurate and unpredictable load problems. The existing multi-agent systems based on various deep learning models has weak ability for advanced multi-parameter prediction while mainly focusing on the underlying communication consensus. To solve this problem, we propose a hybrid model based on a temporal convolutional network with the feature crossover method and light gradient boosting decision trees (called TCN-LightGBDT). First, we select the initial dataset according to the loading parameters' tolerance range and supply supplementing method for the deviated data. Second, we use the temporal convolutional network to extract the hidden data features in virtual loading areas. Further, a two-dimensional feature matrix is reconstructed through the feature crossover method. Third, we combine these features with basic historical features as the input of the light gradient boosting decision trees to predict the adjustment values of different combinations. Finaly, we compare the proposed model with other related deep learning models, and the experimental results show that our model can accurately predict parameter values.

Event-Triggered Adaptive Fuzzy Output-Feedback Control for Nonstrict-Feedback Nonlinear Systems With Asymmetric Output Constraint

This article addresses the event-triggered adaptive fuzzy output-feedback control problem for a class of nonstrict-feedback nonlinear systems with asymmetric and time-varying output constraints, as well as unknown nonlinear functions. By designing a linear observer to estimate the unmeasurable states, a novel event-triggered adaptive fuzzy output-feedback control scheme is proposed. The barrier Lyapunov function (BLF) and the error transformation technique are used to handle the output constraint under a completely unknown initial tracking condition. It is shown that with the proposed control scheme, all the solutions of the closed-loop system are semiglobally bounded, and the tracking error converges to a small set near zero, while the output constraint is satisfied within a predetermined finite time, even when the constraint condition is violated initially. Moreover, with the proposed event-triggering mechanism (ETM), the Zeno behavior can be strictly ruled out. An example is finally provided to demonstrate the effectiveness of the proposed control method.

Cooperative Output Tracking of Unknown Heterogeneous Linear Systems by Distributed Event-Triggered Adaptive Control

This article addresses the cooperative output tracking problem of a class of linear minimum-phase multiagent systems, where the agent dynamics are unknown and heterogeneous. A distributed event-triggered model reference adaptive control strategy is developed. It is shown that under the proposed event-triggered control strategy, the outputs of all the agents synchronize to the output of the leader asymptotically. It is also shown that Zeno behavior can be excluded with the proposed novel event triggering mechanism. In addition, the proposed adaptive control strategy is fully distributed in the sense that no prior knowledge of some global information, such as the eigenvalues of the associated Laplacian matrix and the number of the agents is required. Finally, an example is given to demonstrate the effectiveness of the proposed control strategy.

Adaptive Neural Control for a Class of Nonlinear Multiagent Systems

This article studies the adaptive neural controller design for a class of uncertain multiagent systems described by ordinary differential equations (ODEs) and beams. Three kinds of agent models are considered in this study, i.e., beams, nonlinear ODEs, and coupled ODE and beams. Both beams and ODEs contain completely unknown nonlinearities. Moreover, the control signals are assumed to suffer from a class of generalized backlash nonlinearities. First, neural networks (NNs) are adopted to approximate the completely unknown nonlinearities. New barrier Lyapunov functions are constructed to guarantee the compact set conditions of the NNs. Second, new adaptive neural proportional integral (PI)-type controllers are proposed for the networked ODEs and beams. The parameters of the PI controllers are adaptively tuned by NNs, which can make the system output remain in a prescribed time-varying constraint. Two illustrative examples are presented to demonstrate the advantages of the obtained results.

Adaptive Bipartite Event-Triggered Output Consensus of Heterogeneous Linear Multiagent Systems Under Fixed and Switching Topologies

This article addresses the adaptive bipartite event-triggered output consensus issue for heterogeneous linear multiagent systems. We consider both cooperative interaction and antagonistic interaction between neighbor agents in both fixed and switching topologies. An adaptive bipartite compensator consisting of time-varying coupling weights and dynamic event-triggered mechanism is first proposed to estimate the leader's state in a fully distributed manner. Different from the existing methods, the proposed compensator has three advantages: 1) it does not depend on any global information of the network graph; 2) it avoids the continuous communication between neighbor agents; and 3) it is applicable for the signed communication topology. Assume that the system states are unmeasurable, and we thus design the state observer. Based on the devised compensator and observer, the distributed control law is developed such that the bipartite event-triggered output consensus problem can be achieved. Moreover, we extend the results in fixed topology to switching topology, which is more challenging in that state estimation is updated in two cases: 1) the interaction graph is switched or 2) the event-triggered mechanism is satisfied. It is proven that no agent exhibits Zeno behavior in both fixed and switching interaction topologies. Finally, two examples are provided to illustrate the feasibility of the theoretical results.

Distributed Dynamic Event-Triggered Control for Cooperative Output Regulation of Linear Multiagent Systems

This paper investigates the cooperative output regulation problem for heterogeneous linear multiagent systems under fixed communication graphs via event-triggered control. A fully distributed event-triggered dynamic output feedback control law is proposed based on the feedforward design approach. At the same time, a fully distributed dynamic event-triggering mechanism is designed so that each agent can determine when to broadcast its information to its neighbors. Compared with existing related results, both the control law and the event-triggering mechanism in this paper are independent of any global information. It is shown that with the proposed dynamic event-triggered control strategy, the cooperative output regulation problem can be solved in a fully distributed manner by intermittent communication. Moreover, Zeno behavior can be strictly ruled out for each agent. Finally, the effectiveness of the proposed dynamic event-triggered control strategy is validated by a numerical example.

Distributed bipartite leader-following consensus of linear multi-agent systems with input time delay based on event-triggered transmission mechanism

This study focuses on the distributed bipartite consensus tracking for linear multi-agent systems with input time delay based upon event-triggered transmission mechanism. Both cooperative interaction and antagonistic interaction between neighbor agents are considered. A novel distributed bipartite control technique with event-triggered mechanism is raised to address this consensus issue. Different from the existing methods, our control technique does not need continuous communication among agents, is capable of addressing the case of input delay, and is applicable for the signed communication topology. Moreover, to avoid continuous monitoring of one's own state, a self-triggered control strategy is further proposed. And when the system states cannot be measured, the observer-based bipartite control technique with event-triggered mechanism is thus put forward. Furthermore, the results in leader-following consensus are extended to containment control. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, simulation experiments are used to test the practicability of the theoretical analysis.