Output Consensus of Heterogeneous Linear Multi-Agent Systems by Distributed Event-Triggered/Self-Triggered Strategy

Dynamic event-triggered quantized secure output consensus of heterogeneous multi-agent systems under DoS attacks

This paper investigates secure output consensus problem of heterogeneous multi-agent systems (HMASs) under denial-of-service (DoS) attacks. First, an adaptive dynamic compensator depending on local measurement information is designed for tracking the signal of the virtual exosystem. Second, for mitigating network communication load, a novel adaptive control protocol is developed by introducing dynamic event-triggered control and quantized control strategies. Moreover, Zeno behavior can be eliminated under the proposed scheme. Third, the secure output consensus of HMASs under DoS attacks can be guaranteed by satisfying the designed sufficient conditions. Finally, simulation is shown to verify reliability of the proposed control protocol and theory.

Distributed estimation and control over mobile sensor networks with jointly connected topology: Event-triggered approach

This article deals with the problem of distributed event-triggered tracking control in mobile sensor networks (MSNs) with a jointly connected topology (JCT). Two schemes are proposed for linear and Lipschitz nonlinear MSNs to estimate and track a mobile target. The proposed schemes are established using an event-triggered method to avoid continuous exchange of information between sensor nodes. In comparison with the other research under event-triggered communication strategies where states of the target are available, this paper considers that the states of the target are not available and two event-triggered algorithms are established for sensor nodes to estimate and follow the states of the continuous-time targets that can be seen in various real-world applications. Also, the proposed schemes are designed for the JCT with disconnected graphs which means the communication topology of the MSN is not required to be connected for all time instants. By employing the Cauchy convergence criterion and a common Lyapunov function, sufficient conditions are also established to ensure event-based tracking control subject to JCT. The effectiveness of the proposed work is verified by presenting simulation examples.

Adaptive Bipartite Event-Triggered Time-Varying Output Formation Tracking of Heterogeneous Linear Multi-Agent Systems Under Signed Directed Graph

This study investigates the adaptive bipartite event-triggered time-varying output formation tracking for heterogeneous linear multi-agent systems (MASs) under signed directed communication topology. Both cooperative communication and antagonistic communication among agents are considered. The fully distributed bipartite compensator based on the novel composite event-triggered transmission mechanism is first put forward to estimate the state of the leader. Compared with the existing methods, our compensator can save communication resources using event-triggered transmission mechanism; is independent of the global information of the network graph; and is applicable for the signed directed graph. With the developed compensator, the distributed control protocol is designed to achieve the time-varying output formation tracking. Moreover, the case that the networked systems subject to external disturbances is also considered. To estimate the state of leader with disturbance, the fully distributed bipartite compensator based on an innovative composite event-triggered mechanism is presented. And the novel distributed control protocol is proposed to address the output formation tracking issue for linear MASs with heterogeneous dynamics and external disturbances. It is shown that the Zeno-behavior can be excluded in both transmission mechanisms. Finally, the effectiveness of the developed control methods is illustrated through three simulation examples.

Fully Distributed Pull-Based Event-Triggered Bipartite Fixed-Time Output Control of Heterogeneous Systems With an Active Leader

This article deals with the fully distributed pull-based event-triggered bipartite fixed-time output consensus problem of heterogeneous linear multiagent systems (HLMASs) with an active leader, whose information can be merely accessed by a small fraction of followers. First, a class of fully distributed fixed-time observers is proposed for each follower to estimate the leader's system matrices, position, and control input under the signed communication topology, respectively. Then, based on the estimations of leader's system matrices, two adaptive algorithms are given to solve the regulator equations. Furthermore, the fully distributed fixed-time observer-based controllers associated with state feedback and output feedback are, respectively, proposed by employing the pull-based event-triggered mechanism (ETM) where each agent merely updates controller at its own triggering instants. Correspondingly, some sufficient criteria and the rigorous proofs are provided to ensure the implementation of bipartite output consensus in fixed time by using the Lyapunov stability theory and fixed-time stability theory. Moreover, the strictly positive lower bounds of intervals between two adjacent event-triggered times are derived, which means the Zeno behavior is ruled out. Finally, numerical simulations are performed to demonstrate the theoretical analysis.

Observer-Based Dynamic Event-Triggered Semiglobal Bipartite Consensus of Linear Multi-Agent Systems With Input Saturation

Observer-based dynamic event-triggered semiglobal bipartite consensus (SGBC) is investigated for linear multi-agent systems (MASs) with input saturation under a competitive network. Based on the estimated relative information and low-gain feedback technology, distributed dynamic event-triggered control (DETC) protocols are proposed for solving the observer-based SGBC problems for MASs under a fixed topology and a jointly connected topology, respectively. It is turned out that the SGBC of MASs can be achieved under the proposed protocols. By using gauge transformation and the Lyapunov theory, the bipartite consensus conditions are obtained. Moreover, Zeno behaviors will be excluded. Finally, two simulation examples are presented to verify the theoretical results efficiently.

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.

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.

Accurate Power Sharing and Voltage Regulation for AC Microgrids: An Event-Triggered Coordinated Control Approach

The microgrid with the high proportion of renewable sources has become the trend of the future. However, the negative features, such as renewable energy perturbation, nonlinear counterpart, and so on, are prone to causing the low-power quality of the ac microgrid. To deal with these problems, this article proposes an event-triggered consensus control approach. First, the nonlinear state-space function regarding the ac microgrid is built, which is further transformed into the standard linear multiagent model by using the singular perturbation method. It provides indispensable preprocessing for the direct application of advanced linear control approaches. Then, based on this standard linear multiagent model, the secondary consensus approach with the leader is designed to compensate for the output voltage deviation and achieve accurate power sharing. In order to decrease the communication among various distributed generators, the event-triggered communication method is further proposed. Meanwhile, the Zeno behavior is avoided through the theoretical proof. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.

Observer-Based Multiagent Bipartite Consensus With Deterministic Disturbances and Antagonistic Interactions

This article studies the multiagent bipartite consensus in networks with deterministic disturbances and antagonistic interactions. An observer-based output-feedback controller design is provided to guarantee the bipartite consensus with deterministic disturbances that satisfy the matching condition. Then, by considering that the bandwidths of communication channels are limited in practical systems, the event-triggered scenario of the proposed output controller for the bipartite consensus is further studied; the node-based broadcast updating fashion is utilized and the Zeno behavior is ruled out. Simulations are also offered to support the theoretical results of protocol designs.

A Comment on and Correction to: Opinion Dynamics in the Presence of Increasing Agreement Pressure

We identify counterexamples to the consensus result given in Semonsen et al. (2018). We resolve the counterexamples by replacing Lemma 5 in the given reference with a novel variation of the Banach fixed-point theorem, which explains both the numerical results in the reference and the counterexample(s) in this note and provides a sufficient condition for consensus in systems with increasing peer-pressure. This work is relevant for other papers that have used the proof technique from Semonsen et al. and establishes the veracity of their claims assuming the new sufficient condition.

Adaptive Bipartite Fixed-Time Time-Varying Output Formation-Containment Tracking of Heterogeneous Linear Multiagent Systems

This study investigates the bipartite fixed-time time-varying output formation-containment tracking issue for heterogeneous linear multiagent systems with multiple leaders. Both cooperative communication and antagonistic communication between neighbor agents are taken into account. First, the bipartite fixed-time compensator is put forward to estimate the convex hull of leaders' states. Different from the existing techniques, the proposed compensator has the following three highlights: 1) it is continuous without involving the sign function, and thus, the chattering phenomenon can be avoided; 2) its estimation can be achieved within a fixed time; and 3) the communication between neighbors can not only be cooperative but also be antagonistic. Note that the proposed compensator is dependent on the global information of network topology. To deal with this issue, the fully distributed adaptive bipartite fixed-time compensator is further proposed. It can estimate not only the convex hull of leaders' states but also the leaders' system matrices. Based on the proposed compensators, the distributed controllers are then developed such that the bipartite time-varying output formation-containment tracking can be achieved within a fixed time. Finally, two examples are given to illustrate the feasibility of the main theoretical findings.

Cross-dimensional formation control of second-order heterogeneous multi-agent systems

This paper is concerned with the cross-dimensional formation control of a second-order multi-dimensional heterogeneous multi-agent system. Agents are first separated into several groups according to their position/velocity vector dimensions. Then the cross-dimensional formation control problem is formulated such that agents in the same group form a time-varying formation in their own dimension and agents in different groups cooperatively move in multiple dimensions. This can make follower agents in different dimensions cooperatively track a leader. Moreover, a cross-dimensional formation protocol is designed based on full or partial information of neighboring agents. For higher-dimensional agents, full information of lower-dimensional neighbors is adopted. For lower-dimensional ones, only partial information of higher-dimensional neighbors is used. Furthermore, a necessary and sufficient condition for the second-order heterogeneous multi-agent system to achieve cross-dimensional formation is provided. Accordingly, a criterion for designing cross-dimensional formation protocol is further derived. Finally, under an undirected graph, a lower-dimensional protocol design criterion is obtained if there is no data exchange between lower- and higher-dimensional followers. The effectiveness of the obtained results is demonstrated through cross-dimensional target enclosing performance analysis for multiple robots and quadrotors.

Output Containment Control of Heterogeneous Linear Multiagent Systems With Unbounded Distributed Transmission Delays

In this article, the output containment control problem of heterogeneous linear multiagent systems (MASs) with unbounded distributed transmission delays is considered. A key technical lemma is first established to show that the distributed observers under unbounded distributed transmission delays can be utilized to estimate the convex combination of the states of multiple leaders. Then, a novel distributed output feedback control law is proposed based on those distributed observers. It is shown that under our proposed control law, the output of each follower converges to the convex hull spanned by the outputs of the leaders. In addition, our results include relevant results on output containment control of MASs with bounded distributed or constant transmission delays as special cases. Finally, the effectiveness of the proposed control law is demonstrated by a simulation example.

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.

Guaranteed Cost for an Event-Triggered Consensus Strategy for Interconnected Two Time-Scales Systems With Structured Uncertainty

This article proposes the design of an event-triggered control strategy for consensus of interconnected two-time scales systems with structured uncertainty. The control design under consideration ensures also that consensus is achieved with an overall guaranteed cost. Since each system involves processes evolving on both fast and slow time scales, two Zeno-free event-triggered mechanisms are designed to independently decide the sampling and transmission instants for the slow and fast states, respectively. As the first step, we design an event-triggering consensus protocol in the ideal/nominal case when the interconnected systems are not affected by uncertainties and the interactions happen over a fixed interaction network. Next, the results are extended in order to take into account structured uncertainties affecting the systems' dynamics. At this step, we go further and we provide sufficient conditions for event-triggering consensus with a guaranteed overall cost. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Event/Self-Triggered Consensus Control of Multiagent Systems With Undesirable Sensor Signals

This article focuses on event-triggered consensus control for multiagent systems subject to sensor faults or noises. First, a descriptor state observer with a low-pass filtering characteristic being developed for each agent using output information. The convergence regions of estimation errors can be reduced by a nonsingular suppression matrix. Leader-follower event-triggered consensus protocols with continuous-time communication are designed for multiagent systems based on the estimated states. By virtue of the Jordan form of the Laplacian matrix, the stability conditions are derived by using the Lyapunov analysis. Then, new self-triggered consensus protocols are designed for the multiagent systems to remove the requirement of the continuous monitoring triggering condition and continuous communication simultaneously. The triggering interval is proved greater than 0, and the Zeno behavior is excluded for all agents. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed design.

Cooperative Output Regulation for Linear Multiagent Systems via Distributed Fixed-Time Event-Triggered Control

In this article, we consider the cooperative output regulation for linear multiagent systems (MASs) via the distributed event-triggered strategy in fixed time. A novel fixed-time event-triggered control protocol is proposed using a dynamic compensator method. It is shown that based on the designed control scheme, the cooperative output regulation problem is addressed in fixed time and the agents in the communication network are subject to intermittent communication with their neighbors. Simultaneously, with the proposed event-triggering mechanism, Zeno behavior can be ruled out by choosing the appropriate parameters. Different from the existing strategies, both the compensator and control law are designed with intermittent communication in fixed time, where the convergence time is independent of any initial conditions. Moreover, for the case that the states are not available, the output regulation problem can further be addressed by the distributed observer-based output feedback controller with the fixed-time event-triggered compensator and event-triggered mechanism. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results.

Rendezvous With Connectivity Preservation Problem of Linear Multiagent Systems via Parallel Event-Triggered Control Strategies

This article studies the rendezvous problem of linear multiagent systems by parallel event-triggered connectivity-preserving control strategies. There are two distinguished features of our design. First, the event-triggered control laws can not only guarantee the convergence of the tracking error as existing event-triggered consensus control strategies but also have the additional ability to maintain the connectivity of the time-varying and position-dependent communication network as rendezvous control laws. Second, by combining the potential function technique, output regulation theory, and adaptive control technique, an event-triggered observer is applied to estimate both the leader's system matrix and trajectory, which can work in parallel with the connectivity-preserving event-triggered controller. The executive time instants for the observer and the controller are asynchronous and generated by different triggering functions based on their own locally available measurement errors.

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.

Adaptive Bipartite Tracking Control of Nonlinear Multiagent Systems With Input Quantization

This article studies the bipartite tracking control problem of distributed nonlinear multiagent systems with input quantization, external disturbances, and actuator faults. We use the radial basis function (RBF) neural networks (NNs) to model unknown nonlinearities. Due to the fact that the upper bounds of disturbances and the number of actuator faults are unknown, an intermediate control law is designed based on a backstepping strategy, where a compensation term is introduced to eliminate external disturbances and actuator faults. Meanwhile, a novel smooth function is incorporated into the real distributed controller to reduce the effect of quantization on the virtual controller. The proposed distributed controller not only realizes the bipartite tracking control but also ensures that all signals are bounded in the closed-loop systems and the outputs of all followers converge to a neighborhood of the leader output. Finally, simulation results demonstrate the effectiveness of the proposed control algorithm.

On Containment for Linear Systems With Switching Topologies: A Novel State Transition Matrix Perspective

This article studies the containment control problem for a group of linear systems, consisting of more than one leader, over switching topologies. The input matrices of these linear systems are not required to have full-row rank and the switching can be arbitrary, making the problem quite general and challenging. We propose a novel analysis framework from the viewpoint of a state transition matrix. Specifically, according to the inherent linearity, we successfully establish a connection between state transition matrices of the above multileader system and a virtual leader-following system obtained by combining those leaders. This enlightening result relates the containment problem to a consensus one. Then, by analyzing the property of the state transition matrix, we uncover that each component of any follower's state converges to the convex hull spanned by the corresponding components of the leaders', provided some mild conditions are satisfied. These conditions are derived in terms of the concept of a positive linear system. A special case of the second-order linear system is further discussed to illustrate these conditions. Moreover, two different design methods of the feedback gain matrix are provided, which additionally require that the network topology contains a united spanning tree all the time.

Spatial Linear Dynamic Relationship of Strongly Connected Multiagent Systems and Adaptive Learning Control for Different Formations

This article addresses an important problem of how to improve the learnability of an intelligent agent in a strongly connected multiagent network. A novel spatial-dimensional linear dynamic relationship (SLDR) is developed to formulate the spatial dynamic relationship of an agent with respect to all the related agents. The obtained SLDR virtually exists in the computer to describe the input-output (I/O) relationship in the spatial domain and an iterative adaptation mechanism is developed to update the SLDR using I/O information to show real-time dynamical behavior of multiagent systems with nonrepetitive initial states. Subsequently, an SLDR-based adaptive iterative learning control (SLDR-AILC) is presented with rigorous analysis for iteration-variant formation control targets. Not only the 3-D dynamic behavior of the multiagent network but also the control protocols of the communicated agents are incorporated in the learning mechanism and thus strong learnability of the proposed SLDR-AILC is achieved to improve control performance. The proposed SLDR-AILC is a data-driven scheme where no explicit model structure is needed. Simulations with strongly connected topologies verify the theoretical results.

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.

Distributed Event-Triggered Consensus of General Linear Multiagent Systems Under Directed Graphs

This article investigates the consensus problem of general linear multiagent systems under directed communication graphs with event-triggered mechanisms. First, a novel distributed static event-triggered mechanism with a state-dependent threshold is proposed to solve the consensus problem, both with a positive lower bound on the average time interval of the communication among agents and updates of controllers. Thus, the Zeno behavior is excluded for communication among agents and controller updates. Next, to further reduce the frequencies of communication among agents and updates of controllers, a distributed dynamic event-triggered mechanism is introduced. By applying the static and dynamic mechanisms, the problem can be addressed with the reduced use of system resources compared with that in most existing control algorithms. Finally, numerical simulations are presented to verify the effectiveness of the results.

Design of Hybrid Event-Triggered Containment Controllers for Homogeneous and Heterogeneous Multiagent Systems

This article is concerned with the containment control problem for a class of multiagent systems (MASs) based on event-triggered output feedback. For homogeneous MASs, a distributed observer-based containment control protocol and a distributed hybrid event-triggered scheme are proposed. The observers, containment controllers, and event-triggered conditions are designed simultaneously by means of the matrix transformation technique. The proposed event-triggered mechanism includes not only the traditional triggering function but also a running time upper bound, which saves the communication workload and improves system performance. Furthermore, based on the output regulation framework, a hybrid distributed event-triggered scheme and a distributed containment control protocol for heterogeneous MASs are developed, where the dynamics of the followers vary. Multiply unmanned aerial vehicles are modeled as a linear MAS to verify the effectiveness of the presented algorithm.

Semiglobal Cluster Consensus for Heterogeneous Systems With Input Saturation

In this article, the semiglobal cluster consensus problem is investigated for heterogeneous generic linear systems with input saturation. A general case in a leaderless framework is studied first, and then in order to broaden the scope of application, we consider a special case in which the leader nodes are pinned intermittently. To tackle the above problems, we propose a linear control scheme by using the low-gain feedback technique under the assumptions that each node is asymptotically null controllable and the underlying topology of each cluster (the extended cluster under the intermittent pinning control) has a directed spanning tree. The Lyapunov-based method and the low-gain feedback technique are developed for convergence analysis. It is shown that for both cases, the convergence rate is explicitly specified, which depends on the low-gain parameter and system matrices. Finally, two numerical examples are provided to verify the effectiveness of the theoretical findings.

Secure consensus of multi-agent systems with redundant signal and communication interference via distributed dynamic event-triggered control

This paper studies a class of multi-agent systems (MASs) subject to deception signal and communication interference. The objective of the present work is to establish a flexible and generalized distributed dynamic event-triggered control (DDETC) with impulsive signal to make the investigated MASs achieve secure consensus under redundant signal and communication interference. It is shown that Zeno behavior can be precluded with such a DDETC. The challenging but valuable new designed DDETC scheme shows the trigger is developed to achieve itself away from exceeding the data transmission load through parameter adjustment, to reduce redundant triggering, to flexibly adjust the triggered frequency, and even to replace sampled-data scheme as special cases. By the impulsive DDETC, anti-deception and anti-interference techniques, the secure consensus criteria of MASs are constructed cleverly. Numerical examples with simulations are given to illustrate the effectiveness of the proposed scheme and control protocol.

Output Consensus for Heterogeneous Linear Multiagent Systems With a Predictive Event-Triggered Mechanism

In this paper, an output consensus problem for a heterogeneous linear multiagent system with a predictive event-triggered mechanism on directed graphs is investigated. An event-triggered consensus protocol is proposed by introducing an internal reference model for each agent to handle the heterogeneity existing in the system. With the proposed mechanism, each agent predicts its internal reference model's input by employing the estimate of the internal reference model's state differences between itself and its neighbor agents. As it considers the internal reference model's inputs of agents, the system requires far fewer event-triggered times to achieve consensus, leading to a significant reduction in communication cost among agents. A necessary and sufficient condition of the output consensus for the heterogeneous linear multiagent system is put forth. Furthermore, Zeno behavior can be ruled out for each agent. Some numerical examples are given to demonstrate the effectiveness of the proposed control mechanism.

Bipartite Fixed-Time Output Consensus of Heterogeneous Linear Multiagent Systems

In this article, the bipartite fixed-time output consensus problem of heterogeneous linear multiagent systems (MASs) is investigated. First, a distributed bipartite fixed-time observer is proposed, by which the follower can estimate the leader's state. The estimate value is the same as the leader's state in modulus but may not in sign due to the existence of antagonistic interactions between agents. Then, an adaptive bipartite fixed-time observer is further proposed. It is fully distributed without involving any global information. This adaptive bipartite fixed-time observer can estimate not only the leader's system matrix but also the leader's state. Next, distributed nonlinear control laws are developed based on two observers, respectively, such that the bipartite fixed-time output consensus of heterogeneous linear MASs can be achieved. Moreover, the upper bound of the settling time is independent of initial states of agents. Finally, the examples are given to demonstrate the 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.

Dynamic Intermittent Feedback Design for H∞ Containment Control on a Directed Graph

This article develops a novel distributed intermittent control framework with the ultimate goal of reducing the communication burden in containment control of multiagent systems communicating via a directed graph. Agents are assumed to be under disturbance and communicate on a directed graph. Both static and dynamic intermittent protocols are proposed. Intermittent H_∞ containment control design is considered to attenuate the effect of the disturbance and the game algebraic Riccati equation (GARE) is employed to design the coupling and feedback gains for both static and dynamic intermittent feedback. A novel scheme is then used to unify continuous, static, and dynamic intermittent containment protocols. Finally, simulation results verify the efficacy of the proposed approach.

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.

Impulsive Consensus of Nonlinear Multi-Agent Systems via Edge Event-Triggered Control

In this paper, we mainly investigate two kinds of consensuses of multi-agent systems (MASs) with nonlinear dynamics based on impulsive control, event-triggered control, and sampled-data control. The two types of impulsive protocols are proposed for the case without and with leader agent. Edge event-triggered technique is presented, where for each communication link, occurrence of edge event can activate the mutual state sampling and controller update of the corresponding agents. The control approach combines the characteristics of impulsive control and edge event-triggered control and is defined as "impulsive edge event-triggered control." It has good performance in robustness against disturbance and reduces the communication cost. The results with the aid of the Lyapunov function approach and stability theory of impulsive control show that if some sufficient conditions are satisfied, the consensus of MASs can be guaranteed and the rate of convergence can be exponentially estimated. Additionally, Zeno-behavior can be eliminated by using impulsive edge event-triggered control, which reduces the burden of event detectors. Finally, two simulations are provided to illustrate the effectiveness and performance of our theoretical analysis.

Distributed Control of Nonlinear Multiagent Systems With Unknown and Nonidentical Control Directions via Event-Triggered Communication

In this paper, the leader-following output consensus problem for a class of uncertain nonlinear multiagent systems with unknown control directions is investigated. Each agent system has nonidentical dynamics and is subject to external disturbances and uncertain parameters. The agents are connected through a directed and jointly connected switching network. A novel two-layer distributed hierarchical control scheme is proposed. In the upper layer, to save the communication resources and to handle the switching networks, an event-triggered communication scheme is proposed, and a Zeno-free event-triggered mechanism is designed for each agent to generate the asynchronous triggering time instants. Furthermore, to avoid the continuous monitoring of the system states, a Zeno-free self-triggering algorithm is proposed. In the lower layer, to handle the unknown control directions problem and to achieve the output tracking of the local references generated in the upper layer, the Nussbaum-type function-based technique is combined with internal model principle. With the proposed two-layer distributed hierarchical controller, the leader-following output consensus is achieved. The obtained result is further extended to the formation control problem. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

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

This paper investigates the consensus problem of linear multi-agent systems subject to external disturbances via distributed event-triggered adaptive control. First, a distributed event-triggered adaptive output feedback control strategy is proposed for each agent. It is shown that under this control strategy, the consensus problem can be solved for any connected undirected communication graph in a fully distributed manner without using any global information. Then a distributed self-triggered adaptive output feedback control strategy is designed with which continuous monitoring of the measurement error is no longer needed. It is further shown that for the proposed event-triggered and self-triggered control strategies, no agent will exhibit Zeno behavior. Finally, the effectiveness of the proposed two control strategies is illustrated on a group of two-mass-spring systems.

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.

Event-Triggered Adaptive Tracking Control for Multiagent Systems With Unknown Disturbances

This paper considers the event-triggered tracking control problem of nonlinear multiagent systems with unknown disturbances. The event-triggering mechanism is considered in the controller update, which decreases the amount of communication and reduces the frequency of the controller update in practice. By designing a disturbance observer, the unknown external disturbances are estimated. Moreover, a part of adaptive parameters are only dependent on the number of followers, which weakens the computational burden. It is shown that all the signals are bounded, and the consensus tracking errors are located in a small neighborhood of the origin based on the Lyapunov stability theory and backstepping approach. Finally, the effectiveness of the approach proposed in this paper is proved by simulation results.

Observer-Based Consensus Control for Discrete-Time Multiagent Systems With Coding-Decoding Communication Protocol

In this paper, the consensus control problem is investigated for a class of discrete-time networked multiagent systems (MASs) with the coding-decoding communication protocol (CDCP). Under a directed communication topology, an observer-based control scheme is proposed for each agent by utilizing the relative measurement outputs between the agent itself and its neighboring ones. The signal delivery is in a digital manner, which means that only the sequence of finite coded signals is sent from the observer to the controller. To be specific, the observed data is encoded to certain codewords by a designed coder via the CDCP, and the received codewords are then decoded by the corresponding decoder at the controller side. The purpose of the addressed problem is to design an observer-based controller such that the close-loop MAS achieves the expected consensus performance. First, with the help of the input-to-state stability theory, a theoretical framework for the detectability is established for analyzing and designing the CDCP. Then, under such a communication protocol, some sufficient conditions for the existence of the proposed observer-based controller are derived to guarantee the asymptotic consensus of the MASs. In addition, the controller parameter is explicitly determined in terms of the solution to certain matrix inequalities associated with the information of the communication topology. Finally, a simulation example is given to demonstrate the effectiveness of the developed control strategy.

Event-Triggered Consensus of Homogeneous and Heterogeneous Multiagent Systems With Jointly Connected Switching Topologies

This paper investigates the distributed event-based consensus problem of switching networks satisfying the jointly connected condition. Both the state consensus of homogeneous linear networks and the output consensus of heterogeneous networks are studied. Two kinds of event-based protocols based on local sampled information are designed, without the need to solve any matrix equation or inequality. Theoretical analysis indicates that the proposed event-based protocols guarantee the achievement of consensus and the exclusion of Zeno behaviors for jointly connected undirected switching graphs. These protocols, relying on no global knowledge of the network topology and independent of switching rules, can be devised and utilized in a completely distributed manner. They are able to avoid continuous information exchanges for either controllers' updating or triggering functions' monitoring, which ensures the feasibility of the presented protocols.

Semi-Global Output Consensus for Discrete-Time Switching Networked Systems Subject to Input Saturation and External Disturbances

The semi-global output consensus problem for multiagent systems depicted by discrete-time dynamics subject to external disturbances and input saturation over switching networks is investigated in this paper. Assume that only a small part of subsystems have directly received the output of the exosystem. The distributed consensus algorithms are proposed by adopting the low-gain state feedback and the modified algebraic Riccati equation. Then, the outputs of all subsystems can reach synchronization asymptotically with those of the exosystem by using the proposed consensus protocols on some preconditions. Both the connected switching networks and the jointly connected switching networks are considered for the semi-global output consensus problem, respectively. Some numerical simulation results are shown to validate the theoretical analysis.

Edge Convergence Problems on Signed Networks

This paper focuses on characterizing edge dynamics of signed networks subject to both cooperative and antagonistic interactions and copes with the state convergence problems of the resulting edge systems. To represent the two competitive classes of interactions that emerge in signed networks, signed digraphs are adopted and the relevant edge Laplacian matrices are introduced, with which an edge-based distributed protocol is presented. The relation between the edge Laplacian matrix and the structural balance (or unbalance) of a signed digraph is disclosed by taking advantage of properties of undirected cycles. Further, it is shown that for a signed network, the state of its edge system converges to a constant vector, regardless of whether its associated signed digraph is structurally balanced or unbalanced. This result does not need to impose the assumption upon the digon sign-symmetry of the signed digraph that is generally required by the node-based distributed protocols. In particular, the state convergence results of edges can be exploited to handle traditional bipartite consensus problems for the nodes of signed networks. Simulation examples are given to illustrate the effectiveness of the edge-based analysis method proposed for signed networks.

Event-Based Practical Output Regulation for a Class of Multiagent Nonlinear Systems

This paper explores a cooperative practical output regulation problem for a class of heterogeneous multiagent nonlinear systems by event-based output feedback. Specifically, we shall restrict our attention to the situation of sampled-data-based local measurements. As usual, due to agents heterogeneity, we first convert the problem into a stabilization one for the so-called augmented system, composed of the agent systems and suitably designed continuous-time internal models. Then, we show that this stabilization can be solved by measurement feedback. It finally allows us to establish a valid event-based protocol, leading to a global practical stability property and meanwhile guaranteeing Zeno-free condition.

Bipartite output consensus of heterogeneous linear multi-agent systems by dynamic triggering observer

In this paper, the bipartite output consensus problem of heterogeneous linear multi-agent systems (HL-MASs) is investigated. Compared with related works, both the cooperative interactions and antagonistic interactions between agents exist. First, a novel distributed dynamic triggering observer is designed to recover the leader's state. In order to avoid verifying the dynamic triggering condition continuously, a monitoring scheme is proposed. Then, the communication cost can be reduced. Next, we solve the bipartite output consensus problem of HL-MASs by both state feedback and output feedback control laws. Moreover, detailed analysis on the dynamic event triggering condition is conducted. It is shown that the lower bound of inter-execution time is larger than zero, so Zeno behaviour is excluded. The choice of parameters involved in the dynamic event triggering condition is also analysed. Finally, examples are given for demonstration.

H∞ Consensus for Linear Heterogeneous Multiagent Systems Based on Event-Triggered Output Feedback Control Scheme

In this paper, the H_∞ consensus problem for linear heterogeneous multiagent systems (LHMAS) based on event-triggered output feedback control is investigated. Two novel event-triggered control schemes including nonperiodic and periodic event-triggered control approaches are provided to make the LHMAS with external unknown disturbance achieve H_∞ consensus. Therein, the nonperiodic event-triggered control method is designed by combining the event-triggered approach with time-triggered scheme, which can make the sampled instants be decided by the event-triggered condition and provide a fixed lower bound of sampled interval to avoid the Zeno-behavior. Then, based on this approach, the periodic event-triggered control scheme has a further improvement that only the information at fixed periodic interval is used for the event-triggered condition, which means that this method avoids the continuous-time information transfer. Besides, both schemes take output feedback control, which means that only the output information of each agent and leader is needed in this paper. Finally, a numerical example is given to support our results.