Event‐triggered Control for Cluster Consensus in Multi‐agent Networks

This paper considers the issue of cluster consensus for multiple agents in fixed and undirected networks. Agents in a network are supposed to split into several clusters, and a fraction of the agents in each cluster are pinned by virtual leaders. According to the Lyapunov stability theory and graph theory, some appropriate event‐triggered protocols are developed for consensus of the agents belonging to the same cluster, which can greatly reduce both the number of communication updates and that of control actuation updates. Finally, a numerical example is shown to demonstrate the effectiveness of the proposed theoretical results.     

Distributed Adaptive Event‐Triggered Control for Leader‐Following Consensus of Multi‐Agent Systems

This paper studies the leader‐following consensus problem for Lipschitz nonlinear multi‐agent systems using novel event‐triggered controllers. A distributed adaptive law is introduced for the event‐based control strategy design such that the proposed controllers are independent of system parameters and only use the relative states of neighboring agents, and hence are fully distributed. Due to the introduction of an event‐triggered control scheme, the controller of the agent is only triggered at it's own event times, and thus reduces the amount of communication between controller and actuator and lowers the frequency of controller updates in practice. Based on a quadratic Lyapunov function, the event condition which uses only neighbor information and local computation at trigger instants is established. Infinite triggers within a finite time are also verified to be impossible. The effectiveness of the theoretical results are illustrated through simulation examples.     

Event‐triggered distributed constrained consensus

We consider a distributed consensus problem for continuous‐time multi‐agent systems with set constraints on the final states. To save communication costs, an event‐triggered communication‐based protocol is proposed. By comparing its own instantaneous state with the one previously broadcasted to neighbours, each agent determines the next communication time. Based on this event‐triggered communication, each agent is not required to continuously monitor its neighbours' state and the communication only happens at discrete time instants. We show that, under some mild conditions, the constrained consensus of the multi‐agent system with the proposed protocol can be achieved with an exponential convergence rate. A lower bound of the transmission time intervals is provided that can be adjusted by choosing different values of parameters. Numerical examples illustrate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

Admissible Consensus of Multi‐Agent Singular Systems

Consensus problems are studied for both continuous‐time and discrete‐time multi‐agent singular systems with time‐invariant and directed communication topologies. Under restricted system equivalence of singular agents, sufficient and necessary conditions are obtained for admissible consensus ability with static protocols, which are based on both the relative information of the dynamic states and the absolute information of the static states. For a network of continuous‐time singular systems, the existence of admissible consensualization can be cast into strong stabilizability of the agent dynamics. Once discrete‐time multi‐agent singular systems satisfy the condition of reaching nontrivial final consensus states, strong stabilizability is a sufficient condition to achieve admissible consensualization. Two algorithms are proposed to construct two protocols, which are based on a linear matrix inequality and a modified Riccati equation, respectively. Finally, the algorithms are illustrated by two simulation examples.     

NNs‐Based Event‐Triggered Consensus Control of a Class of Uncertain Nonlinear Multi‐Agent Systems

We are concerned with the consensus problem for a class of uncertain nonlinear multi‐agent systems (MASs) connected through an undirected communication topology via event‐triggered approaches in this paper. Two distributed control strategies, the adaptive centralized event‐triggered control one and adaptive distributed event‐triggered control one, are presented utilizing neural networks (NNs) and event‐driven mechanisms, where the advantages of the proposed control laws lie that they remove the requirement for exact priori knowledge about parameters of individual agents by taking advantage of NNs approximators and they save computing and communication resources since control tasks only execute at certain instants with respect to predefined threshold functions. Also, the trigger coefficient can be regulated adaptively with dependence on state errors to ensure not only the control performance but also the efficiency of the network interactions. It is proven that all signals in the closed‐loop system are bounded and the Zeno behavior is excluded. Finally, simulation examples are presented for illustration of the theoretical claims.     

Distributed Consensus of Multi‐Agent Networks Via Event‐Triggered Pinning Control

This paper is concerned with distributed consensus between two multi‐agent networks with the same topology structure. Considering one network as the leaders' network and the other one as the followers' network, a new event‐triggered pinning control scheme is proposed to realize distributed consensus between these two networks. By utilizing the graph theory and Lyapunov functional method, consensus criteria are derived in the form of linear matrix inequalities. Moreover, distributed consensus of multi‐agent networks with Lipschitz nonlinear dynamics is also discussed. Numerical simulations are provided to demonstrate the effectiveness of the theoretical analysis.     

Suboptimal Output Consensus for Time‐Delayed Singular Multi‐Agent Systems

The current paper investigates guaranteed‐cost output consensus analysis and design problems for high‐order linear time‐invariant singular multi‐agent systems with constant time delays, which can realize suboptimal output consensus control. Firstly, a new output consensus protocol with a suboptimal index and a single delay is proposed to realize the tradeoff design between output consensus regulation performances and control energy consumptions. Then, sufficient conditions for guaranteed‐cost output consensus and consensualization are derived in terms of linear matrix inequalities by a combined tool from the Lyapunov‐Krasovskii approach and the free‐weighting matrix technique, respectively, and the output consensus function is determined on the basis of the First Equivalent Form. Finally, a numerical example is performed to demonstrate the effectiveness and conservativeness of theoretical results.     

Event‐Triggered Consensus of Nonlinear Multi‐Agent Systems with Unknown External Disturbance

This paper addresses the consensus problem of nonlinear multi‐agent systems with unknown external disturbance. First, a distributed observer is proposed to estimate the state and unknown disturbance of each agent simultaneously. Then, a novel event‐triggered control scheme based on the agent state estimation and disturbance estimation is proposed. Unlike the existing strategies, our event‐triggered conditions depend on agent state estimation and disturbance estimation, which are more effective and practical. Under this observer and control strategy, some sufficient conditions are derived to ensure the consensus of the multi‐agent system with unknown external disturbance. Moreover, the Zeno‐behavior of triggering time sequences is also excluded. Finally, a simulation example is given to verify the theoretical analysis.     

Event‐Based Consensus Controller for Linear Multi‐Agent Systems Over Directed Communication Topologies: A Co‐Design Approach

The paper addresses the distributed event‐triggered consensus problem in directed topologies for multi‐agent systems (MAS) with general linear dynamic agents. A co‐design approach is proposed to determine parameters of the consensus controller and its event‐triggered mechanism (ETM), simultaneously. This approach guarantees asymptotic stability along with decreasing data transmission among agents. In the proposed event‐based consensus controller, each agent broadcasts data to the neighbors only at its own triggering instants; this differs from previous studies in which continuous data streams among agents were required. Furthermore, the proposed control law is based on the piecewise constant functions of the measurement values, which are updated at triggering instants. In this case the control scheme decreases the communication network usage, energy consumption, and wear of the actuator. As a result, it facilitates distributed implementation of the proposed consensus controller for real‐world applications. A theorem is proved to outline sufficient conditions to guarantee the asymptotic stability of the closed‐loop system with the event‐based consensus controller. Another theorem is also proved to show the Zeno behavior exclusion. As a case study, the proposed event‐based controller is applied for a diving consensus problem to illustrate the effectiveness of the method.     

Event‐Based Semiglobal Consensus of Homogenous Linear Multi‐Agent Systems Subject to Input Saturation

In this paper, we consider the semiglobal leader‐following consensus of general linear multi‐agent systems subject to input saturation. First, an event‐triggered control protocol is provided to ensure semiglobal consensus of the multi‐agent systems, in which the agents should continuously monitor the information of their neighbors. Second, a self‐triggered control protocol is proposed to guarantee the semiglobal consensus of the multi‐agent systems, in which the agents only have access to the information of their neighbors in discrete time instants. Moreover, both event‐triggered control protocol and self‐triggered control protocol are proved to be Zeno‐free, that is, the inter‐event times for such two protocols have positive lower bounds. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed event‐based semiglobal consensus protocols.     

Event‐triggered output synchronization of heterogeneous multi‐agent systems

This paper proposes a control architecture that employs event‐triggered control techniques to achieve output synchronization of a group of heterogeneous linear time‐invariant agents. We associate with each agent an event‐triggered output regulation controller and an event‐triggered reference generator. The event‐triggered output regulation controller is designed such that the regulated output of the agent approximately tracks a reference signal provided by the reference generator in the presence of unknown disturbances. The event‐triggered reference generator is responsible for synchronizing its internal state across all agents by exchanging information through a communication network linking the agents. We first address the output regulation problem for a single agent where we analyze two event‐triggered scenarios. In the first one, the output and input event detectors operate synchronously, meaning that resets are made at the same time instants, while in the second one, they operate asynchronously and independently of each other. It is shown that the tracking error is globally bounded for all bounded reference trajectories and all bounded disturbances. We then merge the results on event‐triggered output regulation with previous results on event‐triggered communication protocols for synchronization of the reference generators to demonstrate that the regulated output of each agent converges to and remains in a neighborhood of the desired reference trajectory and that the closed‐loop system does not exhibit Zeno solutions. Several examples are provided to illustrate the advantages and issues of every component of the proposed control architecture. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed edge event‐triggered consensus protocol of multi‐agent systems with communication buffer

This paper proposes a distributed edge event‐triggered (DEET) scheme of multi‐agent systems via a communication buffer to reduce unnecessary update of controllers induced by fast information transmission. This edge scheme avoids a synchronous phenomenon in node event‐triggered mechanism, in which the triggering of one agent activates information transmission of all edges linked with this agent. Hence, the node event‐triggered scheme leads to unnecessary update of control protocols while the DEET provides a new approach without constrains on synchronous phenomenon of edge information exchange. That is, the communication on each edge is independent with other edges. In addition, we investigate another case where edge information transmission is subject to quantization and a quantized edge event‐triggered control protocol is proposed. Note that such a quantized protocol guarantees asymptotical consensus instead of bounded consensus in most of the existing literature. Meanwhile, both DEET and quantized edge event‐triggered schemes have nontrivial properties of excluding Zeno behavior. Furthermore, an algorithm is provided to avoid continuous event detection; hence, the communication traffic of the whole network is reduced significantly. Copyright © 2016 John Wiley & Sons, Ltd.     

Tracking Control for Stochastic Multi‐Agent Systems Based on Hybrid Event‐Triggered Mechanism

This paper deals with the leader‐following consensus for nonlinear stochastic multi‐agent systems. To save communication resources, a new centralized/distributed hybrid event‐triggered mechanism (HETM) is proposed for nonlinear multi‐agent systems. HETMs can be regarded as a synthesis of continuous event‐triggered mechanism and time‐driven mechanism, which can effectively avoid Zeno behavior. To model the multi‐agent systems under centralized HETM, the switched system method is applied. By utilizing the property of communication topology, low‐dimensional consensus conditions are obtained. For the distributed hybrid event‐triggered mechanism, due to the asynchronous event‐triggered instants, the time‐varying system method is applied. Meanwhile, the effect of network‐induced time‐delay on the consensus is also considered. To further reduce the computational resources by constantly testing whether the broadcast condition has been violated, self‐triggered implementations of the proposed event‐triggered communication protocols are also derived. A numerical example is given to show the effectiveness of the proposed method.     

Event‐Triggered Control for Couple‐Group Multi‐Agent Systems with Logarithmic Quantizers and Communication Delays

This paper mainly investigates the event‐triggered control for couple‐group multi‐agent systems with communication delay. Logarithmic quantization is considered in the communication channels. Event‐triggered control laws are adopted to reduce the frequency of individual actuation updating for discrete‐time agent dynamics. The proposed protocol is efficient as long as the quantization levels are dense enough, i.e. the density of quantization levels goes to infinity is a sufficient condition for the asymptotic consensus of the multi‐agent systems. It turns out that the bounded consensus depends on not only the density of quantization levels, but also the updating strategy of events. Finally, a simulation example is given to demonstrate the effectiveness of the proposed methods.     

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with timevarying delays are investigated. The idea of guaranteed cost control is introduced into consensus problems for high-dimensional multi-agent systems with time-varying delays, where a cost function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality (LMI), sufficient conditions for guaranteed cost consensus and consensualization are given. Moreover, a guaranteed cost upper bound of the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independent of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.      

Event‐Triggered Control for Multi‐Agent Systems with General Directed Topology and Time Delays

Recent years have witnessed a growing interest in event‐triggered strategies for coordination and cooperative control of multi‐agent systems. However, the most previous works and developments focus on the interactive network that has no communication delays. This paper deals with the consensus problem of an agent system with event‐triggered control strategy under communication time delays. We first propose a time delays system model, then present a novel event triggering function that not only avoids continuous communication but also excludes the Zeno behavior. Furthermore, we provide the consensus analysis using an inequality technique instead of the traditional linear matrix inequality method, and we demonstrate that the inter‐event times for each agent are strictly positive, which implies that the Zeno behavior can be excluded. Finally, simulation results show the effectiveness of the proposed approach and illustrate the correctness of the theoretical results.     

Distributed Consensus of Third‐order Multi‐agent Systems with Communication Delay

This paper studies the consensus problem for a class of general third‐order multi‐agent systems on an undirected connected network. By employing a variables transformation, the consensus control problem can be turned into a asymptotical stability problem. Then we present a necessary and sufficient condition for guaranteeing consensus by using Routh‐Hurwitz stability criterion. And this result can be applied to a special case of third‐order integrator systems. Also we will present a tolerable communication time delay for third‐order integrator systems under the assumption that multi‐agent systems can reach consensus without communication delay.     

Predictive Consensus for Networked Multi‐Agent Systems with Switching Topology and Variable Delay

This paper investigates consensus problems of networked linear time invariant (LTI) multi‐agent systems, subject to variable network delays and switching topology. A new protocol is proposed for such systems with matrix B that has full row rank, based on stochastic, indecomposable, aperiodic (SIA) matrix and the predictive control scheme. With the predictive scheme the network delay is compensated. Consensus analysis based on the seminorm is provided. The conditions are obtained for such systems with periodic switching topology to reach consensus. The proposed protocol can deal with time‐varying delays, switching topology, and an unstable mode. The numerical examples demonstrate the effectiveness of the theoretical results.     

Event‐triggered global leader‐following consensus of a group of neutrally stable linear systems subject to input saturation

This paper studies the global leader‐following consensus problem for a multiagent system using event‐triggered linear feedback control laws. The leader agent is described by a neutrally stable linear system and the follower agents are also described by a neutrally stable linear system but with saturating input. Both the state‐feedback case and the output‐feedback case are considered. In each case, an event‐triggered control law is constructed for each follower agent and an event‐triggering strategy is designed for updating these control laws. These event‐triggered control laws are shown to achieve global leader‐following consensus when the communication topology among the follower agents is strongly connected and detailed balanced and the leader is a neighbor of at least one follower agent. The Zeno behavior is excluded. The theoretical results are illustrated by simulation.     

Node‐to‐node consensus of multi‐agent networks with event‐triggered control and packet losses

This paper studies the node‐to‐node consensus problem for multi‐agent networks possessing a leaders' layer and a followers' layer via the pinning control. In order to realize the consensus and reduce the update frequency of the controller, a suitable event‐triggered mechanism is introduced into the control strategy. Furthermore, the phenomenon of packet loss is considered in the designed controller. Based on the M‐matrix theory and Lyapunov stability theory, this paper presents the sufficient conditions for the node‐to‐node consensus of networks. Meanwhile, it is proved that the Zeno behaviour is excluded. Finally, two numerical simulations are provided to demonstrate the effectiveness of the theoretical results.