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.     

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.     

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.     

Event‐triggered MPC design for distributed systems toward global performance

This paper studies the coordination control problem of stabilizing large‐scale dynamically coupled systems via a novel event‐triggered distributed model predictive control (DMPC) approach. In order to achieve global performance, certain constraints relevant to the triggering instant are imposed on the DMPC optimization problem, and triggering mechanisms are designed by taking into account coupling influences. Specifically, the triggering conditions derived from the feasibility and stability analysis are based on the local subsystem state and the information received from its neighbors. Based on these triggering mechanisms, the event‐triggered DMPC algorithm is built, and a dual‐mode strategy is adopted. As a result, the controllers solve the optimization problem and coordinate with each other asynchronously, which reduces the amount of communication and lowers the frequency of controller updates while achieving global performance. The recursive feasibility of the proposed event‐triggered DMPC algorithm is proved, and sufficient parameter conditions about the prediction horizon and the triggering threshold are established. It shows that the system state can be gradually driven into the terminal set under the proposed strategy. Finally, an academic example and a realistic simulation problem to the water level of a 4‐tank system are provided to verify the effectiveness of the proposed algorithm.     

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 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.     

Event‐triggered Guaranteed Cost Consensus of Networked Singular Multi‐agent Systems

The problem of event‐triggered guaranteed cost consensus of discrete‐time singular multi‐agent systems with switching topologies is investigated in this paper. To save the limited network communication bandwidth of multi‐agent systems, a novel event‐triggered networked consensus mechanism is proposed. Based on the graph theory and singular system theory, sufficient conditions of guaranteed‐cost consensus of discrete‐time singular multi‐agent systems are derived and given in the form of the linear matrix inequalities, respectively. A co‐design approach of the multi‐agent consensus gain matrix and the event‐triggered parameters is presented. Furthermore, based on the approach of second class equivalent transformation for singular systems, the cost function is determined, and an explicit expression of consensus functions is presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

Leader–follower flocking based on distributed event‐triggered hybrid control

In this paper, we proposed a new hybrid control algorithm to achieve leader–follower flocking in multi‐agent systems. In the algorithm, the position is transmitted continuously, whereas the velocity is utilized discretely, which is governed by a distributed event‐triggered mechanism, and the neighbors' velocity is not required to detect the event‐triggered condition for each agent. It is shown that stable flocking is achieved asymptotically while the connectivity of networks is preserved. A numerical example is provided to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Event‐triggered constrained control of positive systems with input saturation

This paper addresses the problem of event‐triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event‐triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event‐triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event‐triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation.     

Event‐triggered output consensus for heterogeneous multiagent systems with fixed and switching directed topologies

This paper studies the event‐triggered output consensus problem of heterogeneous linear multiagent systems characterized via fixed and switching directed graphs. With proper state‐dependent triggering functions, two new event‐triggered output consensus control schemes are proposed for each agent to achieve consensus. Notably, under the proposed control protocols, continuous communication among agents is not required in both controllers updating and triggering threshold detection, which means being completely continuous communication free. The communication instances are reduced significantly, and the periodic or high‐frequency communication is restrained. It is also ensured that events cannot be triggered infinitely in finite time (ie, the Zeno behavior is elegantly avoided). Meanwhile, the simulation examples are given to illustrate the theoretical analysis.     

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.     

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 event‐triggered feedback consensus control with state‐dependent threshold for general linear multi‐agent systems

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under undirected graphs. Based on state feedback, we propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus, without continuous communication in either controller update or triggering condition monitoring. Each agent only needs to monitor its own state continuously to determine if the event is triggered. It is proved that there is no Zeno behavior under the proposed consensus control algorithm. To relax the requirement of the state measurement of each agent, we further propose a novel distributed observer‐based event‐triggered consensus controller to solve the consensus problem in the case with output feedback and prove that there is no Zeno behavior exhibited. Finally, simulation results are given to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed event‐triggered consensus control with fully continuous communication free for general linear multi‐agent systems under directed graph

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under a directed graph. We propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus. In this strategy, continuous communication in both controller update and triggering condition monitoring is not required, which means the proposed strategy is fully continuous communication free. Each agent only needs to monitor its own state continuously to determine if the event is triggered. Additionally, the approach shown here provides consensus with guaranteed positive inter‐event time intervals. Therefore, there is no Zeno behavior under the proposed consensus control algorithm. Finally, numerical simulations are given to illustrate the theoretical results.     

Event‐triggered Control of Linear Systems with Saturated Inputs

This paper investigates the event‐triggered control of linear systems with saturated state feedback and saturated observer‐based feedback, respectively. The problem of simultaneously deriving stabilizing event‐triggered controllers and tackling saturation nonlinearity is cast into a standard linear matrix inequalities problem. Key topics are studied, such as event‐triggered observer design and event‐triggered saturated observer‐based feedback synthesis. Important issues are touched on, including the existence of the positive lower bound for inter‐event times, and self‐triggered algorithms.     

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.     

Fully distributed bipartite output consensus of heterogeneous linear multiagent systems based on event‐triggered transmission mechanism

This study investigates the fully distributed bipartite output consensus issue of heterogeneous linear multiagent systems (HLMASs) based on event‐triggered transmission mechanism. Both the cooperative interaction and the antagonistic interaction between neighbor agents are considered. A fully distributed bipartite compensator consisting of time‐varying coupling gain and dynamic event‐triggered mechanism is first proposed to estimate the leader's states. Different from the existing schemes, the proposed compensator is independent of any global information of the network topology, is capable of achieving intermittent communication between neighbors, and is applicable for the signed communication topology. Then the distributed output feedback control protocol is developed such that the fully distributed bipartite event‐triggered output consensus problem can be achieved. Moreover, we extend the results in HLMASs without external disturbances to HLMASs with disturbances, which is more challenging in three cases (a) the disturbances are not available for measurement, (b) the disturbances suffered by each agent are heterogeneous, and (c) the disturbances are not required to be stable or bounded. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, two examples are provided to illustrate the feasibility of the theoretical results.     

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‐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.     

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.