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.     

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.     

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.     

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.     

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 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‐Triggered Iterative Learning Control for Multi‐Agent Systems with Quantization

The emergence of networked control systems urges the digital control design to integrate communication constraints efficiently. In order to accommodate this requirement, this paper investigates the joint design of tracking problem for multi‐agent system (MAS) in the presence of resource‐limited communication channel and quantization. An event‐triggered robust learning control with quantization is firstly proposed and employed for MAS in this paper. The new event‐triggered distributed robust learning control system with the introduction of logarithmic quantization guarantees the asymptotic tracking property on the finite interval. Convergence analysis is given based on the Lyapunov direct method. Finally, numerical simulations are given to illustrate the efficacy of the event‐triggered approach compared with time‐triggered controllers.     

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.     

Exponential Consensus for Nonlinear Multi‐Agent Systems with Communication and Input Delays via Hybrid Control

This paper aims to investigate the exponential leader‐following consensus for nonlinear multi‐agent systems with time‐varying communication and input delays by using hybrid control. Based on the Lyapunov functional method, impulsive differential equation theory and matrix analysis, we show that all the followers can achieve leader‐following consensus with the virtual leader exponentially even if only a fraction of followers can obtain the leader's information. Two classes of exponential consensus criteria as well as the convergence rates for the controlled multi‐agent systems are presented under very relaxed interaction topology conditions, i.e., the directed interaction topology among the followers is only required to have p(p>1) disjoint strong components. Finally, two numerical examples are given to validate the proposed theoretical results.     

Fixed‐Time Consensus of Multi‐Agent Systems with Directed and Intermittent Communications

This paper proposes a new class of nonlinear protocols for fixed‐time consensus in networked agents with directed and intermittent communications. First of all, based on the assumption of a common positive dwell time for all successful links, it is theoretically shown that the asymptotical consensus can be achieved if the interaction topology with some fixed length of time has a spanning tree. Then, if the length sum of time intervals, over which the directed interaction topology contains a spanning tree, is larger that a threshold value, which is independent of initial conditions, the system will solve a fixed‐time consensus problem. Furthermore, in light of the mirror operation principle of graph theory, the proposed protocol is extended to solve the fixed‐time consensus problem if a common positive dwell time for all active links is strongly connected without the detailed balanced condition. Finally, the effectiveness of the theoretical results is illustrated by simulation results.     

Distributed Fixed‐Time Coordinated Tracking for Nonlinear Multi‐Agent Systems Under Directed Graphs

This paper is concerned with the fixed‐time coordinated tracking problem for a class of nonlinear multi‐agent systems under detail‐balanced directed communication graphs. Different from conventional finite‐time coordinated tracking strategies, the fixed‐time approach developed in this paper guarantees that a settling time bound is prescribed without dependence on initial states of agents. First, for the case of a single leader, a distributed protocol based on fixed‐time stability techniques is proposed for each follower to accomplish the consensus tracking in a fixed time. Second, in the presence of multiple leaders, a new distributed protocol is proposed such that states of followers converge to the dynamic convex hull spanned by those of leaders in a fixed time. In addition, for a class of linear multi‐agent systems, sufficient conditions that guarantee the fixed‐time coordinated tracking are provided. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.     

L2 − L∞ Consensus Control for High‐Order Multi‐Agent Systems with Nonuniform Time‐Varying Delays

This paper considers consensus problem for high‐order multi‐agent systems with dynamically changing topologies and nonuniform time‐varying delays. By means of the tree‐type transformation approach, the model transformation is conducted and the consensus problem is converted into an L₂ ? L_∞ control problem of equivalent reduced‐order systems. Furthermore, a Lyapunov‐Krasovkii function is constructed for stability analysis and sufficient conditions in terms of linear matrix inequalities are derived to ensure the consensus with the prescribed L₂ ? L_∞ performance. A numerical simulation is provided to verify the correctness of the theoretical results.     

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.     

Multi‐Tracking of First Order Multi‐Agent Networks Via Self‐Triggered Control

A multi‐tracking problem of multi‐agent networks is investigated in this paper where multi‐tracking refers to that the states of multiple agents in each subnetwork asymptotically converge to the same desired trajectory in the presence of information exchanges among subnetworks. The multi‐tracking of first order multi‐agent networks with directed topologies was studied. Self‐triggered protocols were proposed along with triggering functions to solve the stationary multi‐tracking and bounded dynamic multi‐tracking. The self‐triggered scheduling is obtained, and the system does not exhibit Zeno behavior. Numerical examples are provided to illustrate the effectiveness of the obtained criteria.     

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.     

Event‐triggered PCS Based Trajectory Tracking Control of Systems with Perturbation

This paper is aimed at reducing network load for saving bandwidth by designing appropriate trigger signals that decide when the transmission should be done. An event‐triggered piecewise continuous systems (PCS) based control for time‐varying trajectory tracking is proposed. By designing the sensor system and controller system, the communication between them is reduced while still retaining a satisfactory closed‐loop behavior of the whole system. The major idea behind a designed sensor system is the use of a Luenberger observer and planning of event‐triggered mechanism (ETM). The main principle behind the designed controller system is the proposal of a new event‐triggered PCS based controller. The development is motivated by consideration of variable network induced time delays. Tracking error is proved to be norm‐bounded in both the original and developed case. Finally, to show the proposed method's performance, we present the simulation results for a mobile cart.     

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.     

Mixed Event‐Triggered Mechanism Modeling and Controlling for Networked Control Systems with Time‐Varying Delays and Uncertainties

This paper is concerned with modeling and controlling under the mixed event‐triggered mechanism (ETM) for networked control systems (NCSs) with time‐varying delays and uncertainties. Firstly, an event‐triggered threshold is set by using both state and state‐independent informations in the mixed ETM. Then the event‐triggered NCSs with network‐induced time‐varying delays which exist in both sensor‐to‐controller and controller‐to‐actuator channels are modeled as a general time‐delay system. Based on the piecewise differentiable characteristic of the time‐varying delay and by using the approach of free weighting matrix and reciprocally convex, a less conservative criterion to be globally uniformly ultimately bounded (GUUB) stability and a controller design method are derived. Furthermore, an algorithm is proposed to obtain the desired mixed ETM and state‐feedback controller which can render the network load and control performance to reach an expected level. Compared with the relative and absolute ETMs, the proposed mechanism can effectively improve the transmission efficiency during the whole working time. Finally, a numerical example is given to show the effectiveness of the proposed approach.     

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.     

Bounded Consensus Algorithms for Multi‐Agent Systems in Directed Networks

In this paper, the consensus problem is investigated via bounded controls for the multi‐agent systems with or without communication. Based on the nested saturation method, the saturated control laws are designed to solve the consensus problem. Under the designed saturated control laws, the transient performance of the closed‐loop system can be improved by tuning the saturation level. First of all, asymptotical consensus algorithms with bounded control inputs are proposed for the multi‐agent systems with or without communication delays. Under these consensus algorithms, the states’ consensus can be achieved asymptotically. Then, based on a kind of novel nonlinear saturation functions, bounded finite‐time consensus algorithms are further developed. It is shown that the states’ consensus can be achieved in finite time. Finally, two examples are given to verify the efficiency of the proposed methods.