Distributed integral‐type event‐triggered synchronization of multiagent systems

This paper investigates the synchronization problem of generic linear multiagent systems via integral‐type event‐triggered control. Each agent can only utilize the intermittent information of its neighboring agents in the control scheme. Based on the integral‐type event conditions, an event‐triggered control protocol is designed to guarantee the synchronization of multiagent systems, and Zeno behavior is excluded by showing the existence of a positive lower bound on the inter‐event intervals. Then, we propose the integral‐type event‐triggered control algorithms to study the leader‐following synchronization. It is shown that under the control algorithms all the followers track the leader and no Zeno behavior occurs. The effectiveness of the proposed control schemes is demonstrated by simulation examples.     

Robust event‐triggered control of second‐order disturbed leader‐follower MASs: A nonsingular finite‐time consensus approach

This paper addresses the finite‐time and the prescribed finite‐time event‐triggered consensus tracking problems for second‐order multi‐agent systems (MASs) with uncertain disturbances. The prescribed finite‐time event‐triggered consensus of the second‐order disturbed MASs was obtained for the first time and the controller is nonsingular. Furthermore, a new self‐triggered control scheme is presented for the finite‐time consensus tracking, and the continuous communication can be avoided in the triggering condition monitoring. Hence, the finite‐time consensus tracking can be achieved with intermittent communication. Moreover, Zeno behavior is excluded for each follower. The efficiency of the proposed algorithms is verified by numerical simulations.     

Observer‐based leader‐following consensus of uncertain nonlinear multi‐agent systems

In this paper, the leader‐following consensus problem of uncertain high‐order nonlinear multi‐agent systems on directed graph with a fixed topology is studied, where it is assumed that the relative states of a follower and its neighbors are immeasurable and only the relative outputs are available. Nonlinear adaptive observers are firstly proposed for each follower to estimate the states of it and its neighbors, and an observer‐based distributed adaptive control scheme is constructed to guarantee that all followers asymptotically synchronize to a leader with tracking errors being semi‐globally uniform ultimate bounded. On the basis of algebraic graph theory and Lyapunov theory, the closed‐loop system stability analysis is conducted. Finally, numerical simulations are presented to illustrate the effectiveness and potential of the proposed new design techniques. Copyright © 2017 John Wiley & Sons, Ltd.     

Observer‐based event‐triggered control for singularly perturbed systems with saturating actuator

This paper investigates an observer‐based event‐triggered control problem of singularly perturbed systems with saturating actuator. A strategy that consists of an observer‐based controller (OBC) and an event‐triggered mechanism (ETM) is considered. Firstly, sufficient conditions, which guarantee that the saturated SPSs are asymptotically stable excluding Zeno phenomenon, are derived via constructing an ε‐dependent Lyapunov‐Krasovskii functional. Then, the OBC and ETM are designed simultaneously based on the aforementioned criteria. Furthermore, an estimate of the basin of attraction and an ε‐bound are given by solving an optimization problem in the form of LMIs. Finally, an electric circuit system and a numerical example are presented to demonstrate the merits of the obtained method.     

Distributed adaptive integral‐type event‐triggered cooperative output regulation of switched multiagent systems by agent‐dependent switching with dwell time

This article presents a distributed adaptive integral‐type event‐triggered scheme (ETS) and an agent‐dependent switching strategy with dwell time to solve the cooperative output regulation problem for switched multiagent systems. First, by constructing an adaptive law to dynamically update the time‐varying coupling weights for all the communication links, a fully distributed ETS is designed, where only the local information of the topology is adopted. Based on the integral‐type triggering condition, the interevent interval is substantially enlarged and Zeno behavior is explicitly ruled out. Second, each agent permits all the subsystems to be unstabilizable. The switching signal for each agent is different, and any adjacent switches of each agent satisfy the preset dwell time. Under the designed switching strategy, the solvability of the regulation problem is guaranteed. Finally, the effectiveness of the designed ETS and switching strategy is substantiated by an example.     

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.     

Model‐based event‐triggered predictive control for networked systems with communication delays compensation

This paper addresses the model‐based event‐triggered predictive control problem for networked control systems (NCSs). Firstly, we propose a discrete event‐triggered transmission scheme on the sensor node by introducing a quadratic event‐triggering function. Then, on the basis of the aforementioned scheme, a novel class of model‐based event‐triggered predictive control algorithms on the controller node is designed for compensating for the communication delays actively and achieving the desired control performance while using less network resources. Two cases, that is, the value of the communication delay of the first event‐triggered state is less or bigger than the sampling period, are considered separately for certain NCSs, regardless of the communication delays of the subsequent event‐triggered states. The codesign problems of the controller and event‐triggering parameter for the two cases are discussed by using the linear matrix inequality approach and the (switching) Lyapunov functional method. Furthermore, we extended our results to the NCSs with systems uncertainties. Finally, a practical ball and beam system is studied numerically to demonstrate the compensation effect for the communication delays with the proposed novel model‐based event‐triggered predictive control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Distributed event‐triggered fixed‐time consensus for leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances

This paper focuses on the distributed event‐triggered fixed‐time consensus control problem of leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances. Two distributed fixed‐time consensus protocols are proposed based on distributed event‐triggered strategies, which can substantially reduce energy consumption and the frequency of the controller updates. It is proved that under the proposed distributed event‐triggered consensus tracking control strategies, the Zeno behavior is avoided. Compared with the finite‐time consensus tracking, the fixed‐time consensus tracking can be achieved within a settling time regardless of the initial conditions. Finally, 2 examples are performed to validate the effectiveness of the distributed event‐triggered fixed‐time consensus tracking controllers.     

Data‐driven optimal event‐triggered consensus control for unknown nonlinear multiagent systems with control constraints

This paper considers optimal consensus control problem for unknown nonlinear multiagent systems (MASs) subjected to control constraints by utilizing event‐triggered adaptive dynamic programming (ETADP) technique. To deal with the control constraints, we introduce nonquadratic energy consumption functions into performance indices and formulate the Hamilton‐Jacobi‐Bellman (HJB) equations. Then, based on the Bellman's optimality principle, constrained optimal consensus control policies are designed from the HJB equations. In order to implement the ETADP algorithm, the critic networks and action networks are developed to approximate the value functions and consensus control policies respectively based on the measurable system data. Under the event‐triggered control framework, the weights of the critic networks and action networks are only updated at the triggering instants which are decided by the designed adaptive triggered conditions. The Lyapunov method is used to prove that the local neighbor consensus errors and the weight estimation errors of the critic networks and action networks are ultimately bounded. Finally, a numerical example is provided to show the effectiveness of the proposed ETADP method.     

Periodic event‐triggered observation and control for nonlinear Lipschitz systems using impulsive observers

In this paper, we investigate the observation and stabilization problems for a class of nonlinear Lipschitz systems, subject to network constraints, and partial state knowledge. In order to address these problems, an impulsive observer is designed, making use of the event‐triggered technique in order to diminish the network communications. Sufficient conditions are given to ensure a milder version of the separation principle for these systems, controlled via an event‐triggered controller. The proposed observer ensures practical state estimation, while the corresponding dynamic controller ensures practical stabilization. The sampling and the data transmission are carried out asynchronously. The dynamic controller is tested in simulation on a flexible joint. Copyright © 2017 John Wiley & Sons, Ltd.     

Fixed‐time sliding mode cooperative control for multiagent networks via event‐triggered strategy

In this article, the problem of event‐triggered‐based fixed‐time sliding mode cooperative control is addressed for a class of leader‐follower multiagent networks with bounded perturbation. First, a terminal integral sliding mode manifold with fast convergent speed is designed. Then, a distributed consensus tracking control strategy based on event‐triggered and sliding mode control is developed that guarantees the multiagent networks achieve consensus within a fixed time which is independent of initial states of agents in comparison with the finite‐time convergence. Furthermore, the update frequency of control law can be considerably reduced and Zeno behavior can be removed by utilizing the proposed event‐triggered control algorithm. Simulation examples are used to show the effectiveness of the new control protocol.     

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.     

LQR‐based optimal topology of leader‐following consensus

In this paper, we consider the optimal topology for leader‐following consensus problem of continuous‐time and discrete‐time multi‐agent systems based on linear quadratic regulator theory. For the first‐order multi‐agent systems, we propose a quadratic cost function, which is independent of the interaction graph, and find that the optimal topology is a star topology. For the second‐order multi‐agent systems, a quadratic cost function is also constructed, whereas the optimal topology for second‐order leader‐following consensus problem is an unevenly weighted star topology. The universality of these findings means that if each follower is connected with the leader, the information exchange between followers is unnecessary and insufficient. Simulation examples are provided to illustrate the effectiveness of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

A novel event‐triggered extended state observer for networked control systems subjected to external disturbances

In this paper, the event‐triggered‐based state estimation problem is investigated for a class of nonlinear networked control systems subjected to external disturbances. A novel event‐triggered extended state observer (ESO) is utilized to estimate the so‐called total disturbance, and an output predictor is adopted for the proposed ESO between two consecutive transmission instants. It is also worth pointing out that, in the newly proposed ESO, an event‐triggered mechanism is adopted to update the measurement signal so as to save the communication resource. The sufficient conditions are provided such that the estimation error dynamics is exponentially ultimately bounded. Furthermore, it is proven that the Zeno behavior does not exist for the event‐triggering rules. A number of numerical simulations are conducted to verify the validity of the theoretical results.     

Distributed event‐triggered containment control for dynamical multiagent networks

This paper studies the event‐triggered containment control problem for dynamical multiagent networks of general MIMO linear agents. An event‐triggered containment control strategy is provided, which consists of a control law based on a relative‐state feedback and a distributed triggering rule based on both the relative‐state information and a time‐dependent threshold function. Compared to the previous related works, our main contribution is that the triggering rule depends only on local information of communication networks. It is proved that under the proposed event‐based controller, the containment errors are uniformly ultimately bounded and the Zeno behavior can be excluded. Moreover, when the derivation constant in the threshold function is equal to zero, the containment control problem can be solved. Then, the results are extended to the event‐triggered observer‐based containment controller design.     

Bounded consensus for multiagent systems by event‐triggered data transmission,time delay,and predictor‐based control

This paper investigates the consensus issue of multiagent systems with data transmission time delay. The state measurement of each local agent is directly sent to a private event‐trigger and further authorized to be broadcasted to its neighbors via communication network only when the threshold of the event‐trigger is violated. Since the controller always receives discrete‐time neighbor information with data transmission time delay, a predictor is employed to estimate the continuous‐time neighbor state. Based on the estimated state, a novel consensus protocol is mainly proposed for achieving the bounded consensus of the multiagent systems. By the proposed method, the asynchronous neighbor information is allowed and the margin of data transmission time delay is also given. Furthermore, it has been proved that the unwanted Zeno phenomena can be naturally excluded. Numerical example is provided to demonstrate the effectiveness of the proposed method.     

Trigger‐based tracking control for a class of uncertain nonlinear systems via an event‐triggered extended state observer

An event‐triggered observer‐based output feedback control issue together with triggered input is investigated for a class of uncertain nonlinear systems subject to unknown external disturbances. Two separate event‐triggered conditions are located on the measurement channel and control channel, respectively. An event‐triggered extended state observer (ETESO) is employed to estimate unmeasurable states and compensate uncertainties and disturbances in real time while it is not required for real‐time output measurement. Then, combined with backstepping method and active disturbance rejection control, an output feedback control scheme is proposed, where an event‐triggered input is developed for reducing the communication rate between the controller and the actuator. The triggered instants are determined by a time‐varying event‐triggered condition. Two simulations, including a numerical example and an permanent‐magnet motor, are illustrated to verify the effectiveness of the proposed schemes.     

Decentralized event‐triggered circle formation control for multiagent systems via synchronous periodic event detection

This paper investigates circle formation problem of multiagent systems over a kind of strongly connected and weight‐unbalanced directed graphs. To solve the concerned problem, decentralized periodic event‐triggered algorithms subject to or not to time delays are proposed, which have the advantages of decreasing the overall burden of the network in terms of finite communication and control input updates. In such algorithms, each agent independently evaluates whether the locally sampled information of itself should be broadcasted to or not to its neighbors. Furthermore, another advantage of our proposed algorithms is to automatically exclude Zeno behavior, which should be seriously considered in a variety of event‐based network systems. Sufficient conditions on circle formation control are derived under which the states of all agents can be ensured to converge to some desired equilibrium point. Simulation results are given to validate the effectiveness of the proposed methods.     

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.