Dynamic event-triggered leader-following consensus control of a class of linear multi-agent systems

We address the leader-following tracking consensus issue for a class of linear multi-agent systems (MASs) via dynamic event-triggered (DET) approaches in this paper. The DET communication mechanism is introduced by an additional internal dynamic variable, and is developed to schedule agents’ data transmission. State observers are also employed to tackle the scenario wherein inner information of follower agents are not available for measurement. And then, state-based and observer-based distributed control proposals are proposed on the basis of dynamic event-triggered mechanism (DETM), respectively. To avoid continuous measurement information monitor, we present a technical approach for generation of the combinational information from their own neighboring agents only at event instants. The stabilities of the resulting closed-loop systems, both state-feedback one and output-feedback one, are rigorously analyzed in theory, and it is proven that all signals in the closed-loop system are bounded and Zeno behavior is also excluded. Simulation examples are presented to illustrate the theoretical claims.     

Finite-time consensus of linear multi-agent system via distributed event-triggered strategy

In this paper, we mainly investigate the finite-time consensus problem of general linear multi-agent systems. The paper proposed a suitable event-triggered control strategy. The strategy has some desirable properties including: distributed, independent, and asynchronous. It is theoretical demonstrated that the multi-agent system can achieve consensus in a certain time regardless of the initial condition under this event-triggered control scheme. In addition, without finding singular triggering problem, we prove the feasibility of this proposed event-triggered control protocol. Finally, we put forward some simulation graphs for the sake of showing the availability of our conclusions.     

Distributed adaptive event-triggered protocol for tracking control of leader-following multi-agent systems

A novel adaptive event-triggered control protocol is developed to investigate the tracking control problem of multi-agent systems with general linear dynamics. By introducing the event-triggered control strategy, each agent can decide when to transfer its state to its neighbors at its own triggering instants, which can greatly reduce communication burden of agents. It is shown that the “Zeno phenomenon” does not occur by verifying that there exists a positive lower bound on the inter-event time intervals of agents under the proposed adaptive event-triggered control algorithm. Finally, an example is provided to testify the effectiveness of the obtained theoretical results.     

Leaderless consensus of multi-agent systems via an event-triggered strategy under stochastic sampling

This paper investigates mean square leaderless consensus of networked nonlinear multi-agent systems. An efficient distributed event-triggered mechanism based on stochastic sampling is introduced to reduce the communication cost and controller updates. The stochastic sampling interval randomly switches between two given values. Mean square consensus criteria for multi-agent systems with strongly connected networks or networks containing directed spanning trees are derived, respectively. Moreover, the case with a special event-triggered weighting matrix and the case without even-triggered strategies are also discussed. Finally, an example is given to verify the theoretical results.     

Leaderless and leader-following consensus of linear multi-agent systems with distributed event-triggered estimators

This paper considers the event-triggered leaderless and leader-following consensus problems for linear multi-agent systems. By introducing event-triggered estimators, two novel control schemes are proposed. Different from the existing event-triggered controllers, which rely on the Fiedler eigenvalue of Laplacian matrix, the developed controllers only use the information from neighboring agents. Meanwhile, the adaptive trigger parameters are designed in the event-triggered mechanisms to improve the self-regulation ability of the event-triggered estimators. In addition, the leaderless consensus and the leader-following consensus can be achieved under the corresponding control protocols. Finally, two simulation examples are given to illustrate the validity of the proposed control protocols.     

Bounded average consensus for multi-agent systems with switching topologies by event-triggered persistent dwell time control

This paper is concerned with the consensus of multi-agent systems (MASs) with switching topologies. A norm-bounded event-trigger is designed where non-global information of the communication graph is involved. By directly employing the asynchronous event-triggered neighbor state information, a distributed persistent dwell time (PDT) based predictor-like consensus protocol is proposed. By the proposed scheme, the dynamics of local subsystems are allowed to be unstable during fast switching time intervals as well as the jump time instants, meanwhile, the bounded average consensus of overall MASs can be achieved. In addition, the Zeno-phenomena is naturally excluded. Numerical example is provided to demonstrate the effectiveness of the proposed method.     

Observer-based output regulation of cooperative-competitive high-order multi-agent systems

In this paper, a coopetitive output regulation problem is considered for general linear multi-agent systems with antagonistic interactions, where not all the agents have access to the state, the output, the system matrix and the output matrix of the exogenous system or exosystem. In this sense, the internal model incorporation of the system matrix of the exosystem is also only available to some agents. Thus, we propose distributed observers for each agent: (i) To estimate the state, the output, the system matrix and the output matrix, and (ii) the unavailable internal model of the exosystem. Then, a distributed dynamic output feedback controller is proposed for each agent to solve the coopetitive output regulation problem. The exponential stability of the closed-loop system is analyzed with the output regulation theory. Finally, some simulation results are presented to validate the proposed control strategy.     

Bipartite output consensus for heterogeneous linear multi-agent systems with fully distributed protocol

This paper addresses the problem of bipartite output consensus of heterogeneous multi-agent systems over signed graphs. First, under the assumption that the sub-graph describing the communication topology among the agents is connected, a fully distributed protocol is provided to make the heterogeneous agents achieve bipartite output consensus. Then for the case that the topology graph has a directed spanning tree, a novel adaptive consensus protocol is designed, which also avoids using any global information. Each of these two protocols consists of a solution pair of the regulation equation and a homogeneous compensator. Numerical simulations show the effectiveness of the proposed approach.     

Integral sliding-mode fixed-time consensus tracking for second-order non-linear and time delay multi-agent systems

In this paper, fixed-time consensus tracking problems under directed interaction topologies for second-order non-linear multi-agent systems with disturbance and second-order multi-agent systems with input delay are investigated. Two continuous integral terminal sliding modes are designed, which can effectively eliminate the singularity and chattering. Correspondingly, two fixed-time distributed control protocols are proposed based on the designed continuous ITSM to ensure that the consensus tracking are achieved in fixed-time. It is shown that the upper bounds of settling time are regardless of initial conditions. The rigorous proofs are given by employing Lyapunov stability theory and fixed-time stability theory. Simulations are provided to verify the effectiveness of the theoretical results.     

Robust distributed tracking control for linear multi-agent systems based on distributed intermediate estimator

This paper considers the distributed tracking control problem for linear multi-agent systems with disturbances and a leader whose control input is nonzero and not available to any follower. Based on the relative output measurements of neighboring agents, a novel distributed observer-based tracking protocol is proposed, where the distributed intermediate estimators are constructed to estimate the leader’s unknown control input and the states of the tracking error system simultaneously, then a distributed tracking protocol is designed based on the derived estimates. It is proved that the states of the tracking error system are uniformly ultimately bounded and an explicit tracking error bound is obtained. A simulation example of aircrafts verifies the effectiveness of the proposed method.     

Distributed impulsive control for heterogeneous multi-agent systems based on event-triggered scheme

In this paper, the distributed impulsive control for heterogeneous multi-agent systems based on event-triggered approach is investigated. According to whether the information transfer of the dynamic compensator is continuous or not, two different kinds of impulsive controllers are designed, respectively. Based on these two kinds of controllers, the corresponding distributed event-triggered conditions are provided, which make the impulsive instants of all agents do not need occur simultaneously. Moreover, the lower bound of impulsive intervals can also be guaranteed for all the event-triggered conditions, which means that the control schemes given in this paper can avoid the Zeno-behavior successfully. Eventually, a simulation example is proposed to support the effectiveness of the results obtained in this paper.     

Event-triggered tracking control for couple-group multi-agent systems

This paper mainly investigates the event-triggered tracking control for couple-group multi-agent systems in a disturbance environment, where the topology of the agents is switching. Consensus protocol is designed for the case that some agents reach a consistent value, while the other agents reach another consistent value. Then, event-triggered control laws are designed to reduce the frequency of individual actuation updating for discrete-time agent dynamics. Moreover, by applying the Lyapunov function method, a sufficient condition of couple-group consensus is established in terms of a matrix inequality when the communication topology is switching. Finally, simulation examples are given to demonstrate the effectiveness of the proposed methods.     

Fractional-order follower observer design for tracking consensus in second-order leader multi-agent systems: Periodic sampled-based event-triggered control

This paper investigates the tracking consensus problem for the second-order leader systems by designing fractional-order observer, where a periodic sampled-based data event-triggered control is employed. In order to track the position information of leader, observers for followers are designed by fractional-order system, where only the relative position information is available. Furthermore, in the process of observers design, a sampled-based event-triggered strategy is proposed so that observers use the event-triggered sampled-data, to reduce the overall load of the network. In our proposed event-triggered strategy, the event detection only works at every sampling time instant which determines whether the sampled-data should be discarded or used. Under this control strategy, the Zeno-behavior is absolutely excluded since the minimum of inter-event times is inherently lower bounded by one sampling period. It is found that the followers can track state of the leader if fractional-order observers are appropriately designed and relevant parameters are properly selected. By using the generalized Nyquist stability criterion, a necessary and sufficient condition for the observer tracking consensus of the second-order leader systems is derived. The results show that the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix, and fractional-order α of observer play a vital role in reaching consensus.     

Mean-square consensus of heterogeneous multi-agent systems with communication noises

This paper addresses the mean-square consensus problems of continuous-time heterogeneous multi-agent systems with communication noises. First, in order to attenuate the communication noises, time-varying consensus gains are applied in the consensus algorithm. Then, by using the tools of algebraic graph theory and stochastic analysis, sufficient conditions for the mean-square consensus are given for the cases with and without a leader. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithms.     

Time-varying output formation tracking of heterogeneous linear multi-agent systems with multiple leaders and switching topologies

This paper studies the time-varying output formation tracking problems for heterogeneous linear multi-agent systems with multiple leaders in the presence of switching directed topologies, where the agents can have different system dynamics and state dimensions. The outputs of followers are required to accomplish a given time-varying formation configuration and track the convex combination of leaders’ outputs simultaneously. Firstly, using the neighboring relative information, a distributed observer is constructed for each follower to estimate the convex combination of multiple leaders’ states under the influences of switching directed topologies. The convergence of the observer is proved based on the piecewise Lyapunov theory and the threshold for the average dwell time of the switching topologies is derived. Then, an output formation tracking protocol based on the distributed observer and an algorithm to determine the control parameters of the protocol are presented. Considering the features of heterogeneous dynamics, the time-varying formation tracking feasible constraints are provided, and a compensation input is applied to expand the feasible formation set. Sufficient conditions for the heterogeneous multi-agent systems with multiple leaders and switching directed topologies to achieve the desired time-varying output formation tracking under the designed protocol are proposed. Finally, simulation examples are given to validate the theoretical results.     

Resilient event-triggered consensus control for nonlinear muti-agent systems with DoS attacks

The distributed event-triggered secure consensus control is discussed for multi-agent systems (MASs) subject to DoS attacks and controller gain variation. In order to reduce unnecessary network traffic in communication channel, a resilient distributed event-triggered scheme is adopted at each agent to decide whether the sampled signal should be transmitted or not. The event-triggered scheme in this paper can be applicable to MASs under denial-of-service (DoS) attacks. We assume the information of DoS attacks, such as the attack period and the consecutive attack duration, can be detected. Under the introduced communication scheme and the occurrence of DoS attacks, a new sufficient condition is achieved which can guarantee the security consensus performance of the established system model. Moreover, the explicit expressions of the triggering matrices and the controller gain are presented. Finally, simulation results are provided to verify the effectiveness of the obtained theoretical results.     

Leader-following consensus of multi-agent systems with limited data rate

This paper investigates the leader-following consensus problem of time-invariant linear multi-agent systems with limited data rate. Based on the idea of assigning a priority level for each agent of the concerned multi-agent system, a novel distributed control law has been proposed. The proposed control law has two distinctive advantages. That is, it is fully distributed in the sense that it does not rely on the eigenvalues of the Laplace matrix associated with the topology. Moreover, the required data rate is independent of the number of agents and remains small even if the number of the agents in multi-agent systems is large. An example is finally given to illustrate the effectiveness of the proposed controller.     

Adaptive finite-time consensus of a class of disturbed multi-agent systems

In this paper, the finite-time exponential consensus problem is addressed for a class of multi-agent systems against some disturbed factors, which include system uncertainties, communication perturbations, and actuator faults. All disturbed factors are supposed to be influenced by internal and external effects of systems. The internal effects are described in terms of dependency on the system states, while the external actions are restricted by constant bounds. To obtain the information of the rate of dependency on the states and constant bounds, an adaptive mechanism is designed to estimate the rate and bounds. Based on these estimates, a distributed adaptive sliding mode controller is constructed to eliminate the effects of those disturbed factors. Then exponential consensus of the closed-loop adaptive multi-agent system is achieved within a finite time based on Lyapunov stability theory. The efficiency of the developed adaptive consensus control strategy is verified by a coupled system with four F-18 aircrafts of decoupled longitudinal model.     

Event-triggered consensus of nonlinear multi-agent systems with stochastic switching topology

This paper is concerned with a leader-follower consensus problem for networked Lipschitz nonlinear multi-agent systems. An event-triggered consensus controller is developed with the consideration of discontinuous state feedback. To further enhance the robustness of the proposed controller, modeling uncertainty and switching topology are also considered in the stability analysis. Meanwhile, a time-delay equivalent approach is adopted to deal with the discrete-time control problem. Particularly, a sufficient condition for the stochastic stabilization of the networked multi-agent systems is proposed based on the Lyapunov functional method. Furthermore, an optimization algorithm is developed to derive the parameters of the controller. Finally, numerical simulation is conducted to demonstrate the effectiveness of the proposed control algorithm.