Dynamic event-triggered adaptive semi-global bipartite consensus of linear multi-agent systems with input saturation under fixed and switching topologies

This paper investigates dynamic event-triggered adaptive leader-following semi-global bipartite consensus (SGBC) of multi-agent systems (MASs) with input saturation. A dynamic event-triggered adaptive control (DETAC) protocol is presented, where the triggering function can regulate its threshold value dynamically. It’s turned out that the SGBC can be achieved via the DETAC protocol under some inequalities. Then, the proposed DETAC protocol is extended to solve bipartite consensus under jointly connected topology. Furthermore, the Zeno behaviors will be avoided. Finally, the rationality of proposed DETAC protocols are tested by simulation results.     

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.     

Distributed bipartite consensus for multi-agent systems with dynamic event-triggered mechanism

This paper address the distributed bipartite consensus problem of multi-agent systems (MASs) under undirected and directed topologies with dynamic event-triggered (DET) mechanism. The relationship among agents not only collaborative interaction but also competitive interaction are taken into account. A novel DET control protocol is raised with internal dynamic variables to guarantee that each agent can reach the bipartite consensus. Compared with the existing static triggering laws, the introduced DET strategy can significantly enlarge the interval time between two triggering instants. In addition, continuous information transmission in either controller updating or between agent and its neighbors is not demanded, which implies that the communication frequency can be extremely decreased. It is also proven that Zeno behavior does not occur. Finally, two numerical examples verify the validity of the presented theoretical results.     

Event-based consensus for second-order multi-agent systems with actuator saturation under fixed and Markovian switching topologies

This paper studies the event-based consensus problem of second-order multi-agent systems with actuator saturation under fixed topology and Markovian switching topologies. By a model transformation, the consensus problem is first converted into the stability problem of the error system. Using discontinuous Lyapunov functional approach, two sufficient conditions on the consensus are derived for second-order multi-agent systems with fixed topology and Markovian switching topologies, respectively. The discontinuous Lyapunov functions take full account of the characteristics of the sawtooth delay, and thus lead to a less conservative consensus criterion. It is shown that the consensus condition depends on the parameters of sampling period, Laplacian matrix, and event-triggered parameter. In addition, this paper provides an effective method to co-design both the consensus controller and the event-triggered parameter. Finally, two numerical examples are provided to illustrate the effectiveness and feasibility of the proposed algorithm.     

Distributed event-triggered adaptive finite-time consensus control for second-order multi-agent systems with connectivity preservation

In this paper, we consider the robust finite-time consensus problem for second-order multi-agent systems (MASs) with limited sensing range and weak communication ability. As a stepping stone, a novel distributed finite-time sliding mode manifold is developed for MASs. Then, by combining artificial potential function technique with the presented sliding mode manifold, a robust distributed control scheme is proposed to enable the finite-time consensus of MASs while preserving the prescribed communication connectivity. Furthermore, the sampling frequency and implementation burden of the proposed controller can be reduced with resort to the event-triggered methodology. Finally, numerical examples are given to show the effectiveness of the proposed method.     

Switched observer-based dynamic event-triggered consensus of multi-agent systems under DoS attacks

This paper investigates the observer-based consensus control for high-order nonlinear multi-agent systems (MASs) under denial-of-service (DoS) attacks. When the DoS attacks appear, the communication channels are destroyed, and the blocked information may ruin the consensus of MASs. A switched state observer is designed for the followers to observe the leader’s state whether the DoS attacks occur or not. Then, a dynamic event-triggered condition is proposed to reduce the consumption of communication resources. Moreover, an observer-based and dynamic event-triggered controller is formulated to achieve leader-following consensus through the back-stepping method. Additionally, the boundedness of all closed-loop signals is obtained based on the Lyapunov stability theory. Finally, the simulation results demonstrate the effectiveness of the presented control strategy under DoS attacks.     

Predefined-time practical consensus for multi-agent systems via event-triggered control

This paper studies the predefined-time practical consensus problem for multiple single-integrator systems through event-triggered control. A new kind of time-varying functions is firstly proposed. Then, new event-triggered control inputs as well as triggering conditions are designed on the basis of the time-varying function and the local broadcasted states. In particular, the control scheme is fully-distributed because no global information of the system and the communication topology is needed. Furthermore, the consensus analysis is presented based on a sufficient condition for predefined-time practical stability. It illustrates that practical consensus can be ensured with a completely pre-specified time. Besides, the exclusion of Zeno behavior at all the time instants is addressed. Numerical results verify the validity of the obtained control method.     

Leaderless consensus control of nonlinear multi-agent systems under directed topologies subject to input saturation using adaptive event-triggered mechanism

This paper deals with the leaderless consensus controller design for nonlinear multi-agent systems (MASs) subject to the input saturation nonlinearity by using an event-triggered (ET) mechanism. An adaptive ET scheme has been established with variable threshold parameter for attaining an efficient control bandwidth. Linear parameter varying (LPV) formulation and region of stability investigation for dealing with the inherent nonlinearity and input saturation, respectively, are focused in the study. A consensus controller design condition has been formulated to ensure the regional stability, to determine the consensus protocol gains, to choose the parameters of ET mechanism, and to select an appropriate adaptation law for ET control. Elimination of Zeno behavior, based on nonlinearity bounds, for the adaptive ET mechanism has been ensured through a rigorous analysis. In contrast to excising methods, a directed communication topology, adaptive ET mechanism, and removal of Zeno behavior as well as elimination of the windup effect of saturation have been considered in our work. A simulation study has been provided for six robotic agents and comparison results with the existing method are revealed.     

Event-triggered bipartite consensus for nonlinear multi-agent systems under switching topologies: A time-varying gain method

In this paper, the event-triggered bipartite consensus problem is investigated for nonlinear multi-agent systems under switching topologies, only part of topologies contain directed spanning tree rooted at the leader. First, a dynamic bipartite compensator is constructed based on relative output information to provide control signal. Then, the time-varying gain method is adopted to propose a compensator-based event-triggered control protocol without Zeno behavior. Notably, the control protocol proposed achieves the bipartite consensus while reducing update frequency effectively. Moreover, a low conservative switching law is designed by the topology-dependent average dwell time strategy, which fully considers the differences among topologies and provides an independent average dwell time for each topology. As an extension, the nonlinear multi-agent systems with non-zero input of leader are further studied. Finally, a practical example is presented to demonstrate the feasibility of proposed control protocol.     

Interval observer based event-triggered consensus control of networked multi-agent systems under DoS attacks

This paper presents an interval observer (IO) based event-triggered control strategy for networked multi-agent systems (MASs) under denial of service (DoS) attacks. The most significant contribution is the proposal of a new event-triggered controller based on distributed IO. Toward this, first, a new distributed IO based on output information is first constructed to estimate the state interval of each agent in the networked MASs. Then a novel distributed IO based event-triggered control (ETC) protocol is constructed using only the information observed by IO. Moreover, it turns out that based on the designed IO based ETC protocol, all agents can reach secure consensus exponentially and Zeno behavior is excluded. Finally, simulation example is used to verify the feasibility of the constructed IO based ETC protocol.     

Leader-following consensus for multi-agent systems with actuator faults via adaptive event-triggered control

In this paper, the leader-following consensus problem is investigated by event-triggered control for multi-agent systems subject to time-varying actuator faults. Firstly, for a case of the leader without control input, a distributed event-triggered fault-tolerant protocol is proposed with the help of adaptive gains. Secondly, the proposed protocol is developed by an auxiliary nonlinear function to compensate the effect of the leader’s unknown bounded input. It is shown that under the both obtained protocols the tracking errors converge to an adjustable neighborhood around the origin, meanwhile the Zeno behavior is avoided. Moreover, the protocols are fully distributed in sense that any global information associated with the network is no longer utilized. Finally, numerical examples are presented to show the validity of the obtained protocols.     

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.     

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.     

Distributed adaptive fault-tolerant formation control for heterogeneous multiagent systems under switching directed topologies

This paper studies the cooperative fault-tolerant formation control problem of tracking a dynamic leader for heterogeneous multiagent systems consisting of multipile unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults under switching directed interaction topologies. Based on local neighborhood formation information, the distributed fault-tolerant formation controllers are constructed to ensure that all follower UAVs and UGVs can accomplish the demanding formation configuration in the state space and track the dynamic leader’s trajectory. By incorporating the sliding mode control and adaptive control technique, the actuator faults and unknown parameters of follower agents can be compensated. Through the theoretical analysis, it is proved that the cooperatively semiglobally uniformly ultimately boundedness of the closed-loop system is guaranteed, and the formation tracking errors converge to a small adjustable neighborhood of the origin. A simulation example is introduced to show the validity of the proposed distributed fault-tolerant formation control algorithm.     

Fixed-time bipartite consensus of nonlinear multi-agent systems using event-triggered control design

This paper focuses on designing a leader-following event-triggered control scheme for a category of multi-agent systems with nonlinear dynamics and signed graph topology. First, an event-triggered controller is proposed for each agent to achieve fixed-time bipartite consensus. Then, it is shown that the Zeno-behavior is rejected in the proposed algorithm. To avoid intensive chattering due to the discontinuous controller, the control protocol is improved by estimating the sign function. Moreover, a triggering function is proposed which avoids continuous communication in the event-based strategy. Finally, numerical simulations are given to show the accuracy of the theoretical results.     

Leader-following consensus control for semi-Markov jump multi-agent systems: An adaptive event-triggered scheme

The problem of event-triggered leader-following consensus control for semi-Markov multi-agent systems is investigated in this paper. A semi-Markov process is used to describe the sudden parameter changes between every agent. An adaptive event-triggered control strategy is proposed to make a balance between reducing unnecessary communication and meeting the required performance. A control protocol which can resist actuator faults is used to ensure the reliable leader-following consensus. By employing the Lyapunov–Krasovskii functional method, some sufficient conditions are provided to guarantee that the leader-following consensus can be achieved in mean-square sense. The consensus controller and the event-triggered parameter can be co-designed. Finally, the effectiveness of the proposed method is verified by a F-404 aircraft engine system.     

Distributed secure consensus control of nonlinear multi-agent systems under sensor and actuator attacks

In this paper, we focus on an output secure consensus control issue for nonlinear multi-agent systems (MASs) under sensor and actuator attacks. Followers in an MAS are in strict-feedback form with unknown control directions and unknown dead-zone input, where both sensors and nonlinear characteristics of dead-zone in actuators are paralyzed by malicious attacks. To deal with sensor attacks, uncertain dynamics in individual follower are separated by a separation theorem, and estimation parameters are introduced for compensating and mitigating the influence from adversaries. The influence from actuator attacks are treated as a total displacement in a dead-zone nonlinearity, and an upper bound, as well as its estimation, is introduced for this displacement. The dead-zone nonlinearity, sensor attacks and unknown control gains are gathered together regarded as composite unknown control directions, and Nussbaum functions are utilized to address the issue of unknown control directions. A distributed secure consensus control strategy is thus developed recursively for each follower in the framework of surface control method. Theoretically, the stability of the closed-loop MAS is analyzed, and it is proved that the MAS achieves output consensus in spite of nonlinear dynamics and malicious attacks. Finally, theoretical results are verified via a numerical example and a group of electromechanical systems.     

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.