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.     

Event-triggered bipartite leader-following consensus of second-order nonlinear multi-agent systems under signed digraph

This paper investigates the bipartite leader-following consensus of second-order multi-agent systems with signed digraph topology. To significantly reduce the communication burden, an event-triggered control algorithm is proposed to solve the bipartite leader-following consensus problem, where a novel event-triggered function is designed. Under some mild assumptions on the network topology and node dynamics, a sufficient condition is derived using Lyapunov stability method and matrix theory to guarantee the bipartite consensus. In particular, it is shown that the continuous communication can be avoided and the Zeno-behavior can be excluded for the designed event-triggered algorithm. Numerical simulations are presented to illustrate the correctness of the theoretical analysis.     

Reliable consensus control for semi-Markov jump multi-agent systems: A leader-following strategy

This paper is devoted to the reliable leader-following consensus realization for a class of nonlinear multi-agent systems. The parameters of every agent are assumed to encounter sudden changes, which are governed by a semi-Markov process. A control protocol which possesses the performance of resisting actuator faults is employed for ensuring the reliable leader-following consensus and an analysis result is established by using the Lyapunov–Krasovskii functional method. Then an easy-to-implement condition is proposed for the issue of leader-following reliable consensus realization. If the condition is satisfied, the desired controller gain can be obtained via the numerical solutions of a set of linear matrix inequalities. At last, the feasibility of the proposed scheme is well explained by an illustrated example.     

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.     

Event-triggered bipartite consensus of second-order multi-agent systems under DoS attacks

This paper is concerned with the secure bipartite consensus of second-order multi-agent systems under denial-of-service (DoS) attacks. The communication network is an antagonistic network, in which there is cooperative or competitive relationship between neighboring agents. Meanwhile, information cannot be transmitted when the system is attacked. A novel event-triggered control algorithm based on sampled data is proposed to save limited resources and exclude the Zeno behavior. By applying the convergence of monotone sequences, graph theory as well as the discrete-time Lyapunov function method, some sufficient conditions on threshold parameters, frequency and duration of DoS attacks, and sampling period are derived to ensure the bipartite consensus under DoS attacks. Finally, the correctness and advantages of theoretical results are demonstrated by a numerical simulation.     

Leader-following consensus of semi-Markov jump nonlinear multi-agent systems under hybrid cyber-attacks

In this paper, the leader-following consensus issue is investigated for a class of nonlinear multi-agent systems with semi-Markov parameters subject to hybrid cyber-attacks. A semi-Markov chain is adopted to describe the variation of switching topologies caused by the complexity of the environment and makes the studied problem more general. Hybrid cyber-attacks consisting of denial-of-service attacks and deception attacks are described with the help of two groups of Bernoulli sequences which are assumed to be independent of each other. On this basis, a sufficient condition for the stability of the consensus error system is established by using linear matrix inequality techniques. Finally, the validity of the results obtained is verified by two numerical examples.     

Stochastic leader-following consensus of discrete-time nonlinear multi-agent systems with multiplicative noises

This paper studies the stochastic leader-following consensus problem of discrete-time nonlinear multi-agent systems (MASs) with multiplicative noises. The measurement information obtained from agents’ neighbors is inevitably affected by communication uncertainties, where the multiplicative noise is one of the important communication uncertainties. Multiplicative noises together with the intrinsic nonlinear dynamics bring more difficulties in the consensus control design under the leader-following topology. To solve the problem, the parameter-dependent Lyapunov functions are constructed to analyze the consensus control of first-order and second-order MASs, respectively. Some sufficient conditions, explicitly related to control gains, intensity of multiplicative noises and the Lipschitz constant regarding nonlinear functions, are established for reaching the mean square (m.s.) and almost sure (a.s.) leader-following consensus. Specifically, the obtained conditions are some scalar inequalities, which are more convenient in engineering application. Numerical simulations are conducted to validate the theoretical results.     

Scaled consensus problem for multi-agent systems with semi-Markov switching topologies: A view from the probability

This paper investigates the stochastic scaled consensus problem for multi-agent systems with semi-Markov switching topologies. Sufficient conditions are established to guarantee the addressed system to realize the scaled consensus with probability one, which means that all agents’ states almost surely reach a dictated proportion. Here, the semi-Markov process concerned is much more general than those utilized in the recent literature, which can be characterized by two important factors: (1) the transition probability matrix, and (2) the polytropical distribution functions of sojourn times. In addition, pinning scaled consensus protocol is designed by employing the pinning control technique, where only the root nodes of the union set of all the topologies are chosen to be pinned, and the final desired state value of the considered system can be realized with probability one. Finally, numerical simulations are provided to illustrate validity of the obtained main 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.     

Second-order group consensus for multi-agent systems via pinning leader-following approach

This paper addresses the group consensus problem of second-order nonlinear multi-agent systems through leader-following approach and pinning control. The network topology is assumed to be directed and weakly connected. The pinning consensus protocol is designed according to the agent property, that is, the inter-act agent and the intra-act agent. Some consensus criteria are proposed to guarantee that the agents asymptotically follow the virtual leader in each group, while agents in different groups behave independently. Numerical example is also provided to demonstrate the effectiveness of the theoretical analysis.     

Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data

This paper deals with the leader-following consensus problem of multi-agent systems with the consideration that each agent can only transmit its position state to the neighbors at irregular discrete sampling times. In the proposed algorithm, a continuous-discrete time observer is designed for the continuous estimation of both position and velocity from the discrete position information of the neighbors. These estimated states are then used for designing a continuous control law which solves the leader-following consensus problem. Moreover, the dynamics of the leader is not fixed and can be controlled through an external input. The stability analysis has been carried out by employing the Lyapunov approach which provides sufficient conditions to tune the parameters according to the maximum allowable sampling period. The developed algorithm has been simulated and then tested on an actual multi-robot system consisting of three differential drive wheeled robots. Both simulation and hardware results validate the effectiveness of the control algorithm.     

Reachable set estimation of multi-agent systems with semi-Markov switching topologies and time-delay

The issue of non-fragile controller’s designed with reachable set estimation and time-delay for multi-agent systems(MASs) is investigated in this paper. The information interaction among agents is governed by a set of switching sequence, which can be described by continue-time discrete state semi-Markov process. By tree-transformation, the MASs firstly converted into reduced-order system, and properly considered the instability of the parameters with the dynamic behavior of the controller, a non-fragile controller is designed to describe the system’s performance cope with the perturbation from the controller. The sufficient conditions are established in forms of a series of linear matrix inequalities which are based on Lyapunov-Krasovskii method, and the agent’s state of error systems is bounded by a finite closed set will be guaranteed. Finally, the availability of the derived theoretical results are verified by two numerical simulations.     

Event-triggered group consensus for multi-agent systems subject to input saturation

This paper investigates group consensus for leaderless multi-agent systems with non-identical dynamics. The consensus protocol is put forward in the form of the distributed event-triggered control subject to saturation, which depends on information from neighboring agents at event-triggered instants. In order to exclude the Zeno behavior and save resources, the given event-triggered condition is detected only at discrete sampling times, where the sampling intervals can be variable. Based on the graph theory, Lyapunov–Krasovskii functional method and by adopting the free-weighting matrix technique, some sufficient group consensus criteria in terms of linear matrix inequalities are derived. Furthermore, optimization problems aiming at maximizing the event-triggered parameter and the consensus region are proposed. Finally, numerical simulations illustrate the effectiveness of the theoretical results.     

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.     

Event-triggered consensus for second-order multi-agent systems with sampled position data via impulsive control

In this paper, the sampled-data-based event-triggered (SDBET) consensus problem of second-order multi-agent systems (MASs) with sampled position data is studied via impulsive control. Firstly, two kinds of SDBET impulsive control protocols are proposed, both of which employ sampled position data only. Secondly, a novel SDBET transmission scheme is designed to ensure the maximum length of triggering intervals exists, which can be regulated by the parameters in the triggering function. Also, the Zeno behavior is naturally excluded under the SDBET transmission scheme. And by using the designed SDBET impulsive control scheme, consensus of second-order MASs can be achieved with lower transmission and control updating frequency than using the periodical impulsive control scheme. Thirdly, sufficient conditions on the communication topology, the length of triggering intervals and control gains are derived to achieve SDBET consensus. It is also shown that to achieve consensus, both the maximum and minimum lengths of triggering intervals should be restricted. Also, a practical method for calculating the sampling period and other triggering parameters is given to ensure that the length of the triggering interval does not exceed the given range, and the SDBET transmission scheme is truly realized. Finally, some numerical examples are given to demonstrate the effectiveness of the theoretical results.     

Positive consensus for multi-agent systems with average dwell time switching

This paper considers the positive consensus for a class of multi-agent systems (MASs) with average dwell time (ADT) switching. First, sufficient and necessary conditions are derived for preserving the positivity of the closed-loop MASs. Second, the performance analysis of the consensus error system is accomplished by using the multiple Lyapunov functions (MLFs) approach, and an ADT switching technique designs the corresponding controlled switching signal. Then, both leaderless and leader-following positive consensus are achieved. Furthermore, to reduce the computational complexity, a novel leader-following positive consensus criterion is derived in the form of linear programming (LP). Finally, simulation examples are given to illustrate the effectiveness of the proposed method.