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.     

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.     

On consensus control of nonlinear multiagent systems satisfying incremental quadratic constraints

In this paper, we investigate the problem of leaderless consensus control for the multiagent systems whose nonlinear dynamics satisfying incremental quadratic constraints. A distributed dynamic consensus protocol, decided by communication among neighboring agents, is presented to render nonlinear agent consensus with appropriate coupling weights. Next, an observer-based distributed protocol is considered to ensure consensus of nonlinear system without knowing full state information. Further, extensions to consensus strategies with nonlinear dynamics for the leader-following fashion are also addressed. By comparison to the traditional nonlinear consensus control methodologies, the proposed approach generalizes the Lipschitz nonlinearity as well as the combined nonlinearity of one-sided Lipschitz condition and quadratic inner-boundness condition towards a more generalized type of nonlinearity, which shows us a less conservative result in the Lyapunov proof. Finally, the numerical simulations for six agents are illustrated to show the feasibility and performance of the proposed control protocol with or without the presence of the observer.     

Observer-based event-triggered tracking consensus of non-ideal general linear multi-agent systems

In this paper, the leader-following consensus problem of general linear multi-agent systems without direct access to real-time state is investigated. A novel observer-based event-triggered tracking consensus control scheme is proposed. In the control scheme, a distributed observer is designed to estimate the relative full states, which are used in tracking consensus protocol to achieve overall consensus. And an event-triggered mechanism with estimated state-dependent event condition is adopted to update the control signals so as to reduce unnecessary data communication. Based on the Lyapunov theorem and graph theory, the proposed event-triggered control scheme is proved to implement the tracking consensus when real-time state cannot direct obtain. Moreover, such scheme can exclude Zeno-behavior. Finally, numerical simulations illustrate the effectiveness of the theoretical results.     

Designing distributed consensus protocols for second-order nonlinear multi-agents with unknown control directions under directed graphs

This paper focuses on the leaderless and leader-following consensus problems of second-order nonlinear multi-agents under directed graphs. Both leaderless and leader-following consensus protocols are proposed for multi-agents with unknown control directions based on the Nussbaum-type gains. For the leaderless case, the proposed protocol can guarantee that the consensus errors asymptotically converge to zero. Moreover, for the leader-following case, the Lyapunov stability analysis shows that the consensus tracking errors can be made arbitrarily small by tuning the control parameters. It should also be noted that these proposed protocols do not require any information about the global communication topology and work with only the relative information of neighboring agents. Illustrative examples are given to show the effectiveness of the proposed control protocols.     

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.     

Finite-time consensus for the second-order leader-following nonlinear multi-agent system with event-triggered communication

This study discusses the finite-time consensus for the second-order leader-following nonlinear multi-agent system with event-triggered communication. An event-triggered control protocol is established to achieve finite-time consensus, which can effectively avoid the Zeno behavior. Due to the unevenness of an event-triggered controller and the occurrence of the event-triggered condition, it is more challenging to analyze the event-triggered finite-time consensus. Based on the knowledge of graph theory, all agents can achieve finite-time consensus via the proposed event-triggered control protocol. Different from homogeneity, a Lyapunov function is constructed to obtain the settling time. Finally, a simulation example illustrates the validity of the main results.     

Leader-following consensus of multi-agent systems with connectivity-mixed attacks and actuator/sensor faults

This study investigates the leader-following consensus issue of multi-agent systems subject to simultaneous connectivity-mixed attacks, actuator/sensor faults and disturbances. Connectivity-mixed attacks are remodeled into connectivity-maintained and connectivity-paralyzed topologies in a switched version, and actuator/sensor faults are established with unified incipient-type and abrupt-type characteristics. Then, unknown input observer-based decoupling and estimation are incorporated to achieve unknown state and fault observations with the normalized technique, and the leader-following consensus-based compensation to faults, resilience to attacks and robustness to disturbances are also realized with the neighboring output information and sensor fault estimation through the distributed framework. Criteria of achieving exponential leader-following consensus of multi-agent systems under cyber-physical threats are derived with dual attack frequency and activation rate indicators. Simulation example is conducted to exemplify the validation and merits of the proposed leader-following consensus algorithm.     

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.     

Consensus of multi-Agent systems with one-Sided lipschitz nonlinearity via nonidentical double event-Triggered control subject to deception attacks

As for the multi-agent systems (MASs) with time-varying switching subject to deception attacks, the leader-following consensus problem is studied in this article. The one-sided Lipschitz (OSL) condition is utilized for the nonlinear functions, which makes the results more general and relaxed than those obtained by Lipschitz condition. The nonidentical double event-triggering mechanisms (ETMs) are adopted for only a fraction of agents, and each agent transmits the data according to its own necessity. Semi-Markov process modeling with time-varying switching probability is adopted for switching topology and deception attacks occurring in transmission channel are considered. By using the cumulative distribution function (CDF) and the linear matrix inequality (LMI) technology, sufficient conditions for MASs to achieve consensus in mean square are obtained. An effective algorithm is presented to obtain the event-based control gains. The merits of the proposed control scheme are demonstrated via a simulation example.     

Improved results on consensus of nonlinear MASs with nonhomogeneous Markov switching topologies and DoS cyber attacks

In this paper, the issue of leader-following consensus for nonlinear multi-agent systems (NMASs) suffered from uncertain nonhomogeneous Markov switching (UNMS) and denial-of-service (DoS) cyber attacks is studied. In contrast with the existing results on NMASs with a fixed topological structure, the communication topology is governed by an UNMS jump process, where the transition rates (TRs) of UNMS are considered to be partially known or completely unknown. Also, the changes of communication topologies caused by frequently DoS cyber attacks are taken into consideration, which will destroy the chains of communication and lead to network paralysis in NMASs. In view of this, based on the stochastic technique and multiple Lyapunov functional protocol, mean-square leader-following consensus conditions related to NMASs with the UNMS and DoS cyber attacks are proposed. Finally, the effectiveness of the presented theoretical results is validated by numerical example.     

Finite-time consensus of neutrally stable multi-agent systems in the presence of input saturation

The problem of finite-time consensus of linear multi-agent systems subject to input saturation is investigated and two control protocols are presented for leaderless and leader-following cases, respectively. The leaderless multi-agent systems with proposed non-smooth protocol can achieve consensus in finite time. The consensus protocol designed for leader-following case with directed topology can solve the finite-time consensus problem, where a priori constraint is adopted to deal with input saturation. Furthermore, the settling time is explicitly derived using finite-time Lyapunov theory. Finally, the effectiveness of the theoretical results is illustrated with several numerical simulations.     

Memory-based event-triggered leader-following consensus for T-S fuzzy multi-agent systems subject to deception attacks

In this paper, the problem of fuzzy model-based leader-following consensus control for multi-agent systems (MASs) under deception attacks is investigated. For the sake of alleviating the communication burden, a novel memory-based event-triggered scheme (METS) is first proposed for the considered MASs to reduce redundant data transmission, and the leader-following consensus can be achieved faster with a smaller adjustment error by applying the historical released packets. Considering the designed METS and upper-bounded attacks synthetically, the closed-loop fuzzy system model is well established. Furthermore, with the help of Lyapunov-Krasovskii technique, some sufficient conditions are derived to ensure the consensus of MASs subject to deception attacks. Finally, a simulation example is introduced to manifest the effectiveness of the proposed method.     

Leader-following consensus of multi-agent systems with jointly connected topology using distributed adaptive protocols

The leader-following consensus problems for multi-agent systems with a linear and Lipschitz nonlinear dynamics are considered. Distributed adaptive protocols and Lipschitz distributed adaptive protocols are respectively designed for the linear and Lipschitz nonlinear cases, under which leader-following consensus is reached for jointly connected topology. Finally, a simulation example is provided to illustrate the theoretical results.     

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.     

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.     

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.     

Global adaptive fuzzy consensus control of nonlinear multi-agent systems via distributed event-triggered communication

This paper investigates globally bounded consensus of leader-following multi-agent systems with unknown nonlinear dynamics and external disturbance via adaptive event-triggered fuzzy control. Different from existing works where filtering and backstepping techniques are applied to design controllers and event-triggered conditions, a matrix inequality is established to obtain the feedback gain matrix and event-triggered functions. To save communication resources, a new distributed event-triggered controller with fully discontinuous communication among following agents is designed. Meanwhile, a strictly positive minimum of inter-event time is provided to exclude Zeno behavior. Furthermore, to achieve globally bounded leader-following consensus, an adaptive fuzzy approximator and a parameter estimator are designed to approximate the unknown nonlinear dynamics and parameters, respectively. Finally, the effectiveness of the proposed method is validated via a simulation example.     

Aperiodically intermittent output feedback consensus control for second-order leader-following multi-agent systems based on observer

This study examines the leader-following consensus problem of a class of second-order nonlinear multi-agent systems, where the velocity information is supposed to be unmeasurable. Under the setting, this paper presents a novel aperiodically intermittent output feedback control protocol such that all followers reach consensus with the leader, in which a distributed state observer is built for each follower to observe the velocity state. Based on the Lyapunov stability theory and some matrix analysis techniques, a couple of sufficient conditions for the leader-following consensus of the nonlinear multi-agent system under study are obtained even though the velocity state is unavailable. Finally, the effectiveness of the theoretical results is verified by 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.