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.     

Sampled-data-based event-triggered secure bipartite tracking consensus of linear multi-agent systems under DoS attacks

This paper investigates secure bipartite consensus tracking of linear multi-agent systems under denial-of-service(DoS) attacks by using event-triggered control mechanism with data sampling. Both bipartite leader-following and containment tracking consensus are considered in this paper. The event-triggered control protocol using sampled-data information is designed to save limited resources. The communication channels are interrupted by intermittent DoS attacks. Sufficient conditions on the sampling periods, attack frequency and attack duration are obtained to ensure secure bipartite tracking consensus of the multi-agent systems. Finally, simulation example is provided to illustrate the effectiveness of 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.     

Event-triggered control for second-order multi-agent systems under denial-of-service attacks and white noises

Under the influence of additive communication noises and system noises, we investigate the event-triggered control problem for second-order multi-agent systems composed of double integrators or LC oscillators under random denial-of-service (DoS) attacks. Different from the previous cases where the attackers completely interrupt communication networks, we consider that attackers interrupt the communication network with a specific probability and can attack part or all communication links randomly. Based on this, the conditions on the attack duration and attack success probability are given when the system can still achieve consensus under random DoS attacks. In addition, the consensus bounds are expressed. Finally, two types of LC oscillator systems are used to illustrate the effectiveness of results.     

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.     

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 secure control of nonlinear multi-agent systems under sensor attacks

In this paper, a security consistent tracking control scheme with event-triggered strategy and sensor attacks is developed for a class of nonlinear multi-agent systems. For the sensor attacks on the system, a security measurement preselector and a state observer are introduced to combat the impact of the attacks and achieve secure state estimation. In addition, command filtering technology is introduced to overcome the “complexity explosion” caused by the use of the backstepping approach. Subsequently, a new dynamic event-triggered strategy is proposed, in which the triggering conditions are no longer constants but can be adjusted in real time according to the adaptive variables, so that the designed event-triggered mechanism has stronger online update ability. The measurement states are only transmitted through the network based on event-triggered conditions. The proposed adaptive backstepping algorithm not only ensures the security of the system under sensor attacks but also saves network resources and ensures the consistent tracking performance of multi-agent systems. The boundedness of all closed-loop signals is proved by Lyapunov stability analysis. Simulation examples show the effectiveness of the control scheme.     

Event-based bipartite consensus of second-order discrete-time multi-agent systems with matrix-weighted signed networks

This article researches the bipartite consensus for discrete-time second-order multi-agent systems on matrix-weighted signed networks, which can describe the inter-dependencies of multidimensional states among states. So as to save limited communication resources, based on the matrix-weighted combined measurements of the position and velocity states, a matrix-weighted event-triggered control algorithm is designed. With the help of the stability theory, variable transformation and the inequality technique, the bipartite consensus conditions which are based on coupling gains, discrete interval, the parameters in the event-triggered rule and communication topology are obtained. Furthermore, the conditions to avoid the controller updating in each discrete-time are supplied. At last, a simulation example is offered to demonstrate the theoretical results.     

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.     

Event-triggered containment control of second-order nonlinear multi-agent systems

This paper investigates the event-triggered containment control for a class of second-order nonlinear multi-agent systems. A centralized event-triggered protocol is first designed, then the result is extended to the decentralized counterpart. By the tools from nonsmooth analysis, it is shown that the containment control objective can be achieved via the presented protocols. To avoid the Zeno behavior, the event-triggered conditions are redesigned. It is proven that all followers can asymptotically converge to the convex hull spanned by multiple leaders via the proposed strategies and the Zeno behavior can be excluded, simultaneously. Two examples are given to illustrate the feasibility of the proposed protocols.     

Event-triggered H∞ control for network-based uncertain Markov jump systems under DoS attacks

This paper investigates the event-triggered $H_{\infty }$ control problem for network-based Markov jump systems subject to denial-of-service (DoS) attacks. In order to reduce the amount of signal transmission, the event-triggering scheme (ETS) is adopted between sensor and controller. Due to DoS attacks invalidating data over networks, a new switched time-delay Markov jump model with unstable subsystems is developed based on state feedback controller. Then with the help of piecewise Lyapunov-Krasovskii functional method, a set of sufficient conditions incorporating constraints of DoS attacks are provided, which guarantees that the resulting switched time-delay Markov jump system is stochastically stable with a certain $H_{\infty }$ performance. Subsequently, we present criterions to obtain the parameters of state feedback gain and ETS. Finally, an example is provided to show the effectiveness of the proposed method.     

Dynamic event-Based resilient consensus of networked lagrangian systems under DoS attacks

In this paper, the dynamic event-based resilient consensus control of the multiple networked Euler-Lagrangian (E-L) systems under the Denial of Service (DoS) attacks is considered. Compared with linear cyber-physical systems, nonlinear networked E-L systems are more complex and closer to actual mechanical systems. For the situation where the topology is a strongly connected directed topology, a controller based on a dynamic event-trigger mechanism is designed to achieve consensus control for the networked E-L system in the absence of DoS attacks. Sufficient conditions are presented, which can guarantee the closed-loop system be stable. Then the resilient consensus problem of event-based controllers under energy-constrained DoS attacks is analyzed. The conditions related to the duration and frequency of DoS attacks are given. Zeno behavior is proved does not exist in the proposed control scheme. Finally, some numerical simulation results are given for verifying the theoretical results.     

Scaled consensus design for multiagent systems under DoS attacks and communication-delays

This paper aims to solve scaled consensus problem for general linear multiagent systems under denial-of-service (DoS) attacks. Firstly, we propose a new scaled disagreement vector and investigate its properties under switching and undirected graphs. Secondly, we establish sufficient conditions in terms of linear matrix inequalities in order to guarantee that the multiagent system achieves scaled consensus under DoS attacks. Contrary to most existing studies where DoS attacks on all the channels are same, in this note, we formulate the problem such that the adversary compromises each agent independently. Moreover, the distributed consensus protocol is investigated for networks with time-varying delay. Finally, two simulation examples are given to demonstrate effectiveness of the proposed design methodologies.     

Event-triggered asynchronous periodic distributed secondary control of microgrids under DoS attacks

A novel distributed secondary voltage and frequency control strategy is proposed with the Zeno-free event-triggered scheme for an island alternating current (AC) microgrid under Denial-of-Service (DoS) attacks. A DoS attack compensation mechanism and an event-triggered mechanism on the basis of the checking scheme are developed. Then, a secure event-checked based event-triggered secondary control method is explored to guarantee the tracking performance of the microgrid under DoS attacks. Further, some linear matrix inequalities (LMIs)-based sufficient conditions are derived to design the controller. What’s more, the proposed asynchronous periodic triggering method can efficiently save communication resources and further reduce the update number of the controller. Finally, the efficiency of this work is verified by an islanded AC microgrid with comparisons.     

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 leader-following consensus of multi-agent systems under semi-Markov switching topology with partially unknown rates

An event-triggered leader-following consensus problem for multi-agent systems with nonlinear dynamics was investigated in this study. The interaction topologies among the agents that we considered are randomly switched ones, governed by a semi-Markov process with partially unknown rates. By building the state error model between the leader and followers, the consensus problem is first converted into a stability problem. Moreover, an event-triggered transmission scheme based on sampling data was proposed to reduce communication redundancy. The consensus controller and event-triggered parameters can be designed effectively. By constructing a Lyapunov–Krasovskii functional (LKF) with a triple integral, the sufficient conditions required to guarantee the event-triggered consensus can be reached with respect to the linear matrix inequalities (LMIs). Ultimately, the validity of the theoretical results is demonstrated by a numerical example.     

Fixed-time bipartite consensus of nonlinear multi-agent systems under directed signed graphs with disturbances

This paper considers the fixed-time bipartite consensus of nonlinear multi-agent systems (MASs) subjected to external disturbances. Under the directed signed networks, several sufficient conditions are proposed to guarantee the fixed-time bipartite consensus of MASs with or without leaders, respectively. Some discontinuous control protocols are developed to realize fixed-time tracking bipartite consensus of MASs with a leader. Moreover, the fixed-time leaderless bipartite consensus under directed signed graph are discussed as well. Two numerical examples are given to verify the effectiveness of the theoretical results.