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.     

Resilient sliding mode control for a class of cyber-physical systems with multiple transmission channels under denial-of-service attacks

This paper investigates the resilient sliding mode control problem for cyber-physical systems (CPSs) with multiple transmission channels under denial-of-service (DoS) attacks. A set of finite-time observers is designed, and a switched integral-type sliding surface is introduced. Thus, the impact of unreliable state estimating channels is reduced, and the disturbance rejection performance is also improved. The number of linear matrix inequalities (LMIs) decreases compared with some existing results in designing the observer-based controller, and the input-to-state stability (ISS) is guaranteed. Moreover, the input saturation and event-triggering scheme are considered in the controller and handled by an auxiliary system. The network congestion in the control channel is thus relieved, and the Zeno behavior is excluded simultaneously. Finally, an example of an unmanned stratospheric airship is given to demonstrate effectiveness of the proposed resilient control approach.     

Mean square consensus of double-integrator multi-agent systems under intermittent control: A stochastic time scale approach

We consider the leader–follower consensus problem for a multi-agent system where information is exchanged only on a non-uniform discrete stochastic time domain. For a second-order multi-agent system subject to intermittent information exchange, we model the tracking error dynamics as a $\mu ?$varying linear system on a discrete stochastic time scale, where μ is the graininess operator. Based on a Lyapunov operator and a positive perturbation operator on the space of symmetric matrices, we derive necessary and sufficient conditions to design a decentralized consensus protocol. This protocol allows us to cast the mean-square exponential consensus problem within the framework of dynamic equations on stochastic time scales. We establish some theoretical results which allow for the computation of the control gain matrix which guarantees the mean-square exponential stability with a given decay rate for the error dynamics. To show the effectiveness of the theoretical results, some simulation and experimental results on multi-robot systems have been performed.     

Probability-guaranteed secure consensus control for time-varying stochastic multi-agent systems under mixed attacks

In this paper, the secure consensus control issue is investigated for a class of discrete time-varying stochastic multi-agent systems (MASs) subject to cyber-attacks. In order to give a comprehensive characterization of malicious threats against communication networks, a generic model is presented to take into account both random false data injection attacks (FDIAs) and replay attacks. The main objective of the problem under study is to design a control protocol via output feedback such that, despite the existence of mixed attacks, all the individual agents can be driven to reside within a desired ellipsoidal region in a pre-specified probability. Sufficient conditions are provided for the existence of the requested controller and the feedback gains are formulated in terms of the solution to certain matrix inequalities. Within the established framework, two optimization problems are considered with the aim to ensure the sub-optimal consensus performances from different perspectives. Finally, a simulation example is employed to illustrate the validity of the proposed control scheme.     

Periodic event-triggered resilient control for cyber-physical systems under denial-of-service attacks

This paper studies the problem of designing a resilient control strategy for cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. By constructing an H_∞ observer-based periodic event-triggered control (PETC) framework, the relationship between the event-triggering mechanism and the prediction error is obtained. Then, inspired by the maximum transmission interval, the input-to-state stability of the closed-loop system is proved. Compared with the existing methods, a Zeno-free periodic PETC scheme is designed for a continuous-time CPS with the external disturbance and measurement noise. In particular, the objective of maximizing the frequency and duration of the DoS attacks is achieved without losing robustness. Finally, two examples are given to verify the effectiveness of the proposed approach.     

Event-triggered sliding mode control of uncertain switched systems under denial-of-service attacks

This study is concerned with the event-triggered sliding mode control problem for a class of cyber-physical switched systems, in which the Denial-of-Service (DoS) attacks may randomly occur according to the Bernoulli distribution. A key issue is how to design the output feedback sliding mode control (SMC) law for guaranteeing the dynamical performance of the closed-loop system under DoS attacks. To this end, an event-triggered mechanism is firstly introduced to reduce the communication load, under which the measurement signal is transmitted only when a certain triggering condition is satisfied. An usable output signal for the controller is constructed to compensate the effect of unmeasured states and DoS attacks. And then, a dynamic output feedback sliding mode controller is designed by means of the attack probability and the compensated output signals. Both the reachability and the mean-square exponential stability of sliding mode dynamics are investigated and the corresponding sufficient conditions are obtained. Finally, some numerical simulation results are provided.     

Resilient observer-based sliding mode control of connected vehicles with denial-of-service attacks

This paper investigates an observer-based sliding mode control (SMC)) for connected vehicles under denial-of-service attacks. The attacks refer to interrupting communication channels between vehicles. Firstly, a reduced order observer is used to estimate the relative acceleration between neighbor vehicles, and a switching communication topology is introduced to model the attack. Then, an observer based sliding mode controller is proposed to achieve desired stability performance. Moreover, a quadratic cost performance is also defined and the cost upper bound is proved. Some sufficient conditions are provided such that the connected vehicles can achieve robust tracking performance, and input-to-state string stability is guaranteed under zero initial errors. Finally, numerical simulations are given to illustrate the validity of the designed controller.     

Hybrid event-based asynchronous finite-time control for cyber-physical switched systems under denial-of-service attacks

This paper investigates the event-based asynchronous finite-time control for a class of cyber-physical switched systems under Denial-of-Service (DoS) attacks. Considering the attack’s characteristics, we put forward a novel attack-instant-constrained hybrid event-triggered scheme (HETS), which can not only contribute to reducing the network transmission overload, but also well descibe the network denial service behavior under attack interference. An asynchronous and ZOH-based controller is delicately constructed to mitigate the influence of DoS attacks and network-induced delay. A double-mode dependent Lyapunov–Krasovskii functional (LKF) is developed to set up some sufficient finite-time stability criteria for the concerned systems in view of the asynchronous switching effect. Finally, an application example of the urban railway system is offered to verify the proposed control algorithm.     

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-triggered control for uncertain stochastic systems under triple network attacks

This paper studies the control problem of uncertain stochastic systems, which takes into account the impact of network attacks. The types of network attacks considered are denial-of-service (DoS) attacks, deception attacks and replay attacks. In order to save network resources and improve communication utilization, the static event-triggered mechanism and adaptive event-triggered mechanism are cited respectively. Firstly, a new Lyapunov-Krasovskii functional is constructed, employing improved Wirtinger-based integral inequality and Jensens inequality, the criteria on stochastic stability in the mean square for uncertain stochastic systems are proposed. Secondly, the design methods of static event-triggered controller and adaptive event-triggered controller are given respectively. Finally, a practical example is given to manifest the effectiveness of the theoretical results.     

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.     

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.     

Consensus-based secondary frequency control under denial-of-service attacks of distributed generations for microgrids

In this paper, Denial-of-Service (DoS) attacks on a microgrid (MG), especially on service-provider-edge routers in the MG, are considered and analysed. To increase the tolerance of the MG for DoS attacks with decreased computing time, we present consensus-based secondary frequency controllers with dynamic P-f droop controllers. Then, with the consideration of the impact on these controllers caused by DoS attacks, a state-space model of the MG is established based on which the stability analysis is derived. Finally, the effectiveness of the method is verified by simulation and experimental results.     

Connectivity-preserving rendezvous of heterogeneous multi-agent systems under denial-of-Service attacks

This article investigates the rendezvous problem of heterogeneous multi-agent systems against Denial-of-Service attacks with preserving initial connectivity under a dynamic communication topology. The algorithm of resisting Denial-of-Service attack is first introduced to connectivity-preserving rendezvous problem of heterogeneous multi-agent systems. First of all, in order to observe the information of the leader, the distributed observers are designed to estimate the state of the leader with the communication network in the presence of Denial-of-Service attack by adaptive algorithm. Then, a switching system model is constructed by taking into account the influence of Denial-of-Service attacks. By means of the obtained model combined with a artificial potential function technique, the proposed distributed control algorithm allows all agents to accomplish rendezvous assignment with connectivity preservation as well as resisting Denial-of-Service attacks. Finally, detailed simulation validates the effectiveness of the proposed distributed observer and controller algorithm.     

Distributed formation control of double-integrator fractional-order multi-agent systems with relative damping and nonuniform time-delays

In this paper, distributed formation control problems are studied for double-integrator fractional-order multi-agent systems (DIFOMASs) with relative damping and nonuniform time-delays. The required state deviations of a group of multi-agent systems are achieved through a local state information interaction, which means that this group of multi-agent systems achieves formation control. In the context of this paper, the dynamic model is first established and the formation control protocol is designed for distributed formation control of DIFOMASs with relative damping under symmetric time-delays and asymmetric time-delays. Then, some sufficient conditions for achieving distributed formation control of DIFOMASs are acquired with the help of graph theory, matrix theory, stability theory and frequency-domain theory. In the end, two simulation examples are performed to verify the efficacy of our proposed method.     

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.     

Time-varying formation control for nonlinear multi-agent systems against actuator attacks

The formation control problem with time-varying characteristics is investigated for the time-delayed nonlinear multi-agent systems against actuator attacks. A neural-network-based adaptive control method is constructed to achieve the desired control objective, which is outputs of the followers can complete the desired transformation of formation configuration. To eliminate the influence of malicious attacks on the actuators, an actuator attacks defense strategy is proposed to resist false data injection attacks occurred in the actuator. The uncertainty of the dynamics caused by nonlinear functions is resolved by the neural-network approximate method. The problem of the time delay is handled by an improved Lyapunov-Krasovskii functional approach, which can also avoid the singularity problem that may occur during the construction of the control method. Based on the Lyapunov stability theory, it is proved that all signals of closed-loop systems are semi-globally stable and the formation error can converge to a small neighborhood of the origin. Finally, the results of simulations are provided to verify the feasibility of the theoretical analysis and the effectiveness of the proposed control method.     

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.     

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.