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.     

Resilient consensus of discrete-time connected vehicle systems with interaction network against cyber-attacks

This paper concerns the consensus of the second-order discrete-time autonomous connected vehicle system (CVS) in presence of cyber-attacks. First, the necessary and sufficient conditions for the autonomous CVS are derived without a cyber-attack. Then, a virtual system in hidden layer, interconnected with the original CVS in platoon layer through the designed interaction network, is introduced to resist cyber attacks. Matrix analysis tool, algebraic graph theory and Lyapunov stability method are used to analyze the convergence of CVS. It is proved that the states of CVS can reach consensus and the state errors converge to a certain bound in the case of attacks existing only in hidden layer, or in the overall system including both hidden layer and platoon layer. Finally, the validity of the proposed control approach is verified by the designed simulations.     

Non-fragile guaranteed cost control for networked nonlinear Markov jump systems under multiple cyber-attacks

This paper is concerned with the problem of non-fragile guaranteed cost control (GCC) for networked nonlinear Markov jump systems subject to multiple cyber-attacks, which are characterized by Takagi–Sugeno (T–S) fuzzy model with time-varying delay. Specifically, a variety of cyber-attacks, including deception attacks and Denial-of-Service (DoS) attacks, are considered, which occur in the forward and feedback communication links, respectively. To achieve stochastic stability under guaranteed cost function (GCF), the paper proposes a Lyapunov–Krasovskii (L–K) function approach. The approach derives sufficient conditions for stochastic stability, and obtains non-fragile controller gains and the uniform upper bound of the GCF using linear matrix inequalities (LMIs) technique. Finally, the effectiveness of the proposed algorithm is evaluated by simulation experiment.     

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.     

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.     

Sliding-mode secure control for jump cyber– physical systems with malicious attacks

This paper develops the secure control strategy design issue for jump cyber–physical systems (CPSs) with malicious attacks. In the jump CPSs, the jump signals are assumed to obey the semi-Markov distribution with the transition probability depends on the stochastic sojourn-time, the physical plant and actuator simultaneous subject to the adversarial attack. A secure control strategy on robust sliding-mode control (SMC) is designed to deal with the malicious attacks. Firstly, an integral sliding-mode hyperplane is constructed, and the sliding-mode dynamics is discussed. Then, the slide-mode parameters are solved by the linear matrix inequality method with prescribed H∞ damping index. Furthermore, a robust sliding-mode controller is presented, and the reachability of the sliding-mode motion is analyzed. Finally, two examples are implemented to prove the potential of the secure control approach.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Distributed event-triggered control for networked control systems with stochastic cyber-attacks

This paper is concerned with the problem of distributed event-triggered controller design for networked control systems (NCSs) with stochastic cyber-attacks. A decentralized event-triggered scheme is introduced to save the energy consumption and alleviate the transmission load of the network. Each sensor can make its own decision to determine whether the sampled data is delivered to the network or not. By taking two kinds of random cyber-attacks into consideration, a novel mathematical model is constructed for distributed event-triggered NCSs. Sufficient conditions which can guarantee the stability of the control system are obtained by applying Lyapunov stability theory, and the design method of the controller gain is presented in an exact expression. Finally, an example is given to demonstrate the effectiveness of the proposed method.     

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.     

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.     

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.     

Attack resilient strategy for event-triggered distributed control scheme of multi-energy systems

In recent years, distributed algorithms have been increasingly used to solve the economic dispatch (ED) problem of multi-energy systems (MES) due to the advantages of high flexibility, strong robustness, and privacy. However, the MES based on the distributed optimization architecture must bear higher cyber-attack risks, so as to maintain the safe and stable operation of MES. To address this issue, an event-triggered fully distributed algorithm is proposed to solve the ED problem, which can effectively mitigate the communication burden. On this basis, an attack resilient strategy against false data injection (FDI) attacks is implemented in the proposed fully distributed algorithm, which can eliminate incorrect measurement of incremental cost and power generation data caused by cyber-attacks. In addition, a reputation value protocol embedded in the proposed attack resilient strategy is designed to effectively reduce the potential of direct isolation of the node. Finally, case studies are given in this paper to validate the effectiveness of the proposed distributed control scheme on a 9-bus MES.