Resilient Event-Triggered Controller Synthesis of Networked Control Systems Under Periodic DoS Jamming Attacks

DFA-mode-dependent stability of impulsive switched memristive neural networks under channel-covert aperiodic asynchronous attacks

This article is concerned with the deterministic finite automaton-mode-dependent (DFAMD) exponential stability problem of impulsive switched memristive neural networks (SMNNs) with aperiodic asynchronous attacks and the network covert channel. First, unlike the existing literature on SMNNs, this article focuses on DFA to drive mode switching, which facilitates precise system behavior modeling based on deterministic rules and input characters. To eliminate the periodicity and consistency constraints of traditional attacks, this article presents the multichannel aperiodic asynchronous denial-of-service (DoS) attacks, allowing for the diversity of attack sequences. Meanwhile, the network covert channel with a security layer is exploited and its dynamic adjustment is realized jointly through the dynamic weighted try-once-discard (DWTOD) protocol and selector, which can reduce network congestion, improve data security, and enhance system defense capability. In addition, this article proposes a novel mode-dependent hybrid controller composed of output feedback control and mode-dependent impulsive control, with the goal of increasing system flexibility and efficiency. Inspired by the semi-tensor product (STP) technique, Lyapunov-Krasovskii functions, and inequality technology, the novel exponential stability conditions are derived. Finally, a numerical simulation is provided to illustrate the effectiveness of the developed approach.

A Cross-Layer Game-Theoretic Approach to Resilient Control of Networked Switched Systems Against DoS Attacks

This article investigates the resilient control strategies of networked switched systems (NSSs) against denial-of-service (DoS) attacks and external disturbance. In the network layer, both the defender and the attacker allocate energy over multiple channels. Considering the impact of switching characteristic in the physical layer on the network layer, a dynamic regulating factor is proposed to adjust the total energy of the defender. To optimize the signal-to-interference-noise ratio and energy consumption simultaneously at each player's side, a multiobjective game problem is formulated. Furthermore, a nondominated sorting genetic algorithm framework is employed, incorporating the knee point selection mechanism to attain the Pareto-Nash equilibrium, based on which the optimal defense strategy can be derived to achieve resilience against DoS attacks. In the physical-layer, taking the dynamic packet loss caused by DoS attacks and external disturbance into account, an minimax controller containing control inputs and the switching signal is designed to guarantee the optimal performance for NSSs through the dynamic game-theoretic approach. Finally, the networked continuous stirred tank reactor system is provided to verify the effectiveness of the proposed method.

Communication Security and Stability in NNCSs: Realistic DoS Attacks Model and ISTA-Supervised Adaptive Event-Triggered Controller Design

This article addresses the challenge of achieving asymptotic stability in nonlinear networked control systems (NNCSs) amid denial-of-service (DoS) attacks, particularly under constrained communication resources. We begin by establishing a practical DoS attack model using the NSL-KDD dataset, which provides a realistic depiction of DoS attack dynamics based on real-world data. We then introduce the iterative shrinkage-thresholding algorithm (ISTA) to supervise the adaptive event-triggered controller (AETC), ensuring that system parameters are adjusted effectively while conserving communication resources. We develop an enhanced data compression mechanism to further mitigate the impact of DoS attacks on communication servers. Additionally, we construct an asymmetric Lyapunov-Krasovskii function (LKF) to rigorously verify the asymptotic stability of NNCSs. Finally, we empirically validate the effectiveness of our proposed AETC using an autonomous vehicle (AV) model.

Resilient event-triggering adaptive neural network control for networked systems under mixed cyber attacks

This paper addresses the resilient event-triggering adaptive neural network (NN) control problem for networked control systems under mixed cyber attacks. Compared with the conventional event-triggered mechanism (ETM) with constant threshold, a novel resilient ETM is designed to withstand the affect of denial-of-service attacks and conserve communication resources. Different from the energy-bounded deception attacks, an unknown state-dependent nonlinear attack signal is considered in this work. To identify the deception attack, the NN technique is utilized to approximate the unknown attack signal. Subsequently, an adaptive controller is established to compensate for the malicious affects of deception attacks on the system. Furthermore, sufficient conditions for the boundedness of the system are derived via applying the Lyapunov functional, and a co-design strategy for control gain and event-triggering parameter is provided. Finally, the feasibility of the proposed approach is validated through a robot manipulator system.

Event-triggered predictive control for cooperation-competition multi-agent systems under DoS attacks

This paper concerns the bipartite consensus problem of multi-agent systems(MASs) with competitive- cooperative network topology under denial-of-service (DoS) attacks. Firstly, this work extensively analyzes the competitive phenomena that may exist in the information interchange of agents in contrast to the single cooperative behavior between agents. Based on this, some necessary conditions are provided for the system to attain the bipartite consensus. In addition, the event-triggered mechanism (ETM) effectively lowers unnecessary information sharing between agents and eliminates Zeno behavior. Furthermore, the predictive method provides the system with exceptional resistance against common energy-limited DoS attacks and the ability to compensate for information loss caused by DoS attacks. Finally, a numerical simulation proves that the proposed approach is feasible.

Resilient event-triggered observer-based control of non-linear systems under denial-of-service attacks with actuator saturation

This paper studies the control problem for a continuous-time networked system with non-linearity in the state equation as well as in the input, as saturation. The system is considered under denial-of-service (DoS), attacks which cause the blockage of input and/or output components in the overall closed-loop model. An event-triggering scheme that is resilient in nature, along with an observer-based control, has been considered under DoS attacks. The resultant scheme ensures efficient network resources and excludes Zeno behavior naturally due to the presence of a minimum positive interevent delay. Then, an event-based switched non-linear model is presented to address both the event-triggering scheme and the presence of DoS blocking attacks. A piece-wise Lyapunov-Krasovskii functional method on the described non-linear model, resulting in the switched system, is considered for achieving an exponentially stable response by driving the required feasibility conditions. In the presence of a non-linear system with saturation in the actuator, the presented design establishes quantitative relationships among the exponential decay rate, active/sleeping intervals of attacks, parameters of the event-triggering condition, and sampling period of the system. After that, linear matrix inequalities are presented for designing an event-triggered controller with an observer, while the design also includes the region of convergence for dealing with the input non-linearity. Finally, comparative results for an offshore structure model with non-linearity in states as well as in actuator, are demonstrated to verify the results of the control scheme that is developed. It has been verified that our design is less conservative than the previous designs, and can handle the non-linearities in the dynamics of plant and actuator saturation more efficiently, while DoS attacks are also present. By applying our proposed method, the overshoot and undershoot are less than ±2.5 percent, while system states converge to the origin within 55 s.

Codesign of FDI Attacks Detection, Isolation, and Mitigation for Complex Microgrid Systems: An HBF-NN-Based Approach

The primary purpose of this article is to design an intelligent false data injection (FDI) attacks detection, isolation, and mitigation scheme for a class of complex microgrid systems with electric vehicles (EVs). First, a networked microgrid with an EV model is well established, which takes load disturbance, wind generation fluctuation, and FDI attacks into account so as to truly reflect the operation process of the complex system. Then, an intelligent hyper basis function neural network (HBF-NN) observer is designed to accurately estimate the state of the microgrids, learn, and reconstruct the possible attack signal online. Subsequently, a novel HBF-NN-based H∞ controller is skillfully designed to mitigate the negative impact of FDI attacks online, so as to ensure the normal operation of the complex systems in an unreliable network environment. Finally, a two-stage integrated intelligent detection and maintenance algorithm is summarized and one simulation is presented to provide tangible evidence of the feasibility and superiority of the proposed FDI attacks detection, isolation, and mitigation methodology.

Neural-Network-Based Adaptive Fault-Tolerant Cooperative Control of Heterogeneous Multiagent Systems With Multiple Faults and DoS Attacks

In this article, the issue of adaptive fault-tolerant cooperative control is addressed for heterogeneous multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults and sensor faults under denial-of-service (DoS) attacks. First, a unified control model with actuator faults and sensor faults is developed based on the dynamic models of the UAVs and UGVs. To handle the difficulty introduced by the nonlinear term, a neural-network-based switching-type observer is established to obtain the unmeasured state variables when DoS attacks are active. Then, the fault-tolerant cooperative control scheme is presented by utilizing an adaptive backstepping control algorithm under DoS attacks. According to Lyapunov stability theory and improved average dwell time method by integrating the duration and frequency characteristics of DoS attacks, the stability of the closed-loop system is proved. In addition, all vehicles can track their individual references, while the synchronized tracking errors among vehicles are uniformly ultimately bounded. Finally, simulation studies are given to demonstrate the effectiveness of the proposed method.

Resilient Event-Based Fuzzy Fault Detection for DC Microgrids in Finite-Frequency Domain against DoS Attacks

This paper addresses the problem of fault detection in DC microgrids in the presence of denial-of-service (DoS) attacks. To deal with the nonlinear term in DC microgrids, a Takagi-Sugeno (T-S) model is employed. In contrast to the conventional approach of utilizing current sampling data in the traditional event-triggered mechanism (ETM), a novel integrated ETM employs historical information from measured data. This innovative strategy mitigates the generation of additional triggering packets resulting from random perturbations, thus reducing redundant transmission data. Under the assumption of faults occurring within a finite-frequency domain, a resilient event-based H-/H∞ fault detection filter (FDF) is designed to withstand DoS attacks. The exponential stability conditions are derived in the form of linear matrix inequalities to ensure the performance of fault detected systems. Finally, the simulation results are presented, demonstrating that the designed FDF effectively detects finite-frequency faults in time even under DoS attacks. Furthermore, the FDF exhibits superior fault detection sensitivity compared to the conventional H∞ method, thus confirming the efficacy of the proposed approach. Additionally, it is observed that a trade-off exists between fault detection performance and the data releasing rate (DRR).

Pinning Spatiotemporal Sampled-Data Synchronization of Coupled Reaction-Diffusion Neural Networks Under Deception Attacks

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

Novel Extended State Observer Design for Uncertain Nonlinear Systems via Refined Dynamic Event-Triggered Communication Protocol

In this article, an extended state observer (ESO) design problem is investigated for uncertain nonlinear systems subject to limited network bandwidth. First, for rational information exchange scheduling, a dynamic event-triggered (DET) communication protocol is proposed. Different from the traditional static event-triggered strategies with fixed thresholds, an internal dynamic variable is introduced to be adaptively adjusted by a dual-directional regulating mechanism. Thus, more desirable tradeoff between observation performance and communication resource efficiency is achieved. Second, inspired by our early work on Takagi-Sugeno fuzzy ESO (TSFESO), a novel paradigm of event-triggered TSFESO is initially proposed. Third, under the DET mechanism, the TSFESO design approach is derived to carry out exponential convergence for estimation error dynamics. Finally, the effectiveness of the proposed method is verified by numerical examples. The nonlinear estimating efficiency and linear numerical tractability are integrated in TSFESO. In addition, a generalized ESO formulation is developed to allow some nonadditive uncertainties incompatible with total disturbance, such as improved event-triggered strategy, and thus, the application sphere of ESO is further expanded.

Event-Triggered and Self-Triggered L∞ Control for Markov Jump Stochastic Nonlinear Systems Under DoS Attacks

This article investigates event-triggered and self-triggered L_∞ control problems for the Markov jump stochastic nonlinear systems subject to denial-of-service (DoS) attacks. When attacks prevent system devices from obtaining valid information over networks, a new switched model with unstable subsystems is constructed to characterize the effect of DoS attacks. On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve L_∞ performance. In particular, considering that ETS based on mathematical expectation is difficult to be implemented on a practical platform, a self-triggering scheme (STS) without mathematical expectation is presented. Meanwhile, to avoid the Zeno behavior resulted from general exogenous disturbance, a positive lower bound is fixed in STS in advance. In addition, the exponent parameters are designed in STS to reduce triggering frequency. Based on the STS, the mean-square asymptotical stability and almost sure exponential stability are both discussed when the system is in the absence of exogenous disturbance. Finally, two examples are given to substantiate the effectiveness of the proposed method.

Hybrid Dynamic Event-Triggered Load Frequency Control for Power Systems With Unreliable Transmission Networks

In this article, we consider the load frequency control problem for a class of power systems based on the dynamic event-triggered control (ETC) approach. The transmission networks are unreliable in the sense that malicious denial-of-service (DoS) attacks may arise in the power system. First, a model-based feedback controller is designed, which utilizes estimated states, and thus can compensate the error between plant states and the feedback data. Then, a dynamic event-triggered mechanism (DETM) is proposed by introducing an internal dynamic variable and a timer variable with jump dynamics. The proposed (DETM) can exclude Zeno behavior by regularizing a prescribed strictly positive triggering interval. Incorporated in the ETC scheme, a novel hybrid model is established to describe the flow and jump dynamics of the power system in the presence of DoS attacks. Based on the hybrid dynamic ETC scheme, the power system stability can be preserved if the attacks frequency and duration sustain within an explicit range. In addition, the explicit range is further maximized based on the measurement trigger-resetting property. Finally, a numerical example is presented to show the effectiveness of our results.

Intelligent Event-Based Fuzzy Dynamic Positioning Control of Nonlinear Unmanned Marine Vehicles Under DoS Attack

This article addresses the dynamic positioning control problem of a nonlinear unmanned marine vehicle (UMV) system subject to network communication constraints and deny-of-service (DoS) attack, where the dynamics of UMV are described by a Takagi-Sugeno (T-S) fuzzy system (TSFS). In order to save limited communication resource, a new intelligent event-triggering mechanism is proposed, in which the event triggering threshold is optimized by a Q -learning algorithm. Then, a switched system approach is proposed to deal with the aperiodic DoS attack occurring in the communication channels. With a proper piecewise Lyapunov function, some sufficient conditions for global exponential stability (GES) of the closed-loop nonlinear UMV system are derived, and the corresponding observer and controller gains are designed via solving a set of matrix inequalities. A benchmark nonlinear UMV system is adopted as an example in simulation, and the simulation results validate the effectiveness of the proposed control method.

Dynamic Event-Triggered Platooning Control of Automated Vehicles Under Random Communication Topologies and Various Spacing Policies

This article addresses the problem of dynamic event-triggered platooning control of automated vehicles over a vehicular ad-hoc network (VANET) subject to random vehicle-to-vehicle communication topologies. First, a novel dynamic event-triggered mechanism is developed to determine whether or not the sampled data packets of each vehicle should be released into the VANET for intervehicle cooperation. More specifically, the threshold parameter in the triggering condition is dynamically adjusted over time according to the vehicular data variations, the dynamic threshold updating laws, and the bandwidth occupancy indication. Second, a unified platooning control framework is established to account for various spacing policies, randomly switching communication topologies, unknown leader control input, and external disturbances. Then, a new scheduling and platooning control co-design approach is presented such that the controlled vehicular platoon can successfully track the leader vehicle under random communication topologies and different spacing policies, including constant spacing, constant time headway spacing, and variable time headway spacing, meanwhile maintaining efficient bandwidth-aware resource management. Finally, comparative studies are provided to substantiate the effectiveness and merits of the proposed co-design approach.

Event-Triggered Resilient L∞ Control for Markov Jump Systems Subject to Denial-of-Service Jamming Attacks

In this article, the event-triggered resilient L_∞ control problem is concerned for the Markov jump systems in the presence of denial-of-service (DoS) jamming attacks. First, a fixed lower bound-based event-triggering scheme (ETS) is presented in order to avoid the Zeno problem caused by exogenous disturbance. Second, when DoS jamming attacks are involved, the transmitted data are blocked and the old control input is kept by using the zero-order holder (ZOH). On the basis of this process, the effect of DoS attacks on ETS is further discussed. Next, by utilizing the state-feedback controller and multiple Lyapunov functions method, some criteria incorporating the restriction of DoS jamming attacks are proposed to guarantee the L_∞ control performance of the event-triggered Markov closed-loop jump system. In particular, the bounded transition rates rather than the exact ones are taken into account. That is appropriate for the practical environment in which transition rates of the Markov process are difficult to measure accurately. Correspondingly, some criteria are proposed to obtain state-feedback gains and event-triggering parameters simultaneously. Finally, we provide two examples to show the effectiveness of the proposed method.

Secure Event-Triggered Consensus Control of Linear Multiagent Systems Subject to Sequential Scaling Attacks

This article investigates secure consensus of linear multiagent systems under event-triggered control subject to a scaling deception attack. Different from probabilistic models, a sequential scaling attack is considered, in which specific attack properties, such as the attack duration and frequency, are defined. Moreover, to alleviate the utilization of communication resources, distributed static and dynamic event-triggered control protocols are proposed and analyzed, respectively. This article aims at providing a resilient event-triggered framework to defend a kind of sequential scaling attack by exploring the relationship among the attack duration and frequency, and event-triggered parameters. First, the static event-triggered control is studied, and sufficient consensus conditions are derived, which impose constraints on the attack duration and frequency. Second, a state-based auxiliary variable is introduced in the dynamic event-triggered scheme. Under the proposed dynamic event-triggered control, consensus criteria involving triggering parameters, attack constraints, and system matrices are obtained. It proves that the Zeno behavior can be excluded. Moreover, the impacts of the scaling factor, triggering parameters, and attack properties are discussed. Finally, the effectiveness of the proposed event-triggered control mechanisms is validated by two examples.

Input to state stabilization of networked systems under a specified packet dropout rate

This paper studies an input to state stabilizing control of networked control systems (NCSs) under a specified packet dropout rate. By considering packet dropouts in the NCSs, the transmission intervals are categorized by small delay intervals (packet-dropout-free case) and large delay intervals (packet-dropout case). Based on such classifications, we establish the concept of average packet dropout rate (ADR) to characterize the quality of service (QoS) for networks. Then, a switched systems approach is used to derive the ISS (input to state stability) conditions by exploiting Lyapunov theory and input delay approach for a specified ADR. In what follows, the controller design method for the NCSs under a specified ADR is reached by solving linear matrix inequalities (LMIs). According to the proposed results, a control and communication co-design method is developed such that one can design the controller gain according to QoS. Finally, simulations on self-steering control of autonomous vehicles are presented to verify the effectiveness of the proposed co-design method.

Secure State Estimation With Switched Compensation Mechanism Against DoS Attacks

This article is concerned with the secure state estimation problem for cyber-physical systems under intermittent denial-of-service (DoS) attacks. Based on a switching scheme and the cascade observer technique, a novel resilient state observer with a switched compensation mechanism is designed. Moreover, a quantitative relationship between the resilience against DoS attacks and the design parameters is revealed. Compared with the existing results, where only the boundedness of the estimation error is guaranteed under DoS attacks, the exponential convergence of the estimation error is achieved by employing the proposed observer scheme, such that the estimation performance is improved. More specifically, in the disturbance-free case, it is proven that the state estimation error converges exponentially to 0 despite the existence of DoS attacks. Finally, simulation results are provided to illustrate the effectiveness and merits of the proposed methods.

Leader-following consensus for multi-agent systems subject to cyber attacks: Dynamic event-triggered control

This paper addresses the event-triggered consensus problem for multi-agent systems (MASs) under cyber attacks in the leader-following framework. Via introducing a recoverable cyber attack and dynamic event-triggered mechanism (DEM), the centralized and distributed event-triggered controllers are co-designed. Meanwhile, some dynamic triggering criteria are given to ensure the MASs can achieve consensus. The DEM contains time-varying dynamic parameters, which can extend the interevent time interval to avoid Zeno phenomenon. The simulation results verify the effectiveness of the proposed scheme.

Observer-Based Security Control for Interconnected Semi-Markovian Jump Systems With Unknown Transition Probabilities

This article investigates the issue of observer-based security control for the interconnected semi-Markovian jump systems with completely unknown and uncertain bounded transition probabilities (TPs). Considering the limited bandwidth of communication network in each subsystem, an adaptive event-triggered mechanism (AETM) is developed to relieve more network burden than the conventional event-triggered mechanism (ETM), where the designed adaptive law can dynamically adjust the triggering threshold. In addition, two Bernoulli distributed variables are utilized to describe the influence of denial-of-service (DoS) attacks and false-data injection (FDI) attacks in the proposed observer-based security control strategy. Moreover, some sufficient criterions are derived for the stochastic stability with an H_∞ attenuation level of augmented systems. Meanwhile, the observer and controller gain matrices can be attained simultaneously with the help of linear matrix inequalities (LMIs). Finally, we provide a practical example to demonstrate the effectiveness of theoretical results.

Event-Triggered Impulsive Control for Nonlinear Stochastic Systems

We study the stabilization problem for nonlinear stochastic systems via an event-triggered impulsive control (ETIC) scheme, where the impulsive control time sequence is generated by the event-triggered mechanism (ETM). Both continuous ETM and periodic ETM are developed by continuous measuring and periodic sampling, respectively. The continuous ETM with time regularization is proposed to exclude the Zeno behavior. The upper bound of the sampling period is given for the periodic ETM. By means of the continuous ETM and periodic ETM, sufficient conditions are given to guarantee the p th moment uniform stability and the p th moment exponential stability of related systems. Moreover, LMI-based conditions of exponential stability in the mean square are established for linear stochastic systems under ETIC. Finally, two examples are presented to illustrate the proposed ETIC schemes, in which an example of the consensus of linear stochastic multiagent systems is considered.

Static and Dynamic Event-Triggered Mechanisms for Distributed Secondary Control of Inverters in Low-Voltage Islanded Microgrids

Due to the high resistance/reactance (R/X) ratio of a low-voltage microgrid (LVMG), virtual complex impedance-based P-· V/Q-ω droop control is adopted in this article as the primary control (PC) technique for stabilizing the system. A distributed event-triggered restoration mechanism (ETSM) is proposed as the secondary control (SC) technique to restore the output-voltage frequency and improve power sharing accuracy. The proposed ETSM ensures that neighboring communication happens only at some discrete instants when a predefined event-triggering condition (ETC) is fulfilled. In general, the design of the ETC is the crucial challenge of an event-triggered mechanism (ETM). Thus, in this article, a static ETM (SETM) is proposed as the ETC at first, where two static parameters are utilized to reduce the triggering frequency. Bounded stability is ensured under the SETM, which means that the output-voltage frequency is restored to the vicinity of its nominal value, and close to fair utilization of the distributed generators (DGs) is achieved. To further improve the power sharing accuracy and accelerate the regulation process, a dynamic ETM (DETM) is then introduced. In the DETM, two dynamic parameters that converge to zero in the steady state are designed, which promises asymptotic stability of the system. Besides, Zeno behavior is excluded in both mechanisms. An LVMG consisting of four DGs is constructed in MATLAB/Simulink to illustrate the effectiveness of the proposed methods, and the simulations correspond with our theoretical analysis.

Security Control of Multiagent Systems Under Denial-of-Service Attacks

Security control aims to guarantee the consensus of multiagent systems (MASs) in the presence of the denial-to-service attacker. Most of the existing distributed controllers are invalid during the attack interval due to the paralyzed communication channels. In order to overcome this difficulty, a novel hybrid distributed control protocol is designed. Here, the controller uses the latest information saved in the buffers in the presence of malicious attacks, which will further enhance the security of MASs. Some sufficient conditions on the coupled strength and attack parameters are derived to achieve the leader-following consensus of MASs. Furthermore, we estimate the upper bounds of denial-of-service (DoS) frequency and DoS duration which the MASs can tolerate before losing consensus. Notice that we also reduce the computational complexity via the property of the Kronecker product. Besides, an observer-based model is proposed and the corresponding consensus criterion is established to reduce the effects of attackers on the controller. Finally, the efficiency of our theoretical results is illustrated by a numerical example.

A Unified Optimization for Resilient Dynamic Event-Triggering Consensus Under Denial of Service

This article proposes a resilient framework for optimized consensus using a dynamic event-triggering (DET) scheme, where the multiagent system (MAS) is subject to denial-of-service (DoS) attacks. When initiated by an adversary, DoS blocks the local and neighboring communication channels in the network. A distributed DET scheme is utilized to limit transmissions between the neighboring agents. A novel convex optimization approach is proposed that simultaneously co-designs all unknown control and DET parameters. The optimization is based on the weighted sum approach and increases the interevent interval for a predefined consensus convergence rate. In the presence of DoS, the proposed co-design framework is beneficial in two ways: 1) the desired level of resilience to DoS is included as a given (desired) input and 2) the upper bound for guaranteed resilience associated with the proposed co-design approach is less conservative (larger) compared to those obtained from other analytical solutions. A structured tradeoff between relevant features of the MAS, namely, the consensus convergence rate, frequency of event triggerings, and level of resilience to DoS attacks, is established. Simulations based on nonholonomic mobile robots quantify the effectiveness of the proposed implementation.

Zonotopic Fault Detection for 2-D Systems Under Event-Triggered Mechanism

This article studies the problem of event-triggered fault detection (FD) for 2-D systems subjected to amplitude-bounded exogenous disturbance and measurement noise via a zonotopic residual evaluation mechanism. An event-triggered mechanism is introduced into the FD framework to save limited communication resources. A finite-frequency (FF) mixed l_∞/h_∞ index is derived to ensure the residual signal is sensitive to a fault signal while robust to disturbance and noise, based on which an optimal mixed l_∞/h_∞ FD filter design criterion is provided. Instead of constant thresholds, novel zonotope-based dynamic thresholds are utilized for residual evaluation. Finally, simulation results are presented to illustrate the effectiveness of the developed mechanism.

Resilient Control for Wireless Cyber-Physical Systems Subject to Jamming Attacks: A Cross-Layer Dynamic Game Approach

For wireless cyber-physical systems (CPSs) suffering jamming attacks, an optimal resilient control method is proposed through a novel cross-layer dynamic game structure in this article. To confirm to practical conditions of the cyber-layer, incomplete communication information is taken into consideration, and a Bayesian Stackelberg game approach is utilized to model interactions between a smart jammer and a cyber-user. Then, an H_∞ optimal resilient controller is studied for the closed-loop system with jam-induced packet losses and external disturbance in the sense of physical layer. With assumptions that the smart jammer has abilities of decoding system inputs and states, the changes of the jamming strategy are studied, and a coupled design between cyber and physical layers is presented with an algorithm to depict the dynamic variations of the CPSs. Moreover, the convergence of the proposed algorithm is also discussed. To validate the advantages of the proposed methods, a numerical simulation is performed in the end.

Observer-based state feedback H∞ control for offshore steel jacket structures under denial-of-service attacks

This article focuses on observer-based state feedback H_∞ control for a jacket structure against DoS attacks and external wave loads. First, a networked model of the structure is formulated as a switched delay system, in which DoS attacks and network-induced delays are considered simultaneously. A matching switched observer is developed for estimating states of the networked jacket structure system. Then, some new sufficient conditions are provided for the observer-based networked H_∞ controller for the resultant switched system. Finally, it is shown from several case studies that the provided mechanism can maintain desired performance of the jacket structure against attacks and wave loads. In addition, the developed control schemes can save the control cost significantly.

Event-based asynchronous and resilient filtering for Markov jump singularly perturbed systems against deception attacks

The dynamic event-based asynchronous and resilient dissipative filter design for Markov jump singularly perturbed systems (MJSPSs) against stochastic deception attacks is discussed in this paper. Firstly, a novel dynamic event-based transmission protocol is provided to further decrease the proportion of sampled data into network. The effect of deception attacks is formulated as a random variable satisfying the Bernoulli distribution. And an asynchronous filter is delicately constructed. Based on the technique of linear matrix inequality (LMI), efficient criteria of stochastically stable for the filtering error systems with a predetermined dissipative performance are obtained. An effective method of jointly design the proposed dynamic event-triggered transmission protocol and the non-synchronous filter is offered. Lastly, a numerical instance and a resistance-capacitance (RC) circuit system are provided to display the effectiveness and the benefit of the developed method.

Distributed Secure Consensus Control With Event-Triggering for Multiagent Systems Under DoS Attacks

Consensus control of multiagent systems (MASs) has applications in various domains. As MASs work in networked environments, their security control becomes critically desirable in response to various cyberattacks, such as denial of service (DoS). Efforts have been made in the development of both time- and event-triggered consensus control of MASs. However, there is a lack of precise calculation of control input during the attacking periods. To address this issue, a distributed secure consensus control with event triggering is developed for linear leader-following MASs under DoS attacks. It is designed with a dual-terminal event-triggered mechanism, which schedules information transmission through two triggered functions for each follower: one on the measurement channel (sensor-to-controller) and the other on the control channel (controller-to-actuator). To deal with DoS attacks, the combined states in the triggered functions are replaced by their estimations from an observer. Sufficient conditions are established for the duration and frequency of DoS attacks. To remove continuous monitoring of the measurement errors, a self-triggered secure control scheme is further developed, which combines the system states and other information at past triggered instants. Theoretical analysis shows that the followers in MASs under DoS attacks are able to track the leader and meanwhile the Zeno behavior is excluded. Case studies are conducted to demonstrate the effectiveness of our distributed secure consensus control of MASs.

Resilient Tracking Control of Networked Control Systems Under Cyber Attacks

This article is concerned with the resilient tracking control of a networked control system under cyber attacks. The attacker is an active adversary whose aim is to severely degrade the tracking performance of the system by launching deception attacks on the sensor-to-controller communication channels and denial-of-service attacks on the controller-to-plant channels, respectively. First, a concept of resilient set-membership tracking control is presented, through which the system's true state is guaranteed to reside in a bounding ellipsoidal set of the reference state regardless of the existence of attacks and unknown-but-bounded (UBB) noises. Second, in the case that full information of the system's state is not implicitly trusted in the presence of attacks, a resilient set-membership estimation strategy is provided to secure the state estimates against the deception attacks. Furthermore, based on a recursive computation of a reference state ellipsoid and confidence state estimation ellipsoids, a convex optimization algorithm in terms of recursive linear matrix inequalities is proposed to obtain the gain parameters for both the desired resilient state estimator and the tracking controller. Finally, the effectiveness of the proposed method is illustrated through an Internet-based three-tank system.

An Analysis on Optimal Attack Schedule Based on Channel Hopping Scheme in Cyber-Physical Systems

In this paper, we investigate the issue of security on the remote state estimation in cyber-physical systems (CPSs), where a wireless sensor utilizes the channel hopping scheme to transmit the data to the remote estimator over multiple channels in the presence of periodic denial-of-service attacks. Assume that the jammer can interfere with a subset of channels at each attack time in active period. For an energy-constraint jammer, the problem of how to select the number of channels at each attack time to maximally deteriorate the CPS performance is investigated. Based on the index of average estimation error, we introduce two different attack strategies, which include selecting identical number of channels and unequal number of channels at each attack time, and further show theoretically that the attack effect by selecting unequal number of channels is better than that of selecting identical number of channels. By formulating the problem of selecting the number of channels as integer programming problems, we present the corresponding algorithm to approximate the optimal attack schedule for both cases. The numerical results are presented to validate the theoretical results and the effectiveness of the proposed algorithms.

Observer-Based Event-Triggered Predictive Control for Networked Control Systems under DoS Attacks

This paper studies the problem of DoS attack defense based on static observer-based event-triggered predictive control in networked control systems (NCSs). First, under the conditions of limited network bandwidth resources and the incomplete observability of the state of the system, we introduce the event-triggered function to provide a discrete event-triggered transmission scheme for the observer. Then, we analyze denial-of-service (DoS) attacks that occur on the network transmission channel. Using the above-mentioned event-triggered scheme, a novel class of predictive control algorithms is designed on the control node to proactively save network bandwidth and compensate for DoS attacks, which ensures the stability of NCSs. Meanwhile, a closed-loop system with an observer-based event-triggered predictive control scheme for analysis is created. Through linear matrix inequality (LMI) and the Lyapunov function method, the design of the controller, observer and event-triggered matrices is established, and the stability of the scheme is analyzed. The results show that the proposed solution can effectively compensate DoS attacks and save network bandwidth resources by combining event-triggered mechanisms. Finally, a smart grid simulation example is employed to verify the feasibility and effectiveness of the scheme's defense against DoS attacks.

Memory-Based Event-Triggering H∞ Load Frequency Control for Power Systems Under Deception Attacks

This article proposes a memory-based event-triggering H_∞ load frequency control (LFC) method for power systems through a bandwidth-constrained open network. To overcome the bandwidth constraint, a memory-based event-triggered scheme (METS) is first proposed to reduce the number of transmitted packets. Compared with the existing memoryless event-triggered schemes, the proposed METS has the advantage to utilize series of the latest released signals. To deal with the random deception attacks induced by open networks, a networked power system model is well established, which couples the effects of METS and random deception attacks in a unified framework. Then, a sufficient stabilization criterion is derived to obtain the memory H_∞ LFC controller gains and event-triggered parameters simultaneously. Compared with existing memoryless LFC, the control performance is greatly improved since the latest released dynamic information is well utilized. Finally, an illustrative example is used to show the effectiveness of the proposed method.

Event-Based Secure Consensus of Mutiagent Systems Against DoS Attacks

This paper studies the problem of event-triggered secure consensus for multiagent systems subject to periodic energy-limited denial-of-service (DoS) attacks, where DoS attacks usually prevent agent-to-agent data transmission. The DoS attacks are assumed to occur periodically based on the time-sequence way and the period of DoS attacks and the uniform lower bound of the communication areas are predetected by some devices. Based on the above assumptions, an event-based protocol consisting of two different measurements corresponding to leader-followers and follower-follower is presented to schedule communications between agents, which can reduce the update frequency of the controller. Then, the stability of the resultant error system is analyzed to derive sufficient conditions of achieving secure consensus by employing the Lyapunov function and the inductive approach. Besides, positive low bounds on any two consecutive intervals of events generated by individual events are calculated to eliminate "Zeno behavior" under the developed triggering condition and event-triggered protocol. Simulation result is provided to verify the theoretical analysis.

Resilient Event-Triggered Control for LFC-VSG Scheme of Uncertain Discrete-Time Power System under DoS Attacks

This paper is concerned with resilient triggered control problem for load frequency control and virtual synchronous generation (LFC-VSG) scheme of discrete-time multi-area power system with parameter uncertainty, governor dead band (GDB), and low inertia under time delay and aperiodic Denial-of-Service (DoS) attacks. To reduce communication load of sleep intervals, event triggered mechanism (ETM) is introduced. A discrete-time switched delay system model is established to describe the dynamic of multi-area power system under resilient static output feedback control law. Combining piecewise Lyapunov–Krasovskii functional (LKF) method with switched system theory, a criterion is derived that the tolerant bound of attack duration and attack frequency can be estimated explicitly. Meanwhile, some sufficient conditions are obtained which can preserve weighted H ∞ performance. By using linear matrix inequalities (LMIs) techniques, a co-design method is proposed to solve the control gains and trigger parameters. A simulation example of a two-area power system was carried out to verify the efficiency of our proposed resilient event based LFC-VSG scheme.

A Sparse Neural Network Based Control Structure Optimization Game under DoS Attacks for DES Frequency Regulation of Power Grid

With the rapid growth of distributed energy sources, power grid has become a flexible and complex networked control system. However, it increases the chances of being a denial-of-service attack, which degrades the performance of the power grid, even causing cascading failures. To mitigate negative effects from denial-of-service attack and enhance the reliability of the power grid, we propose a networked control system structure based optimization scheme that is derived from a Stackelberg game model for the frequency regulation of a power grid with distributed energy sources. In the proposed game model, both denial-of-service attacker and control system designer as a defender are considered without using any analytical model. For defenders, we propose a sparse neural network based DES control and system structure design scheme. The neural network is used to approximate the desired control output and reinforce signals for the improvements of short- and long-term performance. It also introduces the sparse regulation of column grouping in the neural network learning process to explore the structure of control system that involves the placement of sensor, distributed energy sources actuator, and communication topology. For denial-of-service attackers, the related attack constraints and attack rewards are established. The solution of game equilibrium is considered as an optimal solution for both denial-of-service attack strategy and control structure. An offline optimization algorithm is proposed to solve the game equilibrium. The effectiveness of proposed scheme is verified by two cases, which illustrate the optimal solutions of both control structure and denial-of-service attack strategy.