This paper explores the security control problem of a class of hyperbolic partial differential equation (PDE) systems described by a set of nonlinear ordinary differential equation (ODE) under deception attacks. Compared with the control design process of traditional single ODE systems, the strong coupling characteristics of partial differential equation-ordinary differential equation (PDE-ODE) systems make the control design under deception attacks more difficult. By applying the infinite-dimensional backstepping transformation and its inverse transformation, the original PDE subsystem is transformed into a more tractable target system, thus effectively achieving control performance. The neural network approximation algorithm is adopted to separate the coupling effects caused by attacks, focusing on addressing the unknown nonlinear dynamics of the system. Deception attacks are modeled as time-varying weights with unknown control directions, and the Nussbaum function is employed to address the problem of unknown control directions. In addition, a dynamic event-triggered mechanism with a novel switching threshold is designed to alleviate the communication burden. The proposed control algorithm ensures that both the closed-loop system states and the actuator states are bounded. Finally, this conclusion is verified through numerical simulation.

In this paper, an adaptive time-varying formation optimal tracking control strategy is presented for nonlinear heterogeneous multi-agent systems (MASs) with performance constraints and unknown dynamics. A prescribed-time performance function is designed to quantify the tracking error constraints, while an error transformation function is introduced to eliminate initial value constraints and address singularity issues. Notably, the settling time and initial conditions of the performance function are independent of both the initial tracking error and system parameters. To facilitate reinforcement learning (RL)-based optimal formation control, a performance index function is formulated that incorporates the transformed tracking error, control input, and an exponentially discounted term. This design effectively avoids infinite integral values and ensures minimization of the index function. Moreover, stability analysis demonstrates that the time-varying formation tracking errors converge to the desired accuracy within a prescribed time, regulated by a sliding-mode control mechanism. Finally, numerical simulations on two practical examples validate the feasibility and effectiveness of the proposed control strategy.

This paper concentrates on a fault detection-based performance recovery control scheme using an actuator replacing method. The main procedure includes: 1) an integral sliding-mode (ISM) based event-triggered nominal controller; 2) a shifting-function-assisted fault detection design; and 3) an event-triggered reconfigurable controller. Unlike existing FTC schemes, no prior fault model is required. Minor actuator faults are directly attenuated via ISM, whereas significant faults are handled by switching to a backup actuator. For both nominal and reconfigurable phases, a modified Hamilton-Jacobi-Bellman (HJB) equation is solved with a single critic neural network, and an experience replay mechanism mitigates the persistence of excitation requirement while reducing computational complexity. A shifting function guarantees that post-replacement reconstructed states re-enter the prescribed performance bound within a finite window, and an actuator-oriented event-triggered strategy lowers update frequency while ensuring single-actuator operation. The effectiveness of the proposed scheme is validated by two simulation examples.

This article proposes a novel observer-based adaptive neural network-based resilient consensus control approach to address hybrid cyberattacks, disturbances, and nonlinear dynamics in nonlinear leader-following multiagent systems (MASs). Specifically, a dimension expansion methodology is developed to dynamically model and compensate for false data injection (FDI) attacks, while denial-of-service (DoS) attacks are probabilistically characterized via Bernoulli variables, forming a comprehensive hybrid attack mitigation strategy. Then, a cascaded observer is designed, integrating dimension-extended system modeling with disturbance decoupling to simultaneously estimate system states and external disturbances with high precision. Furthermore, an adaptive neural network-based approximation scheme is employed to handle system nonlinearities, eliminating the conservatism of Lipschitz-based methods while enhancing robustness in complex environments. Finally, the simulation result validates that the proposed control method achieves resilient consensus of leader-following MASs under hybrid cyberattacks, disturbances, and nonlinear dynamics.

This article investigates the issue of composite anti-disturbance and attack control for networked systems under unknown actuator attacks and external disturbances. First, a double-ended event-triggering mechanism is designed to reduce unnecessary data transmission in the feedforward and feedback channels. Second, an augmented observer is designed to estimate the system states and disturbances. The intermittent estimation signal is then used to compensate for external disturbances through a novel trigger sampling mechanism. Third, the fuzzy logic system is used to approximate the unknown attack signal, and an adaptive output feedback controller is employed to mitigate its impact on the system. Based on these three key techniques, a novel functional dependent on the sampling instants is constructed to analyze semi-global uniform ultimate boundedness of the closed-loop system and obtain the criterion condition of low conservatism. Additionally, the event-triggering matrix and gains are explicitly solved by matrix transformation. Finally, the feasibility and effectiveness of the proposed method are validated via a visual servo control system and a third-order system.

This article investigates the issue of event-triggered tracking control for Takagi–Sugeno fuzzy systems subject to hybrid attacks. First, the deception attacks occurring on the feedback channel are considered using a Bernoulli process, in which an attacker injects state-dependent malicious signals. Next, the minimal ‘silent’ and maximal ‘active’ periods are defined to describe the duration of aperiodic denial-of-service (DoS) attacks. To take advantage of communication bandwidth and resist DoS attacks, a sampled data-based resilient dynamic event-triggered strategy is designed. Then, an event-based fuzzy tracking controller is designed to guarantee the stability of error system under hybrid attacks. Subsequently, sufficient conditions for the stability analysis are proposed by utilizing a fuzzy-basis-dependent Lyapunov-Krasovskii functional. Meanwhile, the control gains and event-triggering parameters are co-designed by applying linear matrix inequalities. Furthermore, the proposed method is extended to address the tracking control problem of multi-agent systems. Finally, the feasibility of the presented approach is validated by two examples.

This article addresses the real-time security reachable set (RS) control problem for nonlinear semi-Markov jump cyber–physical systems (s-MJCPSs) subject to multiple time-varying delays and actuator attacks. Then, based on the neural network (NN) approximation approach and employing a sliding mode control (SMC) strategy, an adaptive NN SMC scheme is proposed to tackle challenges arising from nonlinear attack functions and mode jumps. The proposed strategy ensures s-MJCPSs stability and mean-square boundedness of system states within a predefined RS. Sufficient conditions for real-time security RS control are derived. Finally, an example is presented to demonstrate the effectiveness of the proposed strategy in realizing adaptive real-time RS control.

This article proposes a sampled-data event-triggered adaptive neural network (NN) control strategy to cope with the digital communication and attack compensation problems of networked systems with actuator attacks and exogenous disturbance. By combining event triggering state, parameter estimation signals, and disturbance observer, a novel digital state feedback controller is designed to reduce its updating frequency and compensate for the deliberate impact of unknown actuator attacks. Moreover, considering that the state is partially measurable, a novel observer-based digital controller is designed via a double-ended event-triggering mechanism (ETM). Then, two new Lyapunov functionals are created to analyze the system stability, and two design methods are given to solve the control gain. Finally, the feasibility and validity of the derived results are verified by a visual servo control system and an offshore structure system.

Combining reinforcement learning (RL) and quantization methods, this article addresses the formation control problem for a class of multi-input multi-output (MIMO) nonlinear multi-agent systems (MASs) subject to denial-of-service (DoS) attacks. Since the information exchange between agents is destroyed by DoS attacks, the leader’s information becomes unavailable. Thus, a distributed formation estimator is designed to obtain the leader’s state. Next, by constructing an logarithmic quantizer, a new dynamic event-triggered quantized control strategy is studied to save communication resources. In order to satisfy both transient and steady-state performances, an improved funnel function is embedded in controller design. In addition, based on optimized backstepping technique, an actor-critic architecture is established to achieve optimized secure formation control by RL method. Finally, the simulation results verify the effectiveness of proposed control scheme.

In this paper, an observer-assisted model free adaptive predictive control algorithm is designed for nonlinear heterogeneous multi-agent systems under denial-of-service (DoS) attacks. To begin with, consensus error of the system is transformed into an equivalent linear data model at the operating point by means of a dynamic linearisation technique. Thereafter, in order to conserve network communication resources, a dynamic event-triggering mechanism is devised for the consensus error and an observer is incorporated to facilitate the acquisition of a time-varying parameter called "pseudo partial derivative" in the linear data model. Subsequently, to mitigate impact of random DoS attacks, we introduce an attack compensation strategy that allows each agent’s output to swiftly revert to the neighbourhood of leaderless consensus objective in DoS-free intervals. Finally, the pseudo partial derivative parameter estimates, observation errors, and consensus errors are rigorously proved to be bounded in mean using the contraction mapping principle. Simulation results on heterogeneous nonlinear multi-agent systems demonstrate that, compared with conventional event-triggered model free control, the proposed approach improves the convergence rate by 33.82%, reduces steady-state consensus error by 93.80%, and decreases pre-convergence fluctuations by 21.91%. Furthermore, it achieves a 64.00% faster recovery speed and a 95.98% higher recovery accuracy after DoS attacks. Meanwhile, the average communication load is reduced by 59.79%.

This paper studies the event-triggered time-varying formation control problem for nonlinear multi-agent systems with actuator faults. Based on the neural network approximation technique, a neural observer is constructed to estimate the unmeasured states of systems. Then, a distributed adaptive event-triggered time-varying formation control manner is proposed utilizing the intermittent estimated states information from the agent and its neighbors. To overcome the problem that estimated states triggering leads to virtual control laws is non-differentiable, a distributed continuous control scheme under regular output-feedback is designed firstly, upon which a distributed event-triggered controller is constructed by replacing estimated states with intermittent estimated ones. It is shown that the designed event-triggered output-feedback time-varying formation fault-tolerant controller can compensate for actuator faults, and all signals in closed-loop systems are semi-globally uniformly ultimately bounded. Finally, simulation results of a practical example are given to verify the effectiveness of the proposed control manner.Note to Practitioners—Formation control has broad application prospects in modern military and civilian fields, such as combat aircraft flying formation, satellite formation, autonomous vehicle formation, etc. In formation control systems, when agents occur actuator faults, it may break the original formation and even cause collision between agents. As a result, the security of formation control systems is facing great challenges in practical engineering applications. On the other hand, communication bandwidth is limited in practical engineering systems, and how to make systems quickly form formation under the limited communication bandwidth has become a key topic. Inspired by the above discussions, a distributed state-triggered output-feedback time-varying formation fault-tolerant control scheme is designed in this paper, in which actuator faults are compensated by using adaptive technology. Meanwhile, to sufficiently save the usage of system communication resources, a dual-channel event-triggered mechanism is designed.

This paper focuses on the membership-functions-dependent reachable set (RS) synthesis of a class of Takagi-Sugeno (T-S) fuzzy singular multi-agent systems subject to deception attacks. To do this, with the help of the T-S fuzzy model, the nonlinear system model is transformed into a quasi-linear system. Then, the control method in the linear system is used to solve this kind of nonlinear problem. Firstly, two suitable non-singular value matrices M and N are obtained by singular value decomposition, and then the singular system is decomposed into algebraic subsystem and differential subsystem by matrices M and N. Secondly, a consensus topology with communication delay under deception attack is designed. In this cases, the sufficient conditions of RS for the simultaneous existence of external disturbances and deception attacks are given, and the specific value of the RS is obtained by solving the linear matrix inequality using the matrix decoupling method. Finally, the effectiveness of the proposed method is verified by taking the actual DC motor built on the physical platform and a class of nonlinear single-species bio-economic system as examples.Note to Practitioners—In the context of contemporary huge industry and engineering, while rapid development, security is also one of the issues that must be considered. However, the modern engineering system has the characteristics of complexity and variability, and a single module cannot operate it completely, so multiple separate modules need to work together through a unique connection. For this reason, security issues will become much more difficult. In addition, in modern network engineering, there are often some criminals who destroy the system, resulting in its normal operation, economic losses, serious situations, or endanger personal safety. Such behavior is usually called network attacks. Deception attacks are part of network attacks, which can harm the system by spreading false information. Therefore, in researching security issues, deception attacks need to be paid attention. Based on the above analysis, the membership-functions-dependent reachable set synthesis of a class of Takagi-Sugeno fuzzy singular multi-agent systems subject to deception attacks is studied in this paper.

This paper tackles the security cooperative tracking control problem for uncertain heterogeneous nonlinear multi-agent systems (MASs) subject to denial-of-service (DoS) attacks. Since the communication between agents can only transmit digital signals, a periodic sampling mechanism is used to reduce bandwidth pressure. Based on these digital signals, a novel distributed switching observer is designed to estimate the state of the reference system for each follower in the case of DoS attacks on aperiodic intermittently blocked communication channels. Then, an attack-parameter-dependent Lyapunov functional is established to analyze the exponential convergence of the error signals and a design scheme of observer gains is proposed. Further, with the help of the sampling observer outputs, follower’s states and adaptive signals, a sampled-data neural network controller is designed to guarantee the boundedness of the tracking errors by backstepping method and impulsive system analysis theory. Finally, a simulation example is performed to showcase the effectiveness of the developed strategy. Note to Practitioners—In industrial systems, since it is difficult for a single plant to complete complex control tasks, the cooperative control of MASs has gradually become a hot research issue. For example, in industrial automated production, a single robotic arm cannot achieve mass production of products, while multiple robotic arms can achieve this task and improve production efficiency. In this context, the study on cooperative control of MASs is of great scientific and economic value. The wireless communication network is the medium of information transfer between the agents and the controllers, while giving attacker an opportunity to attack. When network interaction information is affected by attacks, the performance and stability of the system are easily damaged. Moreover, under the condition of ensuring the performance of the system, the number of packet transmission is as small as possible, which will be conducive to the applications with limited bandwidth or congested network. Taking these problems into consideration, this paper studies sampled-data tracking control for uncertain heterogeneous nonlinear MASs under DoS attacks. This result provides a reference for the design of digital security controller, and can also be applied to intelligent engineering systems.

This article addresses the periodic event-triggered adaptive output feedback control problem for networked system with unknown nonlinear dynamics. Based on the output-dependent periodic event-triggered mechanism (PETM), a nonlinear observer is designed to estimate system states, where the fuzzy-logic systems-based approximation method and adaptive technique are employed to approximate and compensate for uncertainties. To enhance resource utilization efficiency in communication channels, a new observer and parameter estimators-dependent parallel PETM is proposed to schedule intermittent packet transmission. Then, a digital controller is designed to reduce frequent control updating. By constructing novel piecewise Lyapunov functional, it is proven that the underlying system states, the observation error signals and parameter estimation signals are semiglobally uniformly ultimately bounded. In addition, the proposed control method is applied to solve the stabilization problem of networked interconnected systems. Finally, a numerical simulation is performed to show the efficiency of the developed control method.

In this article, the problem of reachable set (RS) synthesis for a class of nonlinear delayed hidden semi-Markov jump systems with actuator saturation and multiple cyberattacks is addressed. First, a dynamic-event-triggered mechanism (DETM) with a time-varying additional threshold is introduced, which can save communication resources more effectively. However, due to the introduction of DETM, the modes of the controller and the system exhibit asynchronous behavior. On the other hand, while network communication facilitates signal transmission, it also exposes the system to an open environment vulnerable to cyberattacks. To address these issues, we devise a security asynchronous controller based on the hidden Markov model. In addition, this article also considers a class of actuator saturation problem. After that, the sufficient conditions for RSs are obtained by applying the stability theory of Lyapunov functional and linear matrix inequalities. The controller gains are obtained by the matrix decoupling method. Finally, the feasibility and practicability of the method are verified by the circuit model and a numerical simulation.

This article presents a co-design method of dynamic periodic event-triggering mechanism (DPETM) and output-based control law for networked control systems (NCSs) subject to inevitable imperfections such as limited network resources, exogenous disturbances and successive packet dropouts. The developed DPETM has the potential to make full use of scarce network resources compared to the periodic sampled-data control on the one hand, and is natural for practical digital platforms instead of a discretized version of continuous event-triggered control (CETC) one the other hand. In this paper, the whole closed-loop system is modeled a unified hybrid system by incorporating bilateral DPETM, successive packet dropouts effects and external disturbances, and an improved hybrid Lyapunov function is constructed for stability analysis. Based on the hybrid framework, some sufficient conditions are presented to guarantee$\mathcal {L}_{2}$-stability of the system while tolerating a maximum allowable number of successive packet dropouts (MANSD). Furthermore, new linear matrix inequality (LMI) conditions for co-design of control law and triggering strategy are derived by introducing some constraints with the free variables and a modified Young’s inequality. In addition, this paper considers two scenarios relating to whether an acknowledgment scheme is employed or not. Finally, the effectiveness of the proposed method is verified by two illustrated examples and comparative studies. Note to Practitioners—With the increasing requirement for reducing unnecessary waste of communication resources in modern industries, it is necessary to consider an alternative paradigm of the time-triggered control. In many digital control applications such as smart power grid, vehicle and remote surgery, the control tasks are often executed periodically, which makes it difficult for the theoretical results of CETC to be directly applied to practical digital platforms. The DPETM proposed in this paper, which only verifies the triggering conditions periodically at each sampling instant, is more suitable for practical digital platforms such as time-sliced embedded architectures compared to CETC. This paper investigates the stability problem for NCSs with DPETM subject to packet dropouts. Different from most of the existing literature on randomness of packet loss, this paper focuses on impact of the continuity of packet dropouts on system performance. Based on the hybrid framework and the Lyapunov approach, a co- design methodology of triggering condition and control law is proposed to ensure that the system satisfies the desired performance and can admit a MANSD.

This paper concentrates on the real-time reachable set synthesis of heterogeneous nonlinear singular multiagent systems with uncertain parameters based on adaptive fault-tolerant control under non-zero initial conditions. A proportional and differential-like adaptive fault-tolerant control protocol is designed to respond to this problem, and a closed-loop singular multiagent system is built through this control protocol. Then a Lyapunov function suitable for the system is constructed, and it is proved that when there is a fault in the system, the error system will ultimately converge to the neighborhood near the origin. In addition, using the free-weighting matrices strategy and particular decoupling method to solve the linear matrix inequalities, the real-time reachable set boundary of the closed-loop singular multiagent control system and the gains of the designed controller are obtained. Finally, the efficacy of the presented strategy is demonstrated by practical examples of multiagent support systems and the DC motor models.Note to Practitioners—Because of the complex and changeable characteristics of a modern engineering system, it can not be operated by a single module, so the research of multiagent systems has become the mainstream trend of modern system research. In the actual project, the safety problem must be addressed. Therefore, our main research content is how to make the machine or system model run within a more accurate security range. In practical applications, some random and unpredictable events often occur, which may lead to failures in the system and make the system unable to operate properly. These behaviors may lead to unknown security problems. When we study security issues, we need to consider the occurrence of this situation. Therefore, when a fault occurs in the system, ensuring the system’s normal operation within the safe range is one of the key topics that need to be studied. Unlike ordinary systems, singular systems can more widely describe the actual system model. Therefore, the study of singular systems is indispensable in actual engineering system research. Based on the above analysis, the real-time reachable set synthesis of heterogeneous nonlinear singular multiagent systems with faults is studied, and the consensus protocol of the proportional and differential-like is designed.

This article proposes an adaptive fuzzy dual-channel event-triggered output feedback control approach for a class of multi-input-multi-output (MIMO) systems with deception attacks and input saturation. Due to the consideration of two pivotal factors simultaneously, including deception attacks and input saturation, the existing methods are difficult to be directly applied. To this end, a novel fuzzy state observer and an auxiliary system are constructed to address unavailable impaired system states and input saturation, respectively. Furthermore, by constructing a new transformation of coordinate and employing adaptive fuzzy technique and single parameter learning approach, the sensor deception attacks, fuzzy weight and external disturbance are reconstructed online into linear composite uncertain terms with single parameter under the framework of backstepping and dynamic surface design. Additionally, the communication and computation burden is significantly reduced by using fewer single-parameter adaptive laws and dual-channel event-triggered strategy (DCETS). The proposed control method guarantees that all signals within the closed-loop system are bounded. Meanwhile, the Zeno behavior is avoided. Finally, a simulation example is provided to verify the availability of the presented approach.

This article focuses on the problem of resilient event-triggered$H_{\infty }$filtering for networked switched Takagi–Sugeno (T-S) fuzzy systems in the presence of Denial-of-Service (DoS) attacks. To improve the utilization efficiency of communication resources and resist the influence of attacks, the resilient mode-dependent event-triggered strategy (ETS) is proposed to determine the necessary data transmission. Different from the existing ETSs for the switching linear systems, the proposed strategy not only removes the two adjacent trigger instants that are strictly less than the average dwell time constraint but also releases data immediately at the end of the attack to mitigate its side effects. Based on the transmitted switching signal and measurable output, the switching fuzzy filter is constructed to estimate the target signal. Unlike the traditional switching filter design, the transmission signals are affected by intermittent interruption of DoS attacks and ETS leads to the asynchronous behavior of system mode and filter mode, which increases the difficulty of filtering error system analysis and filter design. To overcome this challenge, a novel multiple Lyapunov function related to attack signals, system modes, and filter modes is established to analyze the exponential stability and$H_{\infty }$performance of the estimation error system. Furthermore, co-design methods regarding filter gains and event-triggered parameters are given. Finally, simulation results are carried out to substantiate the feasibility of the proposed approach.

This article addresses the problem of event-triggered dynamic output feedback controller design for networked Takagi-Sugeno (T-S) fuzzy systems subject to actuator failure and deception attacks. In order to save network resources effectively, two event-triggered schemes (ETSs) are introduced to test whether the measurement output and control input are transmitted under network communication. While the ETS brings advantages, it also leads to a mismatch between the premise variables of the system and the controller. To solve this problem, an asynchronous premise reconstruct method is considered, which relaxes the condition of the previous results that the premises of the plant and the controller are synchronous. Furthermore, two crucial factors, including actuator failure and deception attacks, are taken into consideration simultaneously. Then, the mean square asymptotic stability conditions of the resultant augmented system are derived by utilizing the Lyapunov stability theory. Besides, controller gains and event-triggered parameters are co-designed with the help of linear matrix inequality techniques. Finally, a cart-damper-spring system and a nonlinear mass-spring-damper mechanical system are presented to verify the theoretical analysis.

This article investigates the problem of reachable set control for a class of discrete-time Takagi–Sugeno fuzzy singular Markov jump systems (T–S FSMJSs) with time-varying delay and disturbance for the first time. By designing the state feedback and output feedback controllers, and based on the Lyapunov functional, two new sufficient conditions for the reachable set control are established. The state feedback and output feedback controller gains are obtained by optimizing the iterative algorithm. Then, all the state trajectories of the closed-loop T–S FSMJSs are contained by the intersection of ellipsoids. Finally, two examples with practical application background are presented to show the validity and usability of the proposed methods.

This article investigates the hierarchical sliding-mode surface (HSMS)-based adaptive critic tracking control problem for nonlinear multiplayer zero-sum games (ZSGs). First, a generalized fuzzy hyperbolic model-based identifier is employed to approximate the unknown nonlinear functions. According to the derived data-driven model, a static control policy is proposed to transform the considered optimal tracking control problem into an optimal regulation control problem of an induced error system. Subsequently, based on sliding mode control technology and the concept of hierarchical design, a novel optimal feedback control policy is developed to regulate the tracking error by minimizing a performance index function related to the HSMS. The solution to the Hamilton–Jacobi–Isaacs equation of nonlinear multiplayer ZSGs is obtained via the HSMS-based critic neural network. Furthermore, the historical stored data are utilized to conquer the difficulty associated with the persistence of excitation conditions. Based on Lyapunov stability theory, it is strictly proven that the tracking error and the critic neural network weight are uniformly ultimately bounded. Finally, two examples are presented to demonstrate the effectiveness of the proposed control scheme.

The security control of a vehicle platoon depends on the network topology and communication quality. Denial of service (DoS) attacks force vehicle formations to destabilize by disrupting digital communications between vehicles. To this end, this paper develops a resilient distributed event-triggered security control strategy to resist the malicious impact of DoS attacks on connected vehicles. By designing a distributed event-triggered mechanism based on sampled data, the controller updating frequency is reduced, thereby promoting utilization rate of network resources. Since the end of the attack is not the sampling instant, this may prolong the duration of the attack. To overcome this problem, a switched sampled-data scheme is proposed to ensure that the control signal acts on the system immediately when the attack ends. Then, a switched system model with artificial delay is established to capture the sampling period, event triggering mechanism and DoS attack purpose. With the analysis methods of switched system and time-delay system, sufficient conditions are obtained to guarantee the same safe distance and speed between vehicles, so that the connected vehicle system can achieve the desired tracking effect. A co-design approach is given with respect to controller gains and triggering parameter. Finally, simulation and experimental studies are provided to demonstrate the effectiveness of the proposed security control method.

In this paper, the resilient controller design and synthesis issues of networked control systems under denial-of-service (DoS) attacks are investigated via an adaptive event-triggered strategy. In a networked control system, DoS attacks have serious impacts on the security of communication, possibly causing degraded stability performance of the system. To remove threats from DoS attacks, an adaptive event-triggered communication mechanism is proposed, which also provides benefits in reducing the consumption of communication resources and relieving the pressure on network bandwidth. Since the system state information is usually not fully known, an observer-based controller is developed to stabilize the system and maintain a desired performance index despite the occurrence of stochastic attacks. Furthermore, a joint design method is proposed to obtain the controller gain, observer gain and event-triggered weight matrix. Finally, practical examples based on a four-tank system, an Internet-based three-tank system and an Internet-based test rig system are presented to illustrate the effectiveness of the proposed techniques to respond and eliminate the impact of DoS attacks.

This article addresses the event-triggered tracking control and filtering problem for Takagi–Sugeno fuzzy-approximation-based discrete-time nonlinear networked systems subject to the effect of denial-of-service attacks. First, the unreliability of the communication channel between the sensor and the actuator/filter is considered, and the packet loss caused by denial-of-service attacks is characterized by the binary Markov chain. Second, two novel resilient adaptive event-triggered mechanisms are proposed to resist the impact of denial-of-service attacks and discard unnecessary data packets, in which the dynamic threshold variable is designed to adjust the event-triggered condition adaptively. A problem caused by the event-triggered mechanism is that the controller or filter cannot receive the system mode signal during the trigger interval. To surmount this problem, this article designs an estimator to compensate for the unavailable system mode. Then, an adaptive event-triggered controller or filter related to the estimated mode is designed to track the desired signal. Under this framework, by constructing a membership-function-dependent Lyapunov function, the conservativeness of the stability criterion is relaxed. Finally, two examples are used to validate the applicability of the proposed approaches.

This paper investigates the asynchronous event-triggered state-feedback control for discrete-time nonlinear singular Markov jump systems subject to reachable set bounding and stochastic cyber-attacks. An event-triggered mechanism is introduced to regulate data transmission and save network resources. While this mechanism brings advantages, it also causes that the mode information of the system and the controller are not synchronized. On the other hand, network communication has brought convenience to signal transmission, and it has also resulted in the network channel being in an open and unreliable environment, which is vulnerable to cyber-attacks. In order to solve these problems, the secure asynchronous controller is designed to effectively resist the influence of attacks. In addition, by using the reachable set analysis approach, the constructed controller ensures that the estimation error is within the boundary of the ellipsoid, and the existence conditions of the required controller are given by solving the linear matrix inequalities. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.

This paper investigates the decentralized event-triggered output feedback control for nonlinear networked interconnected systems under multiple cyber attacks, where denial of service and deception attacks are considered. A resilient period event-triggered strategy is adopted to reduce the occupation of network resources. Considering the impact of cyber attacks, the output-based decentralized security controller is constructed within a unified framework. Sufficient conditions of stochastically finite-time stable of the switched system are given by employing the Lyapunov-Krasovskii functional. Then, the controller gains and event-triggered weight matrix are designed simultaneously. Finally, a chemical reactor system is used to substantiate the effectiveness of the proposed method.