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.

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.

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.

This paper addresses the active disturbance rejection predefined-time consensus tracking problem for non-affine nonlinear multiagent systems (MASs) with self-triggered communication. With the active disturbance rejection strategy, the uncertainty of the system can be estimated and the issue of explosion of complexity under the backstepping framework is handled. To improve the utilization of network resources, a self-triggered mechanism that the next trigger moment is calculated from the current information is adopted, for communication of each follower. The advantage of this triggered mechanism is that the triggering conditions are not required to be continuously monitored. Meanwhile, a time-varying tuning function-based predefined-time method is designed to achieve convergence within the predetermined time. Compared with existing finite/fixed-time convergence consensus schemes, its biggest advantage is that the upper bound of convergence time can be a positive constant arbitrarily selected by users. Additionally, the problem of input saturation is considered in the controller design to improve the generality of our scheme. Finally, the effectiveness of the proposed scheme is verified via simulation example. Note to Practitioners—In this paper, the active disturbance rejection predefined-time consensus tracking control problem for MASs with non-affine properties is discussed, which is embodied in numerous applications, such as sensor networks, space satellites and robot formations. The convergence time required for all agents to conclude consensus is used as an important indicator to evaluate the control performance in the consensus control of MASs. The existing control methods including finite and fixed time methods can only achieve the system to converge in a preset time. Based on this, it is a challenging topic to achieve predefined-time convergence by setting the accurate convergence time t. Meanwhile, to improve the utilisation of network resources, a self-triggered mechanism is designed. The advantage of this triggered mechanism is that the triggering conditions are not required to be continuously monitored, which greatly reduces the control cost. Additionally, the problem of input saturation is considered in the controller design to improve the generality of our scheme.

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.

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 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 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 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.