The paper investigates the problem of distributed robust state estimation over wireless sensor networks for non- Gaussian systems under hybrid cyber-attacks, where both local measurements and exchanged information among neighboring nodes are subject to varying deception attacks. To overcome the limitations of the existing correntropy-based approach, an extended multi-kernel correntropy (MKC) is adopted to evaluate the similarity of different elements between stochastic vectors. Meanwhile, confronting the controversy of solving such maximum-a-posterior-like cost functions during the derivations of the posterior estimate, the half-quadratic optimization approach is employed to transform the maximization problem of non-convex functions into two convex optimization subproblems, and the final solution is obtained through an alternating iterative method. In addition, a novel inverse Kalman-type compensation mechanism is proposed within the MKC framework to compensate for the corrupted local exchanged estimations, which is then fused through the weighted average to yield the final estimation for each sensor of the distributed algorithm. Simulation results demonstrate that the proposed algorithms outperform related work in terms of estimation performance and robustness.

This article addresses the data-driven asynchronous dynamic event-triggeredH∞tracking control problem for singularly perturbed systems (SPSs) with unknown slow dynamics and unknown bounded disturbances. First of all, considering the two-time-scale characteristic of SPSs, anH∞tracking control problem for the slow subsystem and an asymptotic stability problem for the fast subsystem are formulated via time-scale decomposition. Secondly, an asynchronous dynamic event-triggered scheme (ETS) based on dual-rate sampling is proposed to reduce the communication burden. Then, a data-based parameterized model of the augmented system is given, which consists of the reference system and the slow subsystem with unknown dynamics. Further, by combining the data-based parameterized model and employing the full-block S-procedure, the data-based co-design method of tracking controller and event-triggered matrix is developed. The overall stability analysis of the full system under the composite controller is given. Finally, the proposed scheme is verified by a Chua’s circuit and a networked DC motor control system.

Flexible and efficient wide-load tracking in coal-fired power generation systems (CPGSs) is crucial for integrating renewable energy. To address the challenges arising from the dynamic characteristics and task distribution differences during the wide-load operation of thermal power units, this article proposes a novel hierarchical model-agnostic meta reinforcement learning (HMAMRL) framework. This framework combines inner meta-learning for quick adaptation within task categories and outer meta-learning for sharing general task knowledge, ensuring robust generalization under different load conditions. Meanwhile, an adaptive multicriterion reward function design method is proposed to dynamically balance load tracking costs, coal consumption costs, and input fluctuation costs. Moreover, a truncated proximal policy optimization (TPPO) algorithm ensures precise load control within physical constraints. Experimental results on the 160 and 1000 MW CPGSs demonstrate the effectiveness and superiority of the proposed algorithm.

This article investigates the differentially private leader-following consensus control (DPLFCC) problem for multiagent systems (MASs) operating on two-time scales. A new co-design framework with a private preserving scheme and a consensus controller is constructed by building a unique time-scale-dependent Lyapunov function. To achieve the ultimate mean-square leader-following consensus while maintaining differential privacy, the proposed strategy establishes a new distributed consensus controller with noise control for each follower. The initial state of the follower can be made more private by adjusting the noise control gain. It should be pointed out that controller-solving criteria and privacy level performances are designed depending on the time-scale parameter, thereby eliminating the numerical stiffness caused by the two-time-scale property. Furthermore, the results are extended to the leader's privacy-preserving situation. Finally, the effectiveness of the developed algorithm is illustrated by numerical simulation examples.

This article investigates how Denial-of-Service (DoS) attacks impact the time and energy costs (ECs) associated with the emergence of flocking dynamics in the Cucker-Smale system. We propose resilient finite-time and fixed-time control protocols against DoS attacks and establish conditions under which the Cucker-Smale (C-S) system can achieve flocking within a bounded time. The attack patterns are modeled stochastically and are constrained by the effective duration of the attack. Explicit upper bounds for both time and ECs are derived, demonstrating their dependence not only on the group size and control parameters, but also on the duration of DoS attacks. Theoretical analysis and numerical simulations consistently demonstrate that shorter attack durations facilitate faster convergence and lower energy consumption. Additionally, our analysis uncovers a tradeoff between time cost and EC under DoS attacks, suggesting that optimal communication intensity should be carefully adjusted to meet specific performance requirements of practical applications.

Accurate state estimation (SE) for systems affected by unknown non-Gaussian (NG) noise is significantly challenging, especially when compounded by hybrid cyberattacks. In this article, we investigate the fixed-interval smoothing problem for NG systems under such attacks. Since most attack detectors are susceptible to failure in these scenarios, we propose the flag-bit-based detection mechanism by expanding the measurement equation with a marking signal dedicated to identifying attacks exclusively. To improve the estimation accuracy of NG systems at risk of undetected attacks, the robust forward filtering and backward smoothing are derived by solving the new cost functions defined based on the proposed generalized statistical measure (GSM) with enhanced flexibility, based on which we obtain the new robust Rauch-Tung-Striebel smoother. The sufficient conditions for the convergence of both forward and backward passes are rigorously established, which provides the theoretical support of the proposed estimator in terms of optimality and uniqueness. Extensive simulations validate the lower false detection rate of the proposed detector and the improved estimation accuracy of the proposed smoother compared to related works under various noise and attack conditions.

The letter addresses the robust state estimation problem of non-Gaussian systems disturbed by outliers. Unlike the existing correntropy-based state estimation framework, which uses a uniform weight for the evaluated error vectors and solely relies on inaccurate nominal covariance matrices for estimating the system state, this work proposes a novel maximum-correntropy Kalman filter. This new approach utilizes multiple dimensional correntropy to assess the similarity between vectors across different dimensions. Additionally, it adjusts the covariance matrices simultaneously by utilizing the adopted matrix similarity measure within the modified correntropy framework. Simulations on target tracking demonstrate that our proposed algorithm exhibits excellent estimation accuracy and robustness while possessing adaptive capability even under time-varying heavy-tailed noises.

Progressive Gaussian approximate filter (PGAF) provides an efficient way for estimating the states of nonlinear systems with large prior errors and accurate measurements. However, its performance declines when an inaccurate measurement noise covariance matrix (MNCM) is applied, which makes it even more challenging when the MNCM is coupled with progression step size in the measurement update step. To solve this problem, we adopt the sliding window method to accurately estimate the MNCM within the variational Bayesian framework adaptively. In the proposed algorithm, the system state's posterior distribution is obtained through PGAF for forward filtering and Gaussian approximation smoother for backward smoothing within the sliding window. The proposed sliding window based adaptive PGAF outperforms existing nonlinear Gaussian filters as demonstrated using the target tracking examples.

This article studies the joint design of stealthy actuator and sensor attacks against cyber-physical systems with the aim of keeping the system’s state in an unsafe region. The Kullback-Leibler divergence is adopted as the metric of the joint attacks’ stealthiness. The attacker’s objective is realized by making the system’s ellipsoidal invariant reachable set under stealthy joint attacks belong to the unsafe set. Firstly, the relationship between the actuator attack and the shape of the ellipsoid is analyzed and it can be characterized by a non-convex optimization problem. Parameters of the actuator attack are obtained by solving another convex optimization problem constructed through applying a linear transformation to the original problem. Then, the sensor attack is analytically solved from a non-convex optimization problem to move the center of the ellipsoid to the desired target and increase the controller’s cost. Finally, an example of the flotation industrial process is illustrated to demonstrate effectiveness of the attack. Note to Practitioners—This paper aims to study security of cyber-physical systems from the perspective of attackers, which can help defenders fully understand the behavior of attackers. Existing works have not investigated which kind of stealthy attacks can move the state to the unsafe region. In this article, novel stealthy joint attacks are proposed such that the state of the attacked system is kept in the unsafe region. In detail, the actuator attack is to reshape the system’s ellipsoidal invariant reachable set and the sensor attack is to move the center of the ellipsoid to the desired target. In practical applications, the attacker need to obtain the system’s parameters and eavesdrop the input and output data, then solve the actuator attack from a convex optimization problem and compute the sensor attack by analytically solving a non-convex optimization problem. The attacks’ effectiveness is verified through the flotation industrial process. In the future, we will further investigate the design of stealthy attack strategies for nonlinear systems.

This article, from the attacker’s standpoint, develops a model-free stealthy attack that can steer the system state to the predefined target value and evade detection, without prior knowledge of the system dynamics. A constrained Markov decision process (CMDP) is first modeled to characterize the objective of the stealthy attack. On the basis of the established CMDP, an actor–critic reinforcement learning algorithm is proposed to train the attacker’s policy. Furthermore, by introducing a Lyapunov function constructed from the action value function to the algorithm, convergence of the attacked system’s state to the target is theoretically guaranteed. Differing from existing model-free stealthy attacks which are only suitable for linear systems, the proposed approach guarantees the applicability to nonlinear systems. A linear numerical example and a nonlinear example of flotation industrial system are provided to validate the effectiveness of our proposed stealthy attack.

In this article, based upon reinforcement learning (RL) and reduced control techniques, an${H}_{\infty }$output tracking control method is represented for nonlinear two-time-scale industrial systems with external disturbances and unknown dynamics. First, the original${H}_{\infty }$output tracking problem is transformed into a reduced problem of the augmented error system. Based on zero-sum game idea, the Nash equilibrium solution is given and the tracking Hamilton–Jacobi–Isaacs (HJI) equation is established. Then, to handle the issue of unmeasurable states of the virtual reduced system, full-order system state data are collected to reconstruct the reduced system states, and the model-free RL algorithm is proposed to solve the tracking HJI equation. Next, the algorithm implementation is given under the actor–critic–disturbance framework. It is proved that the control policy obtained from reconstructed state data can make the augmented error system asymptotically stable and satisfy theL$_{\mathbf{2}}$gain condition. Finally, the effectiveness of the proposed method is illustrated by the permanent-magnet synchronous motor experiment.

The grid connection of renewable energy poses challenges to the coordinated control of coal-fired power generation systems. Model uncertainty makes model-driven methods less effective due to the lack of adaptive capability. Large inertia of thermal process leads to local aggregation of state information, and the direct grafting reinforcement learning methods will affect the learning efficiency due to insufficient data utilization. To this end, this article proposes dual-prioritized experience replay value distribution deep deterministic policy gradient (DPER-VDP3G) algorithm. Value distribution is introduced to reflect the influence of model uncertainty on the evaluation of coordinated control policy, thus improving the accuracy of prediction cost function. The DPER is designed to reduce the nonuniform sampling bias and remove redundant data to enhance sample diversity. Comparative experiments demonstrate the advantages of the proposed method for improving network training efficiency, ameliorating load tracking accuracy and speed, and reducing energy consumption.

In this article, the$H_{\infty }$control problem is investigated for a class of two-time-scale cyber-physical systems (TTSCPSs). In order to reduce the network bandwidth occupation and lighten the computation burden, an asynchronous dynamic event-triggered protocol (ADETP) is designed to arrange the signal transmissions from sensors to the composite controllers, in which the triggering sequences of fast and slow system components are determined separately. A novel composite controller based on the proposed ADETP is designed dependent on the singular perturbation parameter (SPP) such that the closed-loop TTSCPS is asymptotically stable with meeting a required$H_{\infty }$performance index when the SPP is no more than a given upper bound. Gain matrices of the desired composite controller are parameterized in terms of the solutions to certain matrix inequalities that are readily solvable. Finally, simulation results of a nuclear reactor are presented to verify the effectiveness of the proposed approach.

The subject of attack detection for industrial cyber-physical systems (IPCSs) is covered in this paper, which addresses threats from transient covert attacks (TCAs), also referred to as the second version of replay attacks with a specific frequency and short duration. A comprehensive model of the TCAs is built using the active instant and period of the attacks, as well as the dynamics of a virtual system to replicate IPCS function and produce attack signals. Though watermarking-based detection algorithms have been shown to be effective in detecting TCAs, the induced system performance loss is too significant, and as such, our primary goal is to minimize system performance degradation while maintaining the detection rate. Because the active periods of TCAs are substantially shorter than their sleep ones, or even because they are practically always silent, it makes sense that reducing superfluous watermarking will facilitate system performance. So, using an “event-triggered” strategy, a unique recursive watermarking-based detection algorithm is proposed. Here, the trigger modes of watermarking are divided into three types: forced, high probability, and low probability. The design principles are proven via algorithms and criteria, and a theoretical analysis of the detection rate and the system performance loss is also supplied. The advantages of the suggested algorithms are finally demonstrated by numerical simulations of a quadruple-water-tank system and experiments with a permanent magnet synchronous motor on the dSpace platform.

This article addresses the replay attack detection issue for a class of industrial process operation optimization (IPOO) cyber-physical systems (CPSs). In contrast to conventional CPSs with a single-loop structure, the IPOO CPSs employ a dual-layer network environment consisting of a wireless network for the setpoint optimization loop and a controller area network (CAN) bus for the device control loop. Consequently, the issue of attack detection is more complicated for the IPOO CPSs, and this motivates our current research. First, a unified model of the IPOO CPS is built, with PI controller controlling the physical plants and linear quadratic Gaussian (LQG) controller managing setpoint optimization. Then, a novel joint watermarking detection mechanism is established with the PI controller watermarking, LQG controller watermarking, and a watermarking compensator. The proposed watermarking compensator with an augmented Kalman filter is utilized to efficiently eliminate false alarms brought on by information interactions of the coupled cyber-layers, enabling the accurate detection and location of replay attacks. Furthermore, a linear relationship is established between watermarking parameters and system performance loss. Finally, simulations with a quadruple water tank system are conducted to verify the effectiveness of the proposed algorithm.

This article investigates the tracking control problem for a class of nonlinear multi-input-multi-output (MIMO) uncertain singularly perturbed systems (SPSs) with full-state constraints. The underlying issues become more challenging because two-time-scale characteristics and full state constraints are involved. To this end, first, the adaptive neural network (NN) control method is designed to handle system uncertainties in the design process. Second, the nonlinear state-dependent coordinate transformation functions are employed to avoid the violation of full-state constraints and feasibility conditions for intermediate controllers. Furthermore, by introducing an appropriate ε -dependent Lyapunov function, the potential ill-conditioned numerical problems in the design process of SPSs are avoided, and the stability of the nonlinear SPSs is proven. Finally, two examples are presented to illustrate the validity of the proposed adaptive NN control scheme.

This brief focuses on reachable set estimation for memristive complex-valued neural networks (MCVNNs) with disturbances. Based on algebraic calculation and Gronwall-Bellman inequality, the states of MCVNNs with bounded input disturbances converge within a sphere. From this, the convergence speed is also obtained. In addition, an observer for MCVNNs is designed. Two illustrative simulations are also given to show the effectiveness of the obtained conclusions.

We consider the robust state estimation over sensor networks with non-Gaussian noise, which is often encountered in many applications. Motivated by the fact that the elliptical distribution is the natural extension of the Gaussian distribution and includes a variety of non-Gaussian distributions with heavy-tailed characteristics, we here adopt the elliptical distribution to model the heavy-tailed process and measurement noise. The general state evolution model is used to replace the process equation and the elliptical distribution is denoted as a Gaussian mixture form. Based on that, the posterior estimation of the system state together with the parameters of the process and measurement noises can be inferred by the variational Bayes method. Moreover, the corresponding distributed estimation algorithm is then provided, which enables distributed implementation. The target tracking over sensor networks is used to show the estimation accuracy of the proposed algorithms.

Dynamic memristor (DM)-cellular neural networks (CNNs), which replace a linear resistor with flux-controlled memristor in the architecture of each cell of traditional CNNs, have attracted researchers’ attention. Compared with common neural networks, the DM-CNNs have an outstanding merit: when a steady state is reached, all voltages, currents, and power consumption of DM-CNNs disappeared, in the meantime, the memristor can store the computation results by serving as nonvolatile memories. The previous study on stability of DM-CNNs rarely considered time delay, while delay is quite common and highly impacts the stability of the system. Thus, taking the time delay effect into consideration, we extend the original system to DM-D(delay)CNNs model. By using the Lyapunov method and the matrix theory, some new sufficient conditions for the global asymptotic stability and global exponential stability with a known convergence rate of DM-DCNNs are obtained. These criteria generalized some known conclusions and are easily verified. Moreover, we find DM-DCNNs have$3^{n}$equilibrium points (EPs) and$2^{n}$of them are locally asymptotically stable. These results are obtained via a given constitutive relation of memristor and the appropriate division of state space. Combine with these theoretical results, the applications of DM-DCNNs can be extended to other fields, such as associative memory, and its advantage can be used in a better way. Finally, numerical simulations are offered to illustrate the effectiveness of our theoretical results.

This article investigates the optimal operational control (OOC) problem for a class of industrial systems consisting of multiple unit devices with fast dynamics and an unknown operational process with slow dynamics. First, the OOC problem is formulated as a noncascade optimal control problem of two-time-scale systems with a novel performance function. Second, using singular perturbation theory, a decentralized composite control scheme is proposed by decomposing the original optimal problem into reduced-order fast and slow subsystem problems. Then, in the framework of reinforcement learning, an online controller design method for the slow subsystem is proposed by using the online measurement, and an offline controller design for the fast subsystem is proposed by using the unit device models. The obtained decentralized composite optimal controller achieves both the desired operational index tracking and disturbance rejection without requiring the dynamics of the operational process. Different from the existing cascade design methods, the proposed approach regulates the unit devices and operational process simultaneously, as well as overcomes the potential high dimensionality and ill-conditioned numerical issues. Finally, a mixed separation thickening process and a numerical example are given to illustrate the presented results.

In order to deal with optimal setpoint tracking (OST) problems, a discounted cost function has been introduced in the existing work. However, the optimal tracking controllers developed according to the discounted cost function may not ensure asymptotic tracking and the stability of the closed-loop systems. To overcome these limitations, in this article, we propose a novel adaptive optimal control method to minimize a cost function without a discount factor. The proposed method starts from a reformulation of the infinite-horizon OST problem for linear discrete-time systems with external disturbances. We derive an algebraic Riccati equation for solving the OST problem, whose solution is uniquely determined under mild conditions. It is proved that the obtained controller accommodates the disturbance and realizes the output tracking with zero steady-state error. In the framework of reinforcement learning, a$Q$-learning algorithm is devised to learn the suboptimal control policy by using measured data. The present learning algorithm does not require that the disturbance is measurable and can be implemented completely model-free. Finally, two examples on dc motor system and F-16 aircraft plant are provided to corroborate our design methodology.

This article concentrates on finite-time stabilization and energy consumption estimation for nonlinear systems with and without delay. By constructing an appropriate controller and utilizing inequality techniques, sufficient conditions are proposed to guarantee the finite-time stability of the delayed nonlinear system. Furthermore, the energy consumption produced in system controlling is estimated by inequality techniques. Then, we formulate similar results for the delay-free case. Finally, numerical examples are presented to demonstrate the effectiveness of our theoretical results.

This paper studies one type of delayed memristor-based fractional-order neural networks (MFNNs) on the finite-time stability problem. By using the method of iteration, contracting mapping principle, the theory of differential inclusion, and set-valued mapping, a new criterion for the existence and uniqueness of the equilibrium point which is stable in finite time of considered MFNNs is established when the order α satisfies . Then, when , on the basis of generalized Gronwall inequality and Laplace transform, a sufficient condition ensuring the considered MFNNs stable in finite time is given. Ultimately, simulation examples are proposed to demonstrate the validity of the results.

This article concentrates on the synchronization problem of memristive complex-valued neural networks (CVNNs) with time delays via the pinning control method. Different from general control schemes, the pinning control is beneficial to reduce the control cost by pinning the fractional nodes instead of all ones. By separating the complex-valued system into two equivalent real-valued systems and employing the Lyapunov functional as well as some inequality techniques, the asymptotic synchronization criterion is given to guarantee the realization of synchronization of memristive CVNNs. Meanwhile, sufficient conditions for exponential synchronization of the considered systems is also proposed. Finally, the validity of our proposed results is verified by a numerical example.

This paper investigates the problem of fuzzy controller design for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. By using the average dwell time approach together with the piecewise Lyapunov function technique, a set of well-conditioned sufficient conditions for the existence of controller is proposed, under which the overall switched closed-loop system is asymptotically stable. A state feedback controller depending on the singular perturbation parameter ε, which is shown to work well for all ε ∈ (0, ε0), where ε0is the stability bound of singularly perturbed systems, is developed. In addition, when ε is sufficiently small, the ε-dependent controller can be reduced to an ε-independent one. Then, an ε-independent state feedback stabilization controller design method is proposed in terms of linear matrix inequalities. Furthermore, under the controller, the stability bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to show the feasibility and effectiveness of the obtained results.

In this paper, a new online monitoring approach is proposed for handling the dynamic problem in industrial batch processes. Compared to conventional methods, its contributions are as follows: (1) multimodes are separated correctly since the cross-mode correlations are considered and the common information is extracted; (2) the expensive computing load is avoided since only the specific information is calculated when a mode is monitored online; and (3) after that, two different subspaces are separated, and the common and specific subspace models are built and analyzed, respectively. The monitoring is carried out in the subspace. The corresponding confidence regions are constructed according to their respective models.

This paper investigates the problem of multiobjective control for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed systems. Based on a linear matrix inequality (LMI) approach, a state feedback controller that depends on the singular perturbation parameter epsiv is developed such that: 1) theHinfinperformance of the resulting closed-loop system is less than or equal to some prescribed value; 2) the closed-loop poles of each local system are within a prespecified LMI stability region; and 3) for a given upper bound epsivmacr for the singular perturbation parameter epsiv, both 1) and 2) are guaranteed for all epsiv isin [0,epsivmacr.] It is shown that the epsiv-dependent controller is well defined for any epsiv isin [0,epsivmacr], and can be reduced to an epsiv-independent one if epsiv is sufficiently small. Finally, a practical example is given to show the feasibility and effectiveness of the obtained method.