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 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.

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.

Brain-inspired Spiking Neural Networks (SNNs) leverage sparse spikes to represent information and process them in an asynchronous event-driven manner, offering an energy-efficient paradigm for the next generation of machine intelligence. However, the current focus within the SNN community prioritizes accuracy optimization through the development of large-scale models, limiting their viability in resource-constrained and low-power edge devices. To address this challenge, we introduce a lightweight and hardware-friendly Quantized SNN (Q-SNN) that applies quantization to both synaptic weights and membrane potentials. By significantly compressing these two key elements, the proposed Q-SNNs substantially reduce both memory usage and computational complexity. Moreover, to prevent the performance degradation caused by this compression, we present a new Weight-Spike Dual Regulation (WS-DR) method inspired by information entropy theory. Experimental evaluations on various datasets, including static and neuromorphic, demonstrate that our Q-SNNs outperform existing methods in terms of both model size and accuracy. These state-of-the-art results in efficiency and efficacy suggest that the proposed method can significantly improve edge intelligent computing.

With the development of sensor technology, the rational use of multimodal data has become a research hotspot in the field of remote sensing. The multimodal fusion method can effectively improve the accuracy of remote sensing data classification by using the complementary information of different modalities. However, the existing multimodal fusion methods face many challenges, including difficulties in suppressing spectral noise, fully mining contextual information, and learning the strong adaptive fusion pattern. To address the above challenges, a Gaussian mixture variational dynamic fusion network (GM-VDFN) is proposed. First, a multimodal multiscale spatial graph is constructed, and the graph convolution is used to learn the multiscale features. In this process, a spatial topology constraint based on GM (STC-GM) is proposed, which suppresses spectral noise by constraining the topological consistency of the two modalities. Second, a multiscale dynamic graph aggregation module (MDGAM) is constructed, which can capture the shareable class identification information from multiscale features and mine personalized fusion patterns suitable for each sample. Finally, the evidence lower bound for the multimodal joint distribution is derived, and a multimodal variational autoencoder (M-VAE) is designed. Optimizing the evidence lower bound to model multimodal joint distributions, thereby learning the strong adaptive fusion pattern between modalities. Experimental results on four fusion datasets (Houston 2013, Trento, MUUFL, and Houston 2018) show that GM-VDFN achieved state-of-the-art performance in multimodal remote sensing data classification tasks.

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.

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.