This article tackles the distributed filtering problem over wireless sensor networks for a class of time-varying systems with state saturation and deception attacks. To ensure more reliable and secure data transmission, a novel dynamic decode-and-forward (DDaF) relay scheme is proposed, implemented through coordinated encoders deployed at the sensors’ side and decoders deployed at the relay nodes’ side. The network-based deception attacks occur probabilistically across the communication channels and are characterized by independent Bernoulli random sequences. This study is primarily intended to design distributed filters that effectively estimate the system states in the presence of state saturation, DDaF relays and deception attacks. By employing the stochastic analysis and matrix theories, upper bounds on the second-moment matrices of the filtering errors are derived for the considered system, and subsequently such bounds are minimized with designed filter gains. Furthermore, rigorous mathematical analysis is conducted to examine the uniform boundedness of the upper bounds and their monotonicity with respect to the deception attacks. Finally, simulation results demonstrate effectiveness of the proposed distributed filtering strategy.

We study data-driven control for multi-agent systems subject to denial-of-service (DoS) attacks. In practical applications, direct data-driven control is highly sensitive to high-frequency noise, which often results in degraded performance. To address this problem, we propose a distributed integral algorithm for data-driven control system. Owing to its inherent low-pass filtering property, the proposed algorithm can effectively suppress high-frequency noise. Consequently, the overall control performance is significantly improved even in the presence of such disturbances. Theoretical analysis and illustrative examples are provided to demonstrate the effectiveness of the proposed method.

In many real-world systems, the spatial diffusion process occurs not in the continuous medium but in the discrete, networked substrate, where the multiple interaction layers may coexist. This work introduces a hybrid framework that combines the reaction-diffusion dynamics with cross-network electrical coupling in the FitzHugh-Nagumo (FHN) system on homogeneous and heterogeneous networks. The conditions for Turing instability are derived: for the unidirectionally coupled FHN system on heterogeneous networks and for the bidirectionally coupled FHN system on homogeneous networks. Furthermore, the Turing bifurcation is analysed when the coupling strength serves as the bifurcation parameter. Next, the bidirectionally coupled FHN system on heterogeneous networks is simplified based the slow-fast framework with the pronounced differences between the diffusion rates. The local stability at the stationary state and the necessary parameter bounds for Turing instability are investigated. Numerical simulations on Erdős-Rényi networks validate the analytical thresholds and illustrate the transition from stability to pattern formation. These results open new avenues for understanding how multi-layer network structure and cross-network coupling cooperate to generate the self-organized patterns in the excitable medium.

Three-dimensional (3D) models are widely used in engineering, while their secure transmission and storage remain challenging. Encryption is a common method to protect 3D models. Although existing encryption schemes effectively safeguard the sensitive information, they primarily rely on either full encryption or selective encryption techniques, often overlooking the demand for hierarchical decryption. Hence, this paper proposes a multi-level 3D model protection scheme (ML3DMP) based on the two-dimensional parametric polynomial modulo chaotic map (2D-PPMCM) to balance security and usability. The motivation behind this scheme stems from leveraging the complexity of chaotic maps to enhance the model encryption against potential attacks. The encryption process employs a novel 2D-PPMCM to encrypt different partitions of vertex coordinates of 3D models, thereby enhancing the security of the ciphertext. Notably, 2D-PPMCM is confirmed to exhibit continuous and stable chaotic properties through chaotic performance analysis, such as bifurcation diagram, Lyapunov exponent, trajectory, and other tests. Moreover, it could generate uniform and random chaotic sequences for encryption activities. Simulation performance analysis shows that ML3DMP has good security and effectiveness. Information entropy of the ciphertext exceeds 7.99, and its correlation coefficients are approaching 0.

In this paper, the distributed interval fusion filtering is studied for a class of multirate time-varying nonlinear positive systems subject to unknown-but-bounded disturbances. Multiple sensors with different sampling periods are used to measure the system’s outputs. To extend the transmission distance of the sensors, an amplify-and-forward relay is introduced in the transmission link from sensors to the remote filters. This paper aims to develop a distributed fusion filtering algorithm, guaranteeing that the system states remain within the nonnegative intervals at each update instant and the interval widths have a finite-horizon l1 performance. By using the virtual measurement compensation method, the multirate system is transformed into a single-rate one. Subsequently, sufficient conditions are established, via the interval analysis and the comparison principle, to ensure both the positivity of the local filters and the finite-horizon l1 performance of their interval estimates. Furthermore, the gain matrices of the local interval filters are determined by solving certain recursive linear programming problems. Moreover, an interval-based distributed fusion algorithm is designed to fuse these intervals calculated by the local interval filters so as to provide the tightest interval containing the original system states. Finally, validity of the established distributed interval fusion filtering algorithm is illustrated via two examples.

This article addresses the quadratic filtering problem for a class of two-dimensional (2-D) non-Gaussian systems subject to quantization effects and deception attacks. Under the bandwidth-limited communication network, the measurement signals are quantized via a logarithmic quantizer before being transmitted. The deception attacks occurring during the transmission are modeled by random variables obeying the Bernoulli distributions, and the injected signals are represented as non-Gaussian noises. The primary objective of this article is to design a recursive quadratic filter that estimates the system states with satisfactory performance against the quantization effects and probabilistic attacks. By employing the inductive approach and matrix theories, an upper bound on the second-moment matrix of the filtering error is derived and then minimized at each step. In addition, an analysis of the filtering performance is conducted to establish the uniform boundedness of the minimized upper bound. Finally, a simulation example is presented to illustrate the effectiveness of the proposed filtering scheme.

In this article, the zonotopic set-membership estimation (SME) problem is addressed for a class of nonlinear systems subjected to an encoding-decoding scheme, where the measurement information of each sensor is encoded and then transmitted to the remote fusion center. The objective of this article is to develop a zonotopebased weighted measurement fusion (WMF) method to fuse the received decoding signals, and to design a zonotopic SME algorithm that fully utilizes the higher-order partial derivatives of the nonlinear functions based on the fused signal. A zonotope-based WMF method is proposed by means of the full rank decomposition technique, which enables the fusion of the decoding signals by solving a weighted least squares problem. To design the desired SME algorithm, the nonlinear system is first transformed into a linear time-varying system using the Carleman approximation technique. Then, based on the fused signal, a Kalmantype estimator is constructed and the zonotopes encompassing the prediction error and the estimation error are recursively calculated. The estimator parameter is obtained by minimizing the F -radius of the zonotope enclosing the estimation error at each time instant. Furthermore, effect of the system smoothness level on the F -radius is intensively analyzed. It is shown that incorporating the higher-order partial derivatives into the design of the SME algorithm enables the extraction of additional state constraints, and that the number of extractable constraints increases monotonically with the smoothness level. A method is subsequently proposed to leverage these constraints in order to improve the estimation accuracy. Moreover, the WMF method is proven to provide an equivalent estimation accuracy as compared to the most commonly used parallel fusion method while possessing lower computational complexity. Finally, two simulation experiments are conducted to demonstrate the efficacy and utility of the SME method.

This article is concerned with the zonotopic set-membership fusion estimation (SMFE) problem for a class of complex networks (CNs). The measurements of the CNs are transmitted to a remote fusion center through a shared communication network. Due to the limited network bandwidth, the transmissions of the measurement information occur intermittently, and the nodes’ transmission intervals may exceed their sampling periods. To enhance the utilization of the measurement information, each node of the CN is equipped with a buffer for real-time data storage, so that the fusion center can utilize more measurement information at time instants when the node’s transmission interval is larger than its sampling period. The aim of this article is to design SMFE algorithms based on both the parallel fusion scheme and the data-compression fusion scheme, respectively, using the data received at the fusion center. First, by iterating the state equation of the CN, a batch processing method is proposed to process the input data of the fusion center concurrently. Subsequently, by employing the zonotopic set-membership estimation (SME) technique, the desired SMFE algorithms are designed. Moreover, sufficient criteria are established to ensure that the sizes of the output zonotopes of the SMFE algorithms remain uniformly bounded. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed algorithms.

This paper intends to address the outlier-resistant fusion filtering problem for a class of nonlinear two-dimensional systems with the energy harvesting sensors under the measurement censoring scheme. The energy harvesting technology is considered to provide the energy required for measurement signal transmission, where the energy harvested at each shifting point is characterized by a random variable, and the signal can be successfully transmitted only when the sensor accumulates sufficient energy. The censored measurements are modeled by the well-known Tobit model and further characterized by a series of Bernoulli random variables with local probability approximation. Additionally, a saturation function is introduced to mitigate the impact of abnormal innovations caused by measurement outliers. The design of the fused filter in this paper follows two main steps: firstly, the local filters are established in the presence of incomplete measurements that are caused by energy constraints and censoring, where upper bounds for the filtering error variances are derived and subsequently minimized at each shifting point by selecting appropriate parameters; and secondly, the obtained local estimates are fused by deploying a suitable fusion scheme, where the fused estimate is shown to be more accurate than the local ones. Finally, a numerical example is provided to verify the effectiveness of the proposed outlier-resistant fusion filtering algorithm.

Existing neural network models predominantly rely on pairwise interactions, often neglecting the higher-order interactions inherent in real-world neural systems. Even among studies that do incorporate higher-order structures, the dynamical mechanisms by which hyperedge overlap governs stability and catastrophe behavior remain poorly understood. To bridge this critical gap, this paper proposes a generalized star-topology neural network framework that explicitly incorporates higher-order interactions via hypergraphs, with a specific focus on the dynamical consequences of hyperedge overlap. By distinguishing between low-overlap and high-overlap topological configurations, we rigorously analyze the local stability and the existence of Hopf bifurcations through the derivation of characteristic equations and critical time delay thresholds. Theoretical analysis and extensive numerical simulations reveal a fundamental structural insight: compared to the low-overlap counterpart, the high-overlap configuration functions as a structural stabilizer. It significantly expands the stability domain by elevating bifurcation thresholds and effectively suppresses the amplitude of post-bifurcation limit cycles. Furthermore, scalability and robustness analyses demonstrate that these stabilizing effects persist across varying network scales and provide superior resilience against stochastic perturbations. By contrasting hypergraph dynamics with traditional pairwise frameworks, this work provides a novel mathematical perspective on how higher-order topological redundancy fundamentally shapes and stabilizes the collective dynamics of complex neural networks.

This paper addresses the distributed non-fragile HPo-consensus estimation issue for a class of stochastic parameter two-dimensional (2-D) systems subject to measurement censoring and deception attacks. Initially, an innovative formulation of the HPo-consensus performance criterion is proposed for the 2-D shift-varying system over a finite horizon, aiming to characterize the estimator's capability to attenuate the energy-bounded external disturbances. Subsequently, a stochastic vector dissipativity framework is developed for the 2-D system for the first time, which provides a foundational tool to ensure the existence of the desired distributed HPo-consensus estimator. For each individual node, a recursive linear matrix inequality (LMI) is then derived as a local sufficient condition to guarantee the achievement of the desired HPo-consensus performance. Notably, the proposed local recursive LMI approach could significantly reduce the computational complexity compared with the conventional global conditions. Finally, a numerical example is presented to validate effectiveness of the proposed estimation method.

Set-membership estimation (SME) has attracted increasing attention in recent years due to its capability of providing guaranteed state bounds for systems subject to unknown-but-bounded uncertainties. Compared with the estimation methods dealing with stochastic noises, SME does not rely on probabilistic assumptions on noises, making it particularly suitable for safety-critical systems and the systems in networked environments with incomplete statistical information. Meanwhile, the rapid development of communication networks has significantly promoted the deployment of networked systems, where communication constraints such as time delays, packet dropouts, communication protocols, quantization effects, event-triggered schemes, and cyber attacks inevitably introduce additional challenges to the state estimation. Motivated by these developments, this paper presents a comprehensive survey on SME for networked nonlinear systems under communication constraints. First, the fundamental concepts and the recursive principles of SME are reviewed. Then, representative set representations and the corresponding SME methods for nonlinear systems are systematically summarized, with particular emphasis on the techniques for handling the nonlinear mappings as well as the ellipsoidal and the zonotopic SME approaches. Subsequently, existing SME methods under various communication constraints are classified and reviewed from a unified perspective according to their influences on the measurement transmission and the estimator design. Finally, several open problems and future research directions are discussed.

This paper is devoted to dealing with the robust fusion Tobit Kalman filtering issue for a class of two-dimensional (2-D) shift-varying multi-sensor systems affected by measurement censoring and norm-bounded uncertainties. Besides, to alleviate the negative impact from channel packet dropouts, the redundant channel transmission protocol is introduced. The conditional mathematical expectation and variance of the censored measurement outputs regarding the system state are calculated for the first time for 2-D systems. Then, a set of local robust Tobit Kalman filters are established, where the upper bounds for the second-order moment of the filtering error are derived and subsequently minimized by selecting appropriate filter parameters. Furthermore, by means of the sequential covariance intersection method, the fusion estimation is obtained by fusing the estimates from each local filter. Finally, a numerical example is presented to show effectiveness of the proposed robust fusion Tobit Kalman filtering algorithm.

Interactions between biological species are critical for species coexistence and the maintenance of biodiversity. However, traditional studies on species coexistence mainly focus on direct pairwise interactions between species, often neglecting more complex indirect interactions. Indirect interactions are a form of higher-order interactions(HOIs) and play a significant role. This paper considers a predator-prey model with HOIs, incorporating a Holling-II type functional response and a modified Leslie-Gower term. A cross-diffusion predator-prey model is developed and a state feedback control strategy is introduced. The existence and stability of equilibrium points in the model without diffusion terms are analysed, and the conditions for diffusion-driven Turing instability are derived. Using the HOIs coefficient as the bifurcation parameter, the amplitude equation of the two-dimensional Turing pattern at the Turing bifurcation threshold is derived based on the multi-scale method, which determines the structure and stability of pattern formation. Numerical simulations demonstrate that the bifurcation parameter changes with the control parameter. The feedback control strategy effectively regulates the structure of Turing patterns and their evolutionary process while suppressing Turing instability, thereby mitigating or even eliminating the adverse effects induced by HOIs.

Accurate state-of-charge (SOC) estimation is essential for the safe, efficient, and long-term operation of lithium-ion batteries in electric vehicles and stationary energy storage systems. However, the inherent nonlinearities, temperature dependence, aging effects, and cell-to-cell variations make the direct SOC measurement unfeasible, presenting significant challenges for reliable estimation in practice. This survey provides a critical review of the SOC estimation methods by organizing the literature into three major categories: direct approaches, indirect techniques, and hybrid architectures. For each category, the underlying principles and typical structures are summarized, with a focus on their trade-offs in terms of accuracy, computational complexity, and data requirements. A systematic taxonomy and in-depth discussion of the hybrid SOC estimators are presented, highlighting how combinations of the direct, model-based, and data-driven components can mitigate the individual limitations and improve the overall performance. Building on this foundation, several emerging research directions are also highlighted, including the multi-state joint estimation, fractional-order modelling, and cloud-based and attack-resilient SOC estimation. Overall, this survey aims to provide a guidance on the method selection for specific applications and to identify promising avenues for future researches in advanced battery systems.

Networked multisensor systems operating under the FlexRay protocol (FRP) are widely used in the automotive industry, where reliable state estimation under bounded uncertainties is of fundamental importance. In such systems, the measurement information from multiple sensors is transmitted to the estimator through a network governed by the FRP, which induces scheduling constraints and switching behaviors in the estimation process. These characteristics make it challenging to guarantee the accuracy and boundedness of the state estimates using conventional methods. This article investigates the zonotopic set-membership fusion estimation (SMFE) problem for multisensor systems under the FRP. The research objective is to design a parallel fusion estimation algorithm for the transformed switched system, to establish a sufficient condition guaranteeing the ultimate boundedness of the radii of the resulting zonotopes and to improve the transient estimation performance. An SMFE algorithm is proposed to recursively calculate the zonotopes that constrain the system state by exploiting the properties of zonotopes. A sufficient condition is derived to ensure the ultimate boundedness of the output zonotopes' radii, which explicitly takes into account both the scheduling of the FRP and the adverse effect of zonotope order reduction on estimation performance. Furthermore, a matrix-inequality-based method is developed to construct an additional enclosing zonotope, based on which a tighter zonotope is obtained at each time instant to enhance the transient performance. The efficacy of the proposed SMFE method is demonstrated through two simulation experiments.

This paper addresses the distributed interval state estimation problem for a class of networked positive systems over sensor networks. The process and measurement disturbances, which are unknown-but-bounded, are constrained to a series of intervals, and sensor nodes in the sensor network are allowed to have different sampling periods. Each sensor transmits its measurement information to its neighboring nodes through a communication network, in which the bit rate constraint is introduced to quantify the limited bandwidth of the network channel. The purpose of this paper is to design a distributed interval observer such that, in the simultaneous presence of multirate samplings and bit rate constraints, the true system state is confined to a nonnegative interval provided by the local observer and the width of the interval is exponentially ultimately bounded. By using the zero measurement compensation method, the multirate positive systems are transformed into single-rate switched ones. Subsequently, sufficient conditions guaranteeing the desired estimating performance are derived by utilizing the interval analysis method, and gain matrices of the local interval observer are determined according to the solutions to certain linear programming problems. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed distributed interval estimation algorithm.

This study focuses on the design of set-membership estimators for two-dimensional systems that are vulnerable to both the dynamic uniform quantization effects and the Byzantine attacks. A two-step distributed filter is proposed, which comprehensively accounts for impacts of both the Byzantine attacks and the uniform quantization. Specifically, by performing an in-depth analysis of the trimmed mean in the presence of Byzantine attacks, we establish the piecewise compact error bounds and subsequently determine the most suitable trimming parameters. On this basis, an ellipsoidal boundary processing scheme tailored by the trimmed mean method is developed. By leveraging the S-procedure and the Schur complement lemma, sufficient conditions are formulated to guarantee the inclusion of the true system state within the bounding ellipsoid. Furthermore, the optimal parameters of the filter are calculated through an optimization process aimed at minimizing the trace of the ellipsoidal matrix. To validate the theoretical criteria and illustrate the practical performance of the designed filtering strategy, a numerical example is presented at the end of this paper.

In this article, a distributed polynomial set-membership fusion estimation approach is proposed for target tracking systems under a binary encoding scheme. Each distance measurement of the considered target is encoded via a binary encoding scheme to facilitate digital transmission. Based on the decoding signals, local estimators are designed by employing a polynomial set-membership estimation method. Furthermore, the effects of possible flipping bits occurring during the transmissions from the distance sensors to the local estimators are considered, and a detection scheme for flipping bits is presented by utilizing the obtained local estimation results. Subsequently, an optimal matrix-weighted distributed fusion estimator is developed in the $F$-radius sense of the zonotope restraining the global estimation error. Finally, simulation studies on a target tracking scenario are provided to demonstrate the effectiveness of the proposed approach.