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1.
J Alzheimers Dis Rep ; 8(1): 561-574, 2024.
Article in English | MEDLINE | ID: mdl-38746630

ABSTRACT

Background: Alzheimer's disease may be effectively treated with acupoint-based acupuncture, which is acknowledged globally. However, more research is needed to understand the alterations in acupoints that occur throughout the illness and acupuncture treatment. Objective: This research investigated the differences in acupoint microcirculation between normal mice and AD animals in vivo. This research also examined how acupuncture affected AD animal models and acupoint microcirculation. Methods: 6-month-old SAMP8 mice were divided into two groups: the AD group and the acupuncture group. Additionally, SAMR1 mice of the same month were included as the normal group. The study involved subjecting a group of mice to 28 consecutive days of acupuncture at the ST36 (Zusanli) and CV12 (Zhongwan) acupoints. Following this treatment, the Morris water maze test was conducted to assess the mice's learning and memory abilities; the acoustic-resolution photoacoustic microscope (AR-PAM) imaging system was utilized to observe the microcirculation in CV12 acupoint region and head-specific region of each group of mice. Results: In comparison to the control group, the mice in the AD group exhibited a considerable decline in their learning and memory capabilities (p < 0.01). In comparison to the control group, the vascular in the CV12 region and head-specific region in mice from the AD group exhibited a considerable reduction in length, distance, and diameter r (p < 0.01). The implementation of acupuncture treatment had the potential to enhance the aforementioned condition to a certain degree. Conclusions: These findings offered tangible visual evidence that supports the ongoing investigation into the underlying mechanisms of acupuncture's therapeutic effects.

2.
Article in English | MEDLINE | ID: mdl-38598399

ABSTRACT

In this article, the set-membership state estimation problem is investigated for a class of nonlinear complex networks under the FlexRay protocols (FRPs). In order to address practical engineering requirements, the multirate sampling is taken into account which allows for different sampling periods of the system state and the measurement. On the other hand, the FRP is deployed in the communication network from sensors to estimators in order to alleviate the communication burden. The underlying nonlinearity studied in this article is of a general nature, and an approach based on neural networks is employed to handle the nonlinearity. By utilizing the convex optimization technique, sufficient conditions are established in order to restrain the estimation errors within certain ellipsoidal constraints. Then, the estimator gains and the tuning scalars of the neural network are derived by solving several optimization problems. Finally, a practical simulation is conducted to verify the validity of the developed set-membership estimation scheme.

3.
Article in English | MEDLINE | ID: mdl-38656844

ABSTRACT

This article is concerned with the secure state estimation problem for artificial neural networks (ANNs) subject to unknown-but-bounded noises, where sensors and the remote estimator are connected via open and bandwidth-limited communication networks. Using the encoding-decoding mechanism (EDM) and the Paillier encryption technique, a novel homomorphic encryption scheme (HES) is introduced, which aims to ensure the secure transmission of measurement information within communication networks that are constrained by bandwidth. Under this encoding-decoding-based HES, the data being transmitted can be encrypted into ciphertexts comprising finite bits. The emphasis of this research is placed on the development of a secure set-membership state estimation algorithm, which allows for the computation of estimates using encrypted data without the need for decryption, thereby ensuring data security throughout the entire estimation process. Taking into account the unknown-but-bounded noises, the underlying ANN, and the adopted HES, sufficient conditions are determined for the existence of the desired ellipsoidal set. The related secure state estimator gains are then derived by addressing optimization problems using the Lagrange multiplier method. Lastly, an example is presented to verify the effectiveness of the proposed secure state estimation approach.

4.
Neural Netw ; 174: 106221, 2024 Jun.
Article in English | MEDLINE | ID: mdl-38447426

ABSTRACT

Multi-view graph pooling utilizes information from multiple perspectives to generate a coarsened graph, exhibiting superior performance in graph-level tasks. However, existing methods mainly focus on the types of multi-view information to improve graph pooling operations, lacking explicit control over the pooling process and theoretical analysis of the relationships between views. In this paper, we rethink the current paradigm of multi-view graph pooling from an information theory perspective, subsequently introducing GDMGP, an innovative method for multi-view graph pooling derived from the principles of graph disentanglement. This approach effectively simplifies the original graph into a more structured, disentangled coarsened graph, enhancing the clarity and utility of the graph representation. Our approach begins with the design of a novel view mapper that dynamically integrates the node and topology information of the original graph. This integration enhances its information sufficiency. Next, we introduce a view fusion mechanism based on conditional entropy to accurately regulate the task-relevant information in the views, aiming to minimize information loss in the pooling process. Finally, to further enhance the expressiveness of the coarsened graph, we disentangle the fused view into task-relevant and task-irrelevant subgraphs through mutual information minimization, retaining the task-relevant subgraph for downstream tasks. We theoretically demonstrate that the performance of the coarsened graph generated by our GDMGP is superior to that of any single input view. The effectiveness of GDMGP is further validated by experimental results on seven public datasets.


Subject(s)
Information Theory , Entropy
5.
Comput Biol Med ; 171: 108210, 2024 Mar.
Article in English | MEDLINE | ID: mdl-38417383

ABSTRACT

The timely detection of abnormal electrocardiogram (ECG) signals is vital for preventing heart disease. However, traditional automated cardiology diagnostic methods have the limitation of being unable to simultaneously identify multiple diseases in a segment of ECG signals, and do not consider the potential correlations between the 12-lead ECG signals. To address these issues, this paper presents a novel network architecture, denoted as Branched Convolution and Channel Fusion Network (BCCF-Net), designed for the multi-label diagnosis of ECG cardiology to achieve simultaneous identification of multiple diseases. Among them, the BCCF-Net incorporates the Channel-wise Recurrent Fusion (CRF) network, which is designed to enhance the ability to explore potential correlation information between 12 leads. Furthermore, the utilization of the squeeze and excitation (SE) attention mechanism maximizes the potential of the convolutional neural network (CNN). In order to efficiently capture complex patterns in space and time across various scales, the multi branch convolution (MBC) module has been developed. Through extensive experiments on two public datasets with seven subtasks, the efficacy and robustness of the proposed ECG multi-label classification framework have been comprehensively evaluated. The results demonstrate the superior performance of the BCCF-Net compared to other state-of-the-art algorithms. The developed framework holds practical application in clinical settings, allowing for the refined diagnosis of cardiac arrhythmias through ECG signal analysis.


Subject(s)
Algorithms , Cardiology , Humans , Neural Networks, Computer , Arrhythmias, Cardiac/diagnosis , Electrocardiography/methods
6.
Horm Metab Res ; 2024 Feb 02.
Article in English | MEDLINE | ID: mdl-38307091

ABSTRACT

Perimenopausal period causes a significant amount of bone loss, which results in primary osteoporosis (OP). The Periostin (Postn) may play important roles in the pathogenesis of OP after ovariectomized (OVX) rats. To identify the roles of Postn in the bone marrow mesenchymal stem cell derived osteoblasts (BMSC-OB) in OVX rats, we investigated the expression of Wnt/ß-catenin signaling pathways in BMSC-OB and the effects of Postn on bone formation by development of BMSC-OB cultures. Twenty-four female Sprague-Dawley rats at 6 months were randomized into 3 groups: sham-operated (SHAM) group, OVX group and OVX+Postn group. The rats were killed after 3 months, and their bilateral femora and tibiae were collected for BMSC-OB culture, Micro-CT Analysis, Bone Histomorphometric Measurement, Transmission Electron Microscopy and Immunohistochemistry Staining. The dose/time-dependent effects of Postn on the proliferation, differentiation and mineralization of BMSC-OB and the expression of osteoblastic markers were measured in in vitro experiments. We found increased Postn increased bone mass, promoted bone formation of trabeculae, Wnt signaling and the osteogenic activity in osteoblasts in sublesional femur. Postn have the function to enhance cell proliferation, differentiation and mineralization at a proper concentration and incubation time. Interestingly, in BMSC-OB from OVX rats treated with the different dose of Postn, the osteoblastic markers expression and Wnt/ß-catenin signaling pathways were significantly promoted. The direct effect of Postn may lead to inhibit excessive bone resorption and increase bone formation through the Wnt/ß-catenin signaling pathways after OVX. Postn may play a very important role in the pathogenesis of OP after OVX.

7.
Article in English | MEDLINE | ID: mdl-38198262

ABSTRACT

This article is concerned with the joint state and unknown input (SUI) estimation for a class of artificial neural networks (ANNs) with sensor resolution (SR) under the encoding-decoding mechanisms. The consideration of SR, which is an important specification of sensors in the real world, caters to engineering practice. Furthermore, the implementation of the encoding-decoding mechanism in the communication network aims to accommodate the limited bandwidth. The objective of this study is to propose a set-membership estimation algorithm that accurately estimates the state of the ANN without being influenced by the unknown input while accounting for the SR and the encoding-decoding mechanism. First, a sufficient condition is derived to ensure an ellipsoidal constraint on the estimation error. Then, by addressing an optimization problem, the design of the estimator gains is accomplished, and the minimal ellipsoidal constraint on the state estimation error is obtained. Finally, an example is provided to confirm the validity of the proposed joint SUI estimation scheme.

8.
Article in English | MEDLINE | ID: mdl-38289838

ABSTRACT

This article proposes predefined-time adaptive neural network (PTANN) and event-triggered PTANN (ET-PTANN) models to efficiently compute the time-varying tensor Moore-Penrose (MP) inverse. The PTANN model incorporates a novel adaptive parameter and activation function, enabling it to achieve strongly predefined-time convergence. Unlike traditional time-varying parameters that increase over time, the adaptive parameter is proportional to the error norm, thereby better allocating computational resources and improving efficiency. To further enhance efficiency, the ET-PTANN model combines an event trigger with the evolution formula, resulting in the adjustment of step size and reduction of computation frequency compared to the PTANN model. By conducting mathematical derivations, the article derives the upper bound of convergence time for the proposed neural network models and determines the minimum execution interval for the event trigger. A simulation example demonstrates that the PTANN and ET-PTANN models outperform other related neural network models in terms of computational efficiency and convergence rate. Finally, the practicality of the PTANN and ET-PTANN models is demonstrated through their application for mobile sound source localization.

9.
IEEE Trans Cybern ; PP2024 Jan 25.
Article in English | MEDLINE | ID: mdl-38271175

ABSTRACT

This article investigates the sliding mode control (SMC) problem for a class of uncertain 2-D systems described by the Roesser models with a bounded disturbance. In order to reduce the communication usage between the controller and the actuators, it is supposed that only one actuator node can gain the access to the network at each sampling time along horizontal or vertical direction, where a proper 2-D round-robin protocol is designed to periodically regulate the access token and a set of zero-order holders (ZOHs) is employed to keep the other actuator nodes unchanged until the next renewed signal arrives. Based on a novel 2-D common sliding function, a token-dependent 2-D SMC scheme with first-order sliding mode is appropriately constructed to cope with the impacts from the periodic scheduling signal and the ZOHs. Furthermore, a novel super-twisting-like 2-D SMC scheme with second-order sliding mode is designed to improve the robustness against the bounded disturbance. By resorting to token-dependent Lyapunov-like function, sufficient conditions are obtained to guarantee the ultimate boundedness of the horizontal and vertical states as well as the 2-D common sliding function. For acquiring the optimized gain matrices, two searching algorithms are formulated to solve two optimization problems arising from finding optimized control performance. Finally, two comparative examples are exploited to demonstrate the effectiveness and the advantageous of the proposed first-and second-order 2-D SMC design schemes under round-robin scheduling mechanism.

10.
IEEE Trans Cybern ; 54(1): 641-654, 2024 Jan.
Article in English | MEDLINE | ID: mdl-37535490

ABSTRACT

This article deals with the distributed proportional-integral state estimation problem for nonlinear systems over sensor networks (SNs), where a number of spatially distributed sensor nodes are utilized to collect the system information. The signal transmissions among different sensor nodes are realized via their individual channels subject to energy-constrained Denial-of-Service (EC-DoS) cyber-attacks launched by the adversaries whose aim is to block the nodewise communications. Such EC-DoS attacks are characterized by a sequence of attack starting time-instants and a sequence of attack durations. Based on the measurement outputs of each node, a novel distributed fuzzy proportional-integral estimator is proposed that reflects the topological information of the SNs. The estimation error dynamics is shown to be regulated by a switching system under certain assumptions on the frequency and the duration of the EC-DoS attacks. Then, by resorting to the average dwell-time method, a unified framework is established to analyze the dynamical behaviors of the resultant estimation error system, and sufficient conditions are obtained to guarantee the stability as well as the weighted H∞ performance of the estimation error dynamics. Finally, a numerical example is given to verify the effectiveness of the proposed estimation scheme.

11.
Neural Netw ; 170: 494-505, 2024 Feb.
Article in English | MEDLINE | ID: mdl-38039686

ABSTRACT

This paper addresses the dynamic quaternion-valued Sylvester equation (DQSE) using the quaternion real representation and the neural network method. To transform the Sylvester equation in the quaternion field into an equivalent equation in the real field, three different real representation modes for the quaternion are adopted by considering the non-commutativity of quaternion multiplication. Based on the equivalent Sylvester equation in the real field, a novel recurrent neural network model with an integral design formula is proposed to solve the DQSE. The proposed model, referred to as the fixed-time error-monitoring neural network (FTEMNN), achieves fixed-time convergence through the action of a state-of-the-art nonlinear activation function. The fixed-time convergence of the FTEMNN model is theoretically analyzed. Two examples are presented to verify the performance of the FTEMNN model with a specific focus on fixed-time convergence. Furthermore, the chattering phenomenon of the FTEMNN model is discussed, and a saturation function scheme is designed. Finally, the practical value of the FTEMNN model is demonstrated through its application to image fusion denoising.


Subject(s)
Neural Networks, Computer
12.
Comput Biol Med ; 169: 107879, 2024 Feb.
Article in English | MEDLINE | ID: mdl-38142549

ABSTRACT

The liver is one of the organs with the highest incidence rate in the human body, and late-stage liver cancer is basically incurable. Therefore, early diagnosis and lesion location of liver cancer are of important clinical value. This study proposes an enhanced network architecture ELTS-Net based on the 3D U-Net model, to address the limitations of conventional image segmentation methods and the underutilization of image spatial features by the 2D U-Net network structure. ELTS-Net expands upon the original network by incorporating dilated convolutions to increase the receptive field of the convolutional kernel. Additionally, an attention residual module, comprising an attention mechanism and residual connections, replaces the original convolutional module, serving as the primary components of the encoder and decoder. This design enables the network to capture contextual information globally in both channel and spatial dimensions. Furthermore, deep supervision modules are integrated between different levels of the decoder network, providing additional feedback from deeper intermediate layers. This constrains the network weights to the target regions and optimizing segmentation results. Evaluation on the LiTS2017 dataset shows improvements in evaluation metrics for liver and tumor segmentation tasks compared to the baseline 3D U-Net model, achieving 95.2% liver segmentation accuracy and 71.9% tumor segmentation accuracy, with accuracy improvements of 0.9% and 3.1% respectively. The experimental results validate the superior segmentation performance of ELTS-Net compared to other comparison models, offering valuable guidance for clinical diagnosis and treatment.


Subject(s)
Liver Neoplasms , Humans , Algorithms , Benchmarking , Image Processing, Computer-Assisted
13.
Comput Biol Med ; 169: 107901, 2024 Feb.
Article in English | MEDLINE | ID: mdl-38159400

ABSTRACT

Because of the intricate topological structure and connection of the human brain, extracting deep spatial features from electroencephalograph (EEG) signals is a challenging and time-consuming task. The extraction of topological spatial information plays a crucial role in EEG classification, and the architecture of the spatial convolution greatly affects the performance and complexity of convolutional neural network (CNN) based EEG classification models. In this study, a progressive convolution CNN architecture named EEGProgress is proposed, aiming to efficiently extract the topological spatial information of EEG signals from multi-scale levels (electrode, brain region, hemisphere, global) with superior speed. To achieve this, the raw EEG data is permuted using the empirical topological permutation rule, integrating the EEG data with numerous topological properties. Subsequently, the spatial features are extracted by a progressive feature extractor including prior, electrode, region, and hemisphere convolution blocks, progressively extracting the deep spatial features with reduced parameters and speed. Finally, the comparison and ablation experiments under both cross-subject and within-subject scenarios are conducted on a public dataset to verify the performance of the proposed EEGProgress and the effectiveness of the topological permutation. The results demonstrate the superior feature extraction ability of the proposed EEGProgress, with an average increase of 4.02% compared to other CNN-based EEG classification models under both cross-subject and within-subject scenarios. Furthermore, with the obtained average testing time, FLOPs, and parameters, the proposed EEGProgress outperforms other comparison models in terms of model complexity.


Subject(s)
Brain , Neural Networks, Computer , Humans , Electrodes , Electroencephalography
14.
Heliyon ; 9(12): e22569, 2023 Dec.
Article in English | MEDLINE | ID: mdl-38058450

ABSTRACT

This paper innovatively constructed an analytical and forecasting framework to predict PM2.5 concentration levels for 16 municipal districts in Shanghai. By means of XGBoost parameters adjustment, empirical mode decomposition, and model fusion, improvements are made on XGBoost prediction accuracy and stability so that prediction deviation at extreme points can be avoided. The main findings of this paper can be summarized as follows: 1) Compared with the original model, the goodness of fit of the modified XGBoost model on the test set increased by 17 %, and the root mean square error decreased by 28 %; 2) The variation of PM2.5 concentration in Shanghai has a significant seasonal (cyclical) effect, and its fluctuation period is 3 months (a quarter). In winter, the frequency of extreme value points is significantly higher than that in other seasons; 3) In terms of spatial distribution, the PM2.5 concentration in the central city of Shanghai is higher than that in the rural areas, and the PM2.5 concentration gradually decreases from center city to the surrounding areas. The innovation and contribution of this paper can be summarized as follows: 1) EEMD algorithm verified by SSA was used to decompose the original model without reconstructing all subsequences and get the best weighing among each part of the hybrid model by using variable weight assignment; 2) The city was cut into pieces according to administrative districts in avoid of the duplicate analysis when utilizing advised Kriging interpolation; 3) IDW method was applied to verified Kriging interpolation to increase the accuracy; 4) The latitude and longitude were innovatively converted into the arc length of the corresponding spherical surface; 5) Hierarchical analysis method was used to obtain the order of importance among the PM2.5 monitoring stations, which could improve the accuracy and achieve dimension reduction.

15.
Article in English | MEDLINE | ID: mdl-37971919

ABSTRACT

This brief is concerned with the prediction problem of product popularity under a social network (SN) with positive-negative diffusion (PND). First, a PND model is proposed to enable the simulation of product diffusion, and three user states are defined. Second, an optimal and precise feature vector of every user is extracted through a multi-agent-system-based attention mechanism (MASAM) that is devised. The weight matrix shared in the mechanism of all agents is learned using a distributed learning algorithm provided in MASAM. Third, an MAS model for product diffusion on SN is established based on the feature representations from MASAM. Rules for agent interaction during PND diffusion are suggested, which accelerate the simulation of information spread in SN. Finally, comprehensive experiments are conducted to verify the effectiveness and efficiency of the proposed models and algorithms in prediction and to compare their performance with baseline methods. Furthermore, a case study is provided to illustrate the applicability and extendibility of the developed algorithm.

16.
Article in English | MEDLINE | ID: mdl-37966928

ABSTRACT

This article is concerned with the distributed set-membership fusion estimation problem for a class of artificial neural networks (ANNs), where the dynamic event-triggered mechanism (ETM) is utilized to schedule the signal transmission from sensors to local estimators to save resource consumption and avoid data congestion. The main purpose of this article is to design a distributed set-membership fusion estimation algorithm that ensures the global estimation error resides in a zonotope at each time instant and, meanwhile, the radius of the zonotope is ultimately bounded. By means of the zonotope properties and the linear matrix inequality (LMI) technique, the zonotope restraining the prediction error is first calculated to improve the prediction accuracy and subsequently, the zonotope enclosing the local estimation error is derived to enhance the estimation performance. By taking into account the side-effect of the order reduction technique (utilized in designing the local estimation algorithm) of the zonotope, a sufficient condition is derived to guarantee the ultimate boundedness of the radius of the zonotope that encompasses the local estimation error. Furthermore, parameters of the local estimators are obtained via solutions to certain bilinear matrix inequalities. Moreover, the zonotope-based distributed fusion estimator is obtained through minimizing certain upper bound of the radius of the zonotope (that contains the global estimation error) according to the matrix-weighted fusion rule. Finally, the effectiveness of the proposed distributed fusion estimation method is illustrated via a numerical example.

17.
J Chem Theory Comput ; 19(22): 8460-8471, 2023 Nov 28.
Article in English | MEDLINE | ID: mdl-37947474

ABSTRACT

Data-driven predictive methods that can efficiently and accurately transform protein sequences into biologically active structures are highly valuable for scientific research and medical development. Determining an accurate folding landscape using coevolutionary information is fundamental to the success of modern protein structure prediction methods. As the state of the art, AlphaFold2 has dramatically raised the accuracy without performing explicit coevolutionary analysis. Nevertheless, its performance still shows strong dependence on available sequence homologues. Based on the interrogation on the cause of such dependence, we presented EvoGen, a meta generative model, to remedy the underperformance of AlphaFold2 for poor MSA targets. By prompting the model with calibrated or virtually generated homologue sequences, EvoGen helps AlphaFold2 fold accurately in the low-data regime and even achieve encouraging performance with single-sequence predictions. Being able to make accurate predictions with few-shot MSA not only generalizes AlphaFold2 better for orphan sequences but also democratizes its use for high-throughput applications. Besides, EvoGen combined with AlphaFold2 yields a probabilistic structure generation method that could explore alternative conformations of protein sequences, and the task-aware differentiable algorithm for sequence generation will benefit other related tasks including protein design.


Subject(s)
Algorithms , Amino Acid Sequence , Protein Conformation
18.
Article in English | MEDLINE | ID: mdl-37947945

ABSTRACT

The incidence of bone-related diseases is higher in the elderly population, which greatly affects the patients' quality of life. Throughout this research, we synthesized a biocomposite nanomaterial of CeO2. The unique structural characteristics of CeO2 nanoparticles (CeO2 NPs) were studied by means of XRD, TEM, and SEM. Nanoparticles of an osteosarcoma cell line (MG-63) were assayed for ALP enzyme levels, key proteins in osteoblasts, and stained with Alizarin Red S to assess the physical properties, bioactivity, and calcium deposition of the osteosarcoma cell line. Moreover, we used H2O2 to construct an oxidative stress model to evaluate the antioxidant activity of CeO2 NPs. Experimental data showed that the CeO2 NPs increased the antioxidant capacity of MG-63 cells and significantly increased alkaline phosphatase activity, calcium deposition, and bone growth as manifested by increased expression of bone differentiation proteins BMP2, OCN, OPN, and type I collagen. Interestingly, RNA interference and functional recovery experiments confirmed that CeO2 NPs enhanced the antioxidant activity of MG-63 cells related to NRF2 signaling. In conclusion, the material is expected to be a potential treatment for bone-related diseases.

19.
Article in English | MEDLINE | ID: mdl-37698961

ABSTRACT

The imbalanced development between deep learning-based model design and motor imagery (MI) data acquisition raises concerns about the potential overfitting issue-models can identify training data well but fail to generalize test data. In this study, a Spatial Variation Generation (SVG) algorithm for MI data augmentation is proposed to alleviate the overfitting issue. In essence, SVG generates MI data using variations of electrode placement and brain spatial pattern, ultimately elevating the density of the raw sample vicinity. The proposed SVG prevents models from memorizing the training data by replacing the raw samples with the proper vicinal distribution. Moreover, SVG generates a uniform distribution and stabilizes the training process of models. In comparison studies involving five deep learning-based models across eight datasets, the proposed SVG algorithm exhibited a notable improvement of 0.021 in the area under the receiver operating characteristic curve (AUC). The improvement achieved by SVG outperforms other data augmentation algorithms. Further results from the ablation study verify the effectiveness of each component of SVG. Finally, the studies in the control group with varying numbers of samples show that the SVG algorithm consistently improves the AUC, with improvements ranging from approximately 0.02 to 0.15.


Subject(s)
Algorithms , Brain , Humans , Electrodes , ROC Curve
20.
Article in English | MEDLINE | ID: mdl-37610894

ABSTRACT

This article is concerned with the state estimation problem for a class of complex networks (CNs) with uncertain inner couplings and packet losses over communication networks. The inner couplings are allowed to be uncertain and varying in a specific interval. The amplify-and-forward (AaF) relay protocols are introduced to improve the communication quality and enhance the propagation distance. The Bernoulli random variables are used to characterize the randomly occurring packet losses encountered in communication channels. The focus of this article is on the design of a state estimator for each node of CNs such that a prescribed H∞ performance constraint is satisfied for the dynamical error system over a finite horizon. A sufficient condition is first provided to verify the existence of the desired H∞ state estimator, and the estimator gain is then determined by solving two coupled backward Riccati difference equations (RDEs). Subsequently, a recursive state estimation algorithm is put forward that is suitable for online computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed estimation method.

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