Nonlinear Mapping Research Articles

Data-driven contract design for supply chain coordination with algorithm sharing and algorithm competition

Supply chain members can intelligently learn their decisions based on historical data by using Machine-Learning (ML) algorithms. To coordinate the supply chain, the data-driven contract design problems for three contracts—buyback, quantity flexibility, and combined quantity flexibility and rebate—were investigated for a supply chain with one manufacturer and multiple retailers under algorithm sharing and algorithm competition. The problems were formulated as bi-level optimization models by introducing nonlinear mapping from historical demand data to ordering decisions and using ML algorithms to learn the mapping parameters. The bi-level optimization models were transformed into semi-infinite programming models and solved using the (nested) cutting plane methods. Empirical studies using data from two databases showed that algorithm sharing or algorithm competition, the type of contract used, and learning algorithms were the three factors influencing the performance of supply chain coordination when using a data-driven contract design. Algorithm sharing was found to be more beneficial to the supply chain members than algorithm competition in promoting supply chain coordination. An effective incentive mechanism, such as an individualized buyback ratio and a rebate from the manufacturer to the retailers with a good forecast performance, can encourage the retailers to participate in algorithm sharing and improvement.

Intelligent Sensing of Thermal Error of CNC Machine Tool Spindle Based on Multi-Source Information Fusion.

Aiming at the shortcomings of single-sensor sensing information characterization ability, which is easily interfered with by external environmental factors, a method of intelligent perception is proposed in this paper. This method integrates multi-source and multi-level information, including spindle temperature field, spindle thermal deformation, operating parameters, and motor current. Firstly, the internal and external thermal-error-related signals of the spindle system are collected by sensors, and the feature parameters are extracted; then, the radial basis function (RBF) neural network is utilized to realize the preliminary integration of the feature parameters because of the advantages of the RBF neural network, which offers strong multi-dimensional solid nonlinear mapping ability and generalization ability. Thermal-error decision values are then generated by a weighted fusion of different pieces of evidence by considering uncertain information from multiple sources. The spindle thermal-error sensing experiment was based on the spindle system of the VMC850 (Yunnan Machine Tool Group Co., LTD, Yunnan, China) vertical machining center of the Yunnan Machine Tool Factory. Experiments were designed for thermal-error sensing of the spindle under constant speed (2000 r/min and 4000 r/min), standard variable speed, and stepped variable speed conditions. The experiment's results show that the prediction accuracy of the intelligent-sensing model with multi-source information fusion can reach 98.1%, 99.3%, 98.6%, and 98.8% under the above working conditions, respectively. The intelligent-perception model proposed in this paper has higher accuracy and lower residual error than the traditional BP neural network perception and wavelet neural network models. The research in this paper provides a theoretical basis for the operation, maintenance management, and performance optimization of machine tool spindle systems.

Head pose estimation with particle swarm optimization‐based contrastive learning and multimodal entangled GCN

AbstractHead pose estimation is an especially challenging task due to the complexity nonlinear mapping from 2D feature space to 3D pose space. To address the above issue, this paper presents a novel and efficient head pose estimation framework based on particle swarm optimized contrastive learning and multimodal entangled graph convolution network. Firstly, a new network, the region and difference‐aware feature pyramid network (RD‐FPN), is proposed for 2D keypoints detection to alleviate the background interference and enhance the feature expressiveness. Then, particle swarm optimized contrastive learning is constructed to alternatively match 2D and 3D keypoints, which takes the multimodal keypoints matching accuracy as the optimization objective, while considering the similarity of cross‐modal positive and negative sample pairs from contrastive learning as a local contrastive constraint. Finally, multimodal entangled graph convolution network is designed to enhance the ability of establishing geometric relationships between keypoints and head pose angles based on second‐order bilinear attention, in which point‐edge attention is introduced to improve the representation of geometric features between multimodal keypoints. Compared with other methods, the average error of our method is reduced by 8.23%, indicating the accuracy, generalization, and efficiency of our method on the 300W‐LP, AFLW2000, BIWI datasets.

An Implicit Transformer-based Fusion Method for Hyperspectral and Multispectral Remote Sensing Image

There is an effective way to enhance the spatial resolution of hyperspectral remote sensing images by fusing them with multispectral remote sensing images. However, most of the existing deep fusion techniques adopt discretized explicit models to approximate the complex continuous nonlinear mapping in the fusion process, leading to limitations in enhancing the fidelity of spatial details. Additionally, existing algorithms commonly utilize discrete methods such as bilinear or bicubic interpolation during the hyperspectral upsampling process, leading to the loss of crucial spatial-spectral features. To this end, this study proposes a novel Implicit Transformer Fusion Generative Adversarial Network (ITF-GAN), which incorporates the continuity perception mechanism of implicit neural representation with the powerful self-attention mechanism of the Transformer architecture, which uses point-to-point implicit functions aiming to efficiently process information in both spatial and spectral dimensions. Besides, a guided implicit neural sampling module is introduced in the hyperspectral image up-sampling process to enhance the coordinated expression of features in the spatial and spectral domains, which improves the spatial resolution and spectral fidelity of the fused image during the upsampling process. A series of fusion experiments including 4x, 8x, and 16x scale factors have shown that ITF-GAN has significant advantages over current popular fusion algorithms in both objective evaluation indicators and subjective visual evaluation.

Enhancing mix proportion design of low carbon concrete for shield segment using a combination of Bayesian optimization-NGBoost and NSGA-III algorithm

The demand for segment concrete increases rapidly with the expansion of urban rail transit and underground space, which may lead to carbon emissions (CE). In the production of segment concrete, using supplement cementitious materials (SCM) can be used to reduce CE instead of cement. However, SCM contents are usually determined by many orthogonal experiments, which are often time-consuming and only consider the limited experimental variables. Therefore, a novel hybrid intelligent algorithm combining Bayesian optimization (BO), natural gradient boosting (NGBoost) and non-dominated sorting genetic algorithm (NSGA)-III is proposed, which overcomes these disadvantages. Firstly, NGBoost model after hyperparameter optimization using BO is used to establish a nonlinear mapping relationship between segment concrete mix proportion and performance, which was used as the fitness function of the non-dominated sorting genetic algorithm (NSGA-III). Secondly, the optimal Pareto solutions were obtained through NSGA-III, and the reasonable range of segment concrete mixing proportion was obtained. Finally, a segment concrete production case was used to verify the effectiveness of the proposed algorithm. The results showed that the proposed hybrid algorithm combining proposed scheme decision strategy can obtain an optimal design scheme for concrete mix proportion. In addition, the comprehensive optimization rate of the obtained optimal scheme compared to the experimental optimal group was 11.5%. Moreover, the amount of phosphorous slag (PS) and granulated blast furnace slag (GBFS) in the optimal scheme was 26%, with a mass ratio of 1:2. Compared to the experimental optimal group, the optimal scheme can reduce the cost and CE per cubic meter by 31.64 yuan and 31.04 kg, respectively. Furthermore, the hybrid algorithm proposed can accurately obtains an optimal amount of SCM, which could be used as a supporting tool to reduce the production cost and CE of segment concrete. Overall, this research contributes to combining machine learning algorithms with actual production processes, which overcomes the data limitations of traditional experiments. It also provides a new intelligent approach and reference cases for the low-carbon design and sustainable development of building materials such as concrete.

On multiple impacts of functional gradient magneto-electro-elastic plates with convex and concave configurations and prediction based on PSO-BPNN

Revealing the coupling mechanism between the nonlinear effect and the multi-physical fields in the bistable plate, as well as the interaction between multiple impacts, promotes the innovative development of morphing structures. Improved neural network technology contributes to the adaptive design and functional integration of morphing structures. The multiple impacts of functional gradient magneto-electro-elastic (FG-MEE) plates with convex and concave configurations are investigated. In the Reddy high-order shear plate theory considering the bistable configuration, functional gradient models and magneto-electro-mechanical effect models are constructed. To measure the contact forces in the multi-impact process, the modified Hertz contact model is introduced. Through the Hamiltonian variational principle, the nonlinear multiple impact dynamics of the FG-MEE plates with convex and concave configurations are modeled. To obtain the bistable configuration induced by the magneto-electro-mechanical coupling effects, the two-step perturbation method is extended in multiple physical fields. Further, the two-step perturbation method and the Galerkin method are extended to acquire the higher-order truncated solutions for the multiple impact responses of FG-MEE plates with convex and concave configurations. Based on the numerical result database of multiple impact response, the nonlinear mapping relationship between the structure characteristics, load characteristics and multiple impact responses of bistable FG-MEE plate is constructed by the particle swarm optimization-back propagation (PSO-BP) technology. Ultimately, the coupling effects between the multi-physical fields and nonlinear behaviors in FG-MEE plates with convex and concave configurations are comparatively analyzed, and the interactions between multiple impacts are systematically revealed.

Distributed adaptive finite-time output feedback containment control for nonstrict-feedback stochastic multi-agent systems via command filters

In this paper, distributed adaptive finite-time output feedback containment control based on command filters is proposed for nonstrict-feedback stochastic multi-agent systems (SMASs) with unmodeled dynamics, input quantization and prescribed performance. The unknown states are estimated using a high-gain observer, the unmodeled dynamics is handled by introducing a measurable dynamic signal, and the input signal is processed using an integrated quantizer that combines the advantages of uniform quantizer and hysteretic quantizer. The hyperbolic tangent function and time-varying function are applied to construct the performance function, and the constrained containment error is transformed into an unconstrained system through nonlinear mapping (NM). Unknown smooth functions are handled with the superb approximation capability of radial basis function neural networks (RBFNNs). Based on stochastic finite-time theory and dynamic surface control (DSC) method, nonlinear command filters are introduced to reduce the use of black-box functions and simplify the controller design. Finally, the theoretical analysis and two sets of experimental results demonstrate that all signals in the controlled system are semi-global finite-time stability in probability (SGFSP) and the designed controller works well.

Low-Rank Multilabel Learning Based on Nonlinear Mapping

Low-Rank Multilabel Learning Based on Nonlinear Mapping

Resolution Enhancement of SOHO/MDI Magnetograms

Research on the solar magnetic field and its effects on solar dynamo mechanisms and space weather events has benefited from the continual improvements in instrument resolution and measurement frequency. The augmentation and assimilation of historical observational data timelines also play a significant role in understanding the patterns of solar magnetic field variation. Within the realm of astronomical data processing, super-resolution (SR) reconstruction refers to the process of using a substantial corpus of training data to learn the nonlinear mapping between low-resolution (LR) and high-resolution (HR) images, thereby achieving higher-resolution astronomical images. This paper is an application study in high-dimensional nonlinear regression. Deep learning models were employed to perform SR modeling on SOHO/MDI magnetograms and SDO/HMI magnetograms, thus reliably achieving resolution enhancement of full-disk SOHO/MDI magnetograms and enhancing the image resolution to obtain more detailed information. For this study, a data set comprising 9717 pairs of data from 2010 April to 2011 February was used as the training set, 1332 pairs from 2011 March were used as the validation set and 1034 pairs from 2011 April were used as the test set. After data preprocessing, we randomly cropped 128 × 128 sub-images as the LR cases from the full-disk MDI magnetograms, and the corresponding 512 × 512 sub-images as HR ones from the HMI full-disk magnetograms for model training. The tests conducted have shown that the study successfully produced reliable 4× SR reconstruction of full-disk MDI magnetograms. The MESR model’s results (0.911) were highly correlated with the target HMI magnetographs as indicated by the correlation coefficient values. Furthermore, the method achieved the best PSNR, SSIM, MAE and RMSE values, indicating that the MESR model can effectively reconstruct magnetograms.

Deep Learning With Physics-Embedded Neural Network for Full Waveform Ultrasonic Brain Imaging.

The convenience, safety, and affordability of ultrasound imaging make it a vital non-invasive diagnostic technique for examining soft tissues. However, significant differences in acoustic impedance between the skull and soft tissues hinder the successful application of traditional ultrasound for brain imaging. In this study, we propose a physics-embedded neural network with deep learning based full waveform inversion (PEN-FWI), which can achieve reliable quantitative imaging of brain tissues. The network consists of two fundamental components: forward convolutional neural network (FCNN) and inversion sub-neural network (ISNN). The FCNN explores the nonlinear mapping relationship between the brain model and the wavefield, replacing the tedious wavefield calculation process based on the finite difference method. The ISNN implements the mapping from the wavefield to the model. PEN-FWI includes three iterative steps, each embedding the F CNN into the ISNN, ultimately achieving tomography from wavefield to brain models. Simulation and laboratory tests indicate that PEN-FWI can produce high-quality imaging of the skull and soft tissues, even starting from a homogeneous water model. PEN-FWI can achieve excellent imaging of clot models with constant uniform distribution of velocity, randomly Gaussian distribution of velocity, and irregularly shaped randomly distributed velocity. Robust differentiation can also be achieved for brain slices of various tissues and skulls, resulting in high-quality imaging. The imaging time for a horizontal cross-sectional imag e of the brain is only 1.13 seconds. This algorithm can effectively promote ultrasound-based brain tomography and provide feasible solutions in other fields.

Finite algebras in the design of multivariate cryptography algorithms

A new approach to the design of multivariate public-key cryptalgorithms is introduced. It envisages using non-linear mappings defined as squaring and cubic operations in finite fields represented as finite algebras. The developed approach allows significant reduction of the size of public key and thereby make post-quantum algorithms of multivariate cryptography much more practical. In the developed algorithms, the secret key includes a set of values of structural constants that determine the modifications of the finite fields used and the coefficients in the set of sixth degree polynomials that make up the public key

Domain Adaptation and Semantic Drawing Driven Sketch-to-Photo Retrieval using Collaborative Generative Representation Learning

Abstract: Sketch-based face recognition is an interesting task in vision and multimedia research yet it is quite challenging due to the great difference between face photos and sketches. In this paper we propose a novel approach for photo-sketch generation aiming to automatically transform face photos into detail-preserving personal sketches. Unlike the traditional models synthesizing sketches based on a dictionary of exemplars we develop a fully convolutional network to learn the end-to-end photosketch mapping. Our approach takes whole face photos as inputs and directly generates the corresponding sketch images with efficient inference and learning in which the architecture is stacked by only convolutional kernels of very small sizes. The exemplar-based method is most frequently used in face sketch synthesis because of its efficiency in representing the nonlinear mapping between face photos and sketches. However, the sketches synthesized by existing exemplar-based methods suffer from block artifacts and blur effects. In addition, most exemplar-based methods ignore the training sketches in the weight representation process. To improve synthesis performance, a novel joint training model is proposed in this paper, taking sketches into consideration. First, we construct the joint training photo and sketch by concatenating the original photo and its sketch with a high-pass filtered image of their corresponding sketch. Then, an offline random sampling strategy is adopted for each test photo patch to select the joint training photo and sketch patches in the neighboring region. Finally, a novel locality constraint is designed to calculate the reconstruction weight, allowing the synthesized sketches to have more detailed information

A Dual-Branch Self-Boosting Network Based on Noise2Noise for Unsupervised Image Denoising

While unsupervised denoising models have shown progress in recent years, their noise reduction capabilities still lag behind those of supervised denoising models. This limitation can be attributed to the lack of effective constraints during training, which only utilizes noisy images and hinders further performance improvements In this work, we propose a novel dual-branch self-boosting network called DBSNet, which offers a straightforward and effective approach to image denoising. By leveraging task-dependent features, we exploit the intrinsic relationships between the two branches to enhance the effectiveness of our proposed model. Initially, we extend the classic Noise2Noise (N2N) architecture by adding a new branch for noise component prediction to the existing single-branch network designed for content prediction. This expansion creates a dual-branch structure, enabling us to simultaneously decompose a given noisy image into its content (clean) and noise components. This enhancement allows us to establish stronger constraint conditions and construct more powerful loss functions to guide the training process. Furthermore, we replace the UNet structure in the N2N network with the proven DnCNN (Denoising Convolutional Neural Network) sequential network architecture, which enhances the nonlinear mapping capabilities of the DBSNet. This modification enables our dual-branch network to effectively map a noisy image to its content (clean) and noise components simultaneously. To further improve the stability and effectiveness of training, and consequently enhance the denoising performance, we introduce a feedback mechanism where the network’s outputs, i.e., content and noise components, are fed back into the dual-branch network. This results in an enhanced loss function that ensures our model possesses excellent decomposition ability and further boosts the denoising performance. Extensive experiments conducted on both synthetic and real-world images demonstrate that the proposed DBSNet outperforms the unsupervised N2N denoising model as well as mainstream supervised models trained with supervised methods. Moreover, the evaluation results on real-world noisy images highlight the desirable generalization ability of DBSNet for practical denoising applications.

Raw infrared image enhancement via an inverted framework based on infrared basic prior

Existing raw infrared image enhancement methods can effectively compress image and improve contrast. However, there still exist limitations. First, enhanced images are often over-exposed. Second, a high contrast but low noise enhanced image is difficult to be obtained due to the fact that the noise level increases with contrast. Third, the targets are not sufficiently salient in enhanced image. In this paper, we design an inverted enhancement framework to address the three limitations simultaneously. Specifically, we analyze the widely recognized features of raw infrared image and call them infrared image basic prior. That is, infrared detectors are often used to detect targets under special conditions and our attention mechanism is to focus on high radiation objects, but there are few targets in the scene. Then we modify the traditional image enhancement framework into an inverted framework based on infrared image basic prior and design an inverted nonlinear gray mapping curve, which avoids over-exposure and noise over-amplification. Furthermore, result is further improved by using layer decomposition model and gamma correction. Enhanced result yields the targets of our main interest. Finally, the extended applications are performed and show ability to stimulate the effectiveness of algorithms of related fields. Experiments show that our approach yields better results than state-of-the-art methods. A video of results is provided at https://github.com/wangyuro/Datashare1.

Intelligent Stroke Disease Prediction Model Using Deep Learning Approaches.

Stroke is a high morbidity and mortality disease that poses a serious threat to people's health. Early recognition of the various warning signs of stroke is necessary so that timely clinical intervention can help reduce the severity of stroke. Deep neural networks have powerful feature representation capabilities and can automatically learn discriminant features from large amounts of data. This paper uses a range of physiological characteristic parameters and collaborates with deep neural networks, such as the Wasserstein generative adversarial networks with gradient penalty and regression network, to construct a stroke prediction model. Firstly, to address the problem of imbalance between positive and negative samples in the stroke public data set, we performed positive sample data augmentation and utilized WGAN-GP to generate stroke data with high fidelity and used it for the training of the prediction network model. Then, the relationship between observable physiological characteristic parameters and the predicted risk of suffering a stroke was modeled as a nonlinear mapping transformation, and a stroke prediction model based on a deep regression network was designed. Finally, the proposed method is compared with commonly used machine learning-based classification algorithms such as decision tree, random forest, support vector machine, and artificial neural networks. The prediction results of the proposed method are optimal in the comprehensive measurement index F. Further ablation experiments also show that the designed prediction model has certain robustness and can effectively predict stroke diseases.

Response Surface Methodology Approach to Optimize Parameters for Coagulation Process Using Polyaluminum Chloride (PAC)

Coagulation is a process affected by multiple variables, nonlinear mapping and multiple perturbations. In order to realize the precise dosage of flocculants, polyaluminum chloride (PAC) was taken as the research object to explore the effects of temperature, water turbidity, pH and CODMn on the dosage of PAC and coagulation effect. A response surface methodology (RSM) experiment was carried out based on a single-factor experiment. The turbidity, pH and dosage of a single parameter, as well as the interaction term and secondary term, all have significant influence on coagulation effect. The optimal reaction conditions were calculated using Design-Expert software: pH, 7.48; turbidity, 14.59 NTU; dosage, 24.01 mg/L; and the error between the experimental value and the predicted value, 4.08%. Establishing a model with residual turbidity as a consideration index can help to calculate the optimal dosage of PAC, which is conducive to a reasonable and accurate control of the dosage of PAC in the coagulation process, so as to achieve the goal of low turbidity of effluent and low production cost.

Constructive approach and randomization of a two-parameter chaos system for securing data

Secure communication techniques are important due to the increase in the number of technology users across the world. Likewise, a more random encryption algorithm suitable to secure data from unauthorised users is highly expected. This paper proposes a two-parameter nonlinear chaos map that is sensitive to the trio seed (s0, \alpha, \lambda) and has better information encryption. We introduce the parameter \alpha to linearise the conventional chaos system, which in turn brings a delay in the cryptosystems. The delay is a phenomenon that changes the chaotic features of a system. A small delay in the system leads to more aperiodicity and the unpredictability of the chaotic attractions. We normalise the new chaos map and use the Lipschitz and pseudo-contractive operators to obtain its irregularity region in Hilbert spaces. We also analyse the chaos map in terms of trajectory, Lyapunov exponent, complexity, and information entropy. Results obtained show that the new chaos map has a wide chaotic range and better statistical properties. It also maintains low complexity due to its linearity and produces more key spaces than most existing chaotic maps.

PRGNN: Modeling high-order proximity with relational graph neural network for knowledge graph completion

Relational Graph Neural Networks (RGNNs) are designed to extract structural information from relational graphs and have garnered attention in the domain of Knowledge Graph Completion (KGC). However, recent empirical investigations have indicated that some prominent RGNN-based methodologies have not significantly enhanced precision, prompting questions regarding the efficacy of RGNNs in KGC applications.In this paper, we introduce a novel RGNN-based KGC approach, the Proximity Relational Graph Neural Network (PRGNN), which excels at modeling high-order proximities among entities. PRGNN is founded on a notably straightforward yet effective RGNN framework that discards unnecessary components commonly incorporated in previous approaches, such as attention layers, and linear and non-linear mappings. We demonstrate that PRGNN empowers traditional KGC techniques to apprehend high-order proximities among entities more effectively. Through extensive experimentation on benchmark datasets, we establish that PRGNN consistently outperforms conventional KGC methods and achieves state-of-the-art results. Furthermore, we show that PRGNN necessitates considerably less training time (ranging from one-third to one-fifth) and fewer parameters (ranging from half to two-thirds), rendering it an exceptionally efficient approach. All data and code have been made available at 11https://github.com/zhudanhao/PRGNN..

Clean and robust multi-level subspace representations learning for deep multi-view subspace clustering

Deep multi-view subspace clustering has achieved increasing attention owing to its encouraging ability to address the nonlinear multi-view data. Despite significant progress, most existing deep multi-view subspace clustering methods still suffer from the following drawbacks. First, they usually focus on utilizing the last-level feature from the last encoder layer of the auto-encoder related to each view, yet often overlook exploiting the earlier-level features from the earlier encoder layers as well as integrating the multi-level features from multiple encoder layers. Second, when learning the subspace representation from the self-expressive layer, they rarely consider the cleanliness and robustness of the learned subspace representation. To overcome these drawbacks, this paper proposes a novel clean and robust multi-level subspace representations learning for deep multi-view subspace clustering (CRMSRL). Specifically, the auto-encoder is adopted to nonlinearly map each view into the multi-level features, and then multiple self-expressive layers are added between the encoder layers and their corresponding decoder layers to provide multiple information flow paths through the auto-encoder and learn the multi-level subspace representations corresponding to the multi-level features. Consequently, the intricate hierarchical information embedded in the multi-level features is passed to the corresponding multi-level subspace representations. Moreover, with the idea of robust principal component analysis (RPCA), the learned multi-level subspace representations can be further purified to achieve the cleaner and more robust ones. In addition, to excavate the structural consistency among different views, the common layer is designed to interact with different view-specific self-expressive layers and achieve the high-quality common subspace representation, which can be applied to the spectral clustering algorithm to obtain the final clustering results. Experimental results show that CRMSRL outperforms twelve state-of-the-art baseline methods on six benchmark datasets. In particular, CRMSRL achieves 4.5% improvements on the MSRCV1 dataset in terms of accuracy, compared with the best baseline method.

Integral reinforcement learning‐based optimal tracking control for uncertain nonlinear systems under input constraint and specified performance constraints

AbstractThis article addresses the optimal tracking control problem with prescribed performance for uncertain nonlinear systems subject to input constraint and unknown disturbances. First, a fixed‐time monotonic convergence function is introduced to restrain tracking error, and a nonlinear mapping technique is employed to transform the constrained error into an unconstrained variable, then the fixed‐time output tracking issue is boiled down to the boundedness problem of the transformed variable. With the aid of a nonquadratic cost function, the input constraint is encoded into the optimization problem. To solve the unknown disturbances, an auxiliary system and an auxiliary disturbance policy are constructed, and the optimal control problem is formulated as a two‐player zero‐sum game. Moreover, a Hamilton–Jacobi–Isaacs (HJI) equation associated with this nonquadratic zero‐sum game is established to give the optimal control and the worst‐case disturbance policy solution. Subsequently, to avoid using knowledge of the system dynamics, three neural network approximators, namely, actor, critic, and disturbance, which are tuned online and simultaneously for approximating the solution of HJI, are constructed based on the integral reinforcement learning algorithm. Theoretical analysis shows that the reconstructed error system states and the weight estimation errors are semi‐globally uniformly ultimately bounded. Finally, the simulation study further tests the availability of the proposed control strategy.