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For nonlinear systems subjected to external disturbances, an adaptive terminal sliding mode control (TSM) approach with fixed-time convergence is presented in this paper. The introduction of the fixed-time TSM with the sliding surface and the new Lemma of fixed-time stability are the main topics of discussion. The suggested approach demonstrates quick convergence, smooth and non-singular control input, and stability within a fixed time. Existing fixed-time TSM schemes are often impacted by unknown dynamics such as uncertainty and disturbances. Therefore, the proposed strategy is developed by combining the fixed-time TSM with an adaptive scheme. This adaptive method deals with an uncertain dynamic system when there are external disturbances. The stability of a closed-loop structure in a fixed-time will be shown by the findings of the Lyapunov analysis. Finally, the outcomes of the simulations are shown to evaluate and demonstrate the efficacy of the suggested method. As a result, examples with different cases are provided for a better comparison of suggested and existing control strategies.
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Algoritmos , Dinámicas no Lineales , Incertidumbre , Simulación por Computador , Modelos TeóricosRESUMEN
The performance of the robotic manipulator is negatively impacted by outside disturbances and uncertain parameters. The system's variables are also highly coupled, complex, and nonlinear, indicating that it is a multi-input, multi-output system. Therefore, it is necessary to develop a controller that can control the variables in the system in order to handle these complications. This work proposes six control structures based on neural networks (NNs) with proportional integral derivative (PID) and fractional-order PID (FOPID) controllers to operate a 2-link rigid robot manipulator (2-LRRM) for trajectory tracking. These are named as set-point-weighted PID (W-PID), set-point weighted FOPID (W-FOPID), recurrent neural network (RNN)-like PID (RNNPID), RNN-like FOPID (RNN-FOPID), NN+PID, and NN+FOPID controllers. The zebra optimization algorithm (ZOA) was used to adjust the parameters of the proposed controllers while reducing the integral-time-square error (ITSE). A new objective function was proposed for tuning to generate controllers with minimal chattering in the control signal. After implementing the proposed controller designs, a comparative robustness study was conducted among these controllers by altering the initial conditions, disturbances, and model uncertainties. The simulation results demonstrate that the NN+FOPID controller has the best trajectory tracking performance with the minimum ITSE and best robustness against changes in the initial states, external disturbances, and parameter uncertainties compared to the other controllers.
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Robotic manipulators are nonlinear systems, multi-input multi-output, highly coupled and complicated whose performance is negatively impacted by external disturbances and parameter un-certainties. Therefore, the controllers designed for such systems must be capable of managing their complexity. The main aim of this study is to tackle the trajectory tracking issue of the three-Link Rigid Robot Manipulator (3-LRRM) based on designing three control structures using a combi-nation Neural Network (NN) with Proportional, Integral and Derivative (PID) actions named Neural Controller Like PIPD (NN-PIPD) controller, Neural Network plus PID (NN + PID) controller NN + PID controller and Elman Neural Network Like PID (ELNN-PID) controller. The parameters of the proposed controllers are adjusted utilizing the Coot Optimization Algorithm (COOA) in order to reduce the Integral Time Square Error (ITSE). A novel objective function for tuning process to produce a controller with minimum value of the chattering in the control signal is proposed. The performance of the proposed controllers is evaluated in terms of disturbance rejection, model uncertainty, fluctuating initial conditions and reference trajectory tracking. According to the simulation results proved that the suggested NN-PIPD controller outperforms all other proposed controller structures for tracking performance, stability, and robustness. As a result of the com-parison analysis the optimal controller was considered to be an NN-PIPD controller for tracking trajectory, rejecting disturbances, and parameter variation with minimizing ITSE of 0.001777.
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The integration of renewable energy resources into the smart grids improves the system resilience, provide sustainable demand-generation balance, and produces clean electricity with minimal leakage currents. However, the renewable sources are intermittent in nature. Therefore, it is necessary to develop scheduling strategy to optimise hybrid PV-wind-controllable distributed generator based Microgrids in grid-connected and stand-alone modes of operation. In this manuscript, a priority-based cost optimization function is developed to show the relative significance of one cost component over another for the optimal operation of the Microgrid. The uncertainties associated with various intermittent parameters in Microgrid have also been introduced in the proposed scheduling methodology. The objective function includes the operating cost of CDGs, the emission cost associated with CDGs, the battery cost, the cost of grid energy exchange, and the cost associated with load shedding. A penalty function is also incorporated in the cost function for violations of any constraints. Multiple scenarios are generated using Monte Carlo simulation to model uncertain parameters of Microgrid (MG). These scenarios consist of the worst as well as the best possible cases, reflecting the microgrid's real-time operation. Furthermore, these scenarios are reduced by using a k-means clustering algorithm. The reduced procedures for uncertain parameters will be used to obtain the minimum cost of MG with the help of an optimisation algorithm. In this work, a meta-heuristic approach, grey wolf optimisation (GWO), is used to minimize the developed cost optimisation function of MG. The standard LV Microgrid CIGRE test network is used to validate the proposed methodology. Results are obtained for different cases by considering different priorities to the sub-objectives using GWO algorithm. The obtained results are compared with the results of Jaya and PSO (particle swarm optimization) algorithms to validate the efficacy of the GWO method for the proposed optimization problem.
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Multi-criteria decision-making (MCDM) presents a significant challenge in decision-making processes, aiming to ascertain optimal choice by considering multiple criteria. This paper proposes rank order centroid (ROC) method, MCDM technique, to determine weights for sub-objective functions, specifically, addressing issue of automatic generation control (AGC) within two area interconnected power system (TAIPS). The sub-objective functions include integral time absolute errors (ITAE) for frequency deviations and control errors in both areas, along with ITAE of fluctuation in tie-line power. These are integrated into an overall objective function, with ROC method systematically assigning weights to each sub-objective. Subsequently, a PID controller is designed based on this objective function. To further optimize objective function, Jaya optimization algorithm (JOA) is implemented, alongside other optimization algorithms such as teacher-learner based optimization algorithm (TLBOA), Luus-Jaakola algorithm (LJA), Nelder-Mead simplex algorithm (NMSA), elephant herding optimization algorithm (EHOA), and differential evolution algorithm (DEA). Six distinct case analyses are conducted to evaluate controller's performance under various load conditions, plotting data to illustrate responses to frequency and tie-line exchange fluctuations. Additionally, statistical analysis is performed to provide further insights into efficacy of JOA-based PID controller. Furthermore, to prove the efficacy of JOA-based proposed controller through non-parametric test, Friedman rank test is utilized.
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Bone marrow (BM) is an essential part of the hematopoietic system, which generates all of the body's blood cells and maintains the body's overall health and immune system. The classification of bone marrow cells is pivotal in both clinical and research settings because many hematological diseases, such as leukemia, myelodysplastic syndromes, and anemias, are diagnosed based on specific abnormalities in the number, type, or morphology of bone marrow cells. There is a requirement for developing a robust deep-learning algorithm to diagnose bone marrow cells to keep a close check on them. This study proposes a framework for categorizing bone marrow cells into seven classes. In the proposed framework, five transfer learning models-DenseNet121, EfficientNetB5, ResNet50, Xception, and MobileNetV2-are implemented into the bone marrow dataset to classify them into seven classes. The best-performing DenseNet121 model was fine-tuned by adding one batch-normalization layer, one dropout layer, and two dense layers. The proposed fine-tuned DenseNet121 model was optimized using several optimizers, such as AdaGrad, AdaDelta, Adamax, RMSprop, and SGD, along with different batch sizes of 16, 32, 64, and 128. The fine-tuned DenseNet121 model was integrated with an attention mechanism to improve its performance by allowing the model to focus on the most relevant features or regions of the image, which can be particularly beneficial in medical imaging, where certain regions might have critical diagnostic information. The proposed fine-tuned and integrated DenseNet121 achieved the highest accuracy, with a training success rate of 99.97% and a testing success rate of 97.01%. The key hyperparameters, such as batch size, number of epochs, and different optimizers, were all considered for optimizing these pre-trained models to select the best model. This study will help in medical research to effectively classify the BM cells to prevent diseases like leukemia.
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Breast cancer (BC) is the most common cancer among women, making it essential to have an accurate and dependable system for diagnosing benign or malignant tumors. It is essential to detect this cancer early in order to inform subsequent treatments. Currently, fine needle aspiration (FNA) cytology and machine learning (ML) models can be used to detect and diagnose this cancer more accurately. Consequently, an effective and dependable approach needs to be developed to enhance the clinical capacity to diagnose this illness. This study aims to detect and divide BC into two categories using the Wisconsin Diagnostic Breast Cancer (WDBC) benchmark feature set and to select the fewest features to attain the highest accuracy. To this end, this study explores automated BC prediction using multi-model features and ensemble machine learning (EML) techniques. To achieve this, we propose an advanced ensemble technique, which incorporates voting, bagging, stacking, and boosting as combination techniques for the classifier in the proposed EML methods to distinguish benign breast tumors from malignant cancers. In the feature extraction process, we suggest a recursive feature elimination technique to find the most important features of the WDBC that are pertinent to BC detection and classification. Furthermore, we conducted cross-validation experiments, and the comparative results demonstrated that our method can effectively enhance classification performance and attain the highest value in six evaluation metrics, including precision, sensitivity, area under the curve (AUC), specificity, accuracy, and F1-score. Overall, the stacking model achieved the best average accuracy, at 99.89%, and its sensitivity, specificity, F1-score, precision, and AUC/ROC were 1.00%, 0.999%, 1.00%, 1.00%, and 1.00%, respectively, thus generating excellent results. The findings of this study can be used to establish a reliable clinical detection system, enabling experts to make more precise and operative decisions in the future. Additionally, the proposed technology might be used to detect a variety of cancers.
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A disturbance/uncertainty estimation and disturbance rejection technique are proposed in this work and verified on a ground two-wheel differential drive mobile robot (DDMR) in the presence of a mismatched disturbance. The offered scheme is the an improved active disturbance rejection control (IADRC) approach-based enhanced dynamic speed controller. To efficiently eliminate the effect produced by the system uncertainties and external torque disturbance on both wheels, the IADRC is adopted, whereby all the torque disturbances and DDMR parameter uncertainties are conglomerated altogether and considered a generalized disturbance. This generalized disturbance is observed and cancelled by a novel nonlinear sliding mode extended state observer (NSMESO) in real-time. Through numerical simulations, various performance indices are measured, with a reduction of 86% and 97% in the ITAE index for the right and left wheels, respectively. Finally, these indices validate the efficacy of the proposed dynamic speed controller by almost damping the chattering phenomena and supplying a high insusceptibility in the closed-loop system against torque disturbance.
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With the emergence of delay- and energy-critical vehicular applications, forwarding sense-actuate data from vehicles to the cloud became practically infeasible. Therefore, a new computational model called Vehicular Fog Computing (VFC) was proposed. It offloads the computation workload from passenger devices (PDs) to transportation infrastructures such as roadside units (RSUs) and base stations (BSs), called static fog nodes. It can also exploit the underutilized computation resources of nearby vehicles that can act as vehicular fog nodes (VFNs) and provide delay- and energy-aware computing services. However, the capacity planning and dimensioning of VFC, which come under a class of facility location problems (FLPs), is a challenging issue. The complexity arises from the spatio-temporal dynamics of vehicular traffic, varying resource demand from PD applications, and the mobility of VFNs. This paper proposes a multi-objective optimization model to investigate the facility location in VFC networks. The solutions to this model generate optimal VFC topologies pertaining to an optimized trade-off (Pareto front) between the service delay and energy consumption. Thus, to solve this model, we propose a hybrid Evolutionary Multi-Objective (EMO) algorithm called Swarm Optimized Non-dominated sorting Genetic algorithm (SONG). It combines the convergence and search efficiency of two popular EMO algorithms: the Non-dominated Sorting Genetic Algorithm (NSGA-II) and Speed-constrained Particle Swarm Optimization (SMPSO). First, we solve an example problem using the SONG algorithm to illustrate the delay-energy solution frontiers and plotted the corresponding layout topology. Subsequently, we evaluate the evolutionary performance of the SONG algorithm on real-world vehicular traces against three quality indicators: Hyper-Volume (HV), Inverted Generational Distance (IGD) and CPU delay gap. The empirical results show that SONG exhibits improved solution quality over the NSGA-II and SMPSO algorithms and hence can be utilized as a potential tool by the service providers for the planning and design of VFC networks.
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Algoritmos , Transportes , Fenómenos Físicos , Evolución BiológicaRESUMEN
In this investigation, the adaptive fractional-order non-singular fixed-time terminal sliding mode (AFoFxNTSM) control for the uncertain dynamics of robotic manipulators with external disturbances is introduced. The idea of fractional-order non-singular fixed-time terminal sliding mode (FoFxNTSM) control is presented as the initial step. This approach, which combines the benefits of a fractional-order parameter with the advantages of NTSM, gives rapid fixed-time convergence, non-singularity, and chatter-free control inputs. After that, an adaptive control strategy is merged with the FoFxNTSM, and the resulting model is given the label AFoFxNTSM. This is done in order to account for the unknown dynamics of the system, which are caused by uncertainties and bounded external disturbances. The Lyapunov analysis reveals how stable the closed-loop system is over a fixed time. The pertinent simulation results are offered here for the purposes of evaluating and illustrating the performance of the suggested scheme applied on a PUMA 560 robot.
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In this paper, we address the problems of fraud and anomalies in the Bitcoin network. These are common problems in e-banking and online transactions. However, as the financial sector evolves, so do the methods for fraud and anomalies. Moreover, blockchain technology is being introduced as the most secure method integrated into finance. However, along with these advanced technologies, many frauds are also increasing every year. Therefore, we propose a secure fraud detection model based on machine learning and blockchain. There are two machine learning algorithms-XGboost and random forest (RF)-used for transaction classification. The machine learning techniques train the dataset based on the fraudulent and integrated transaction patterns and predict the new incoming transactions. The blockchain technology is integrated with machine learning algorithms to detect fraudulent transactions in the Bitcoin network. In the proposed model, XGboost and random forest (RF) algorithms are used to classify transactions and predict transaction patterns. We also calculate the precision and AUC of the models to measure the accuracy. A security analysis of the proposed smart contract is also performed to show the robustness of our system. In addition, an attacker model is also proposed to protect the proposed system from attacks and vulnerabilities.
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Cadena de Bloques , Algoritmos , Fraude , Aprendizaje Automático , TecnologíaRESUMEN
The exponential growth of intelligent vehicles(IVs) development has resulted in a complex network. As the number of IVs in a network increases, so does the number of connections. As a result, a great deal of data is generated. This complexity leads to insecure communication, traffic congestion, security, and privacy issues in vehicular networks (VNs). In addition, detecting malicious IVs, data integration, and data validation are major issues in VNs that affect network performance. A blockchain-based model for secure communication and malicious IV detection is proposed to address the above issues. In addition, this system also addresses data integration and transaction validation using an encryption scheme for secure communication. A multi-chain concept separates the legitimate and malicious data into two chains: the Integrity chain (I-chain) and Fraud chain (F-chain). This multi-chain mechanism solves the storage problem and reduces the computing power. The integration of blockchain in the proposed model provides privacy, network security, transparency, and immutability. To address the storage issue, the InterPlanetary File System (IPFS) is integrated with Certificate Authority (CA). A reputation mechanism is introduced to detect malicious IVs in the network based on ratings. This reputation mechanism is also used to prevent Sybil attack. The evaluation of the proposed work is based on the cost of smart contracts and computation time. Furthermore, two attacker models are presented to prevent the selfish mining attack and the Sybil attack. Finally, a security analysis of the proposed smart contracts with their security vulnerabilities is also presented.
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Cadena de Bloques , Seguridad Computacional , Comunicación , Redes de Comunicación de Computadores , PrivacidadRESUMEN
Every year, nearly two million people die as a result of gastrointestinal (GI) disorders. Lower gastrointestinal tract tumors are one of the leading causes of death worldwide. Thus, early detection of the type of tumor is of great importance in the survival of patients. Additionally, removing benign tumors in their early stages has more risks than benefits. Video endoscopy technology is essential for imaging the GI tract and identifying disorders such as bleeding, ulcers, polyps, and malignant tumors. Videography generates 5000 frames, which require extensive analysis and take a long time to follow all frames. Thus, artificial intelligence techniques, which have a higher ability to diagnose and assist physicians in making accurate diagnostic decisions, solve these challenges. In this study, many multi-methodologies were developed, where the work was divided into four proposed systems; each system has more than one diagnostic method. The first proposed system utilizes artificial neural networks (ANN) and feed-forward neural networks (FFNN) algorithms based on extracting hybrid features by three algorithms: local binary pattern (LBP), gray level co-occurrence matrix (GLCM), and fuzzy color histogram (FCH) algorithms. The second proposed system uses pre-trained CNN models which are the GoogLeNet and AlexNet based on the extraction of deep feature maps and their classification with high accuracy. The third proposed method uses hybrid techniques consisting of two blocks: the first block of CNN models (GoogLeNet and AlexNet) to extract feature maps; the second block is the support vector machine (SVM) algorithm for classifying deep feature maps. The fourth proposed system uses ANN and FFNN based on the hybrid features between CNN models (GoogLeNet and AlexNet) and LBP, GLCM and FCH algorithms. All the proposed systems achieved superior results in diagnosing endoscopic images for the early detection of lower gastrointestinal diseases. All systems produced promising results; the FFNN classifier based on the hybrid features extracted by GoogLeNet, LBP, GLCM and FCH achieved an accuracy of 99.3%, precision of 99.2%, sensitivity of 99%, specificity of 100%, and AUC of 99.87%.
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Aprendizaje Profundo , Enfermedades Gastrointestinales , Algoritmos , Inteligencia Artificial , Diagnóstico Precoz , Enfermedades Gastrointestinales/diagnóstico por imagen , Humanos , Redes Neurales de la ComputaciónRESUMEN
In order to extract efficient power generation, a wind turbine (WT) system requires an accurate maximum power point tracking (MPPT) technique. Therefore, a novel robust variable-step perturb-and-observe (RVS-P&O) algorithm was developed for the machine-side converter (MSC). The control strategy was applied on a WT based permanent-magnet synchronous generator (PMSG) to overcome the downsides of the currently published P&O MPPT methods. Particularly, two main points were involved. Firstly, a systematic step-size selection on the basis of power and speed measurement normalization was proposed; secondly, to obtain acceptable robustness for high and long wind-speed variations, a new correction to calculate the power variation was carried out. The grid-side converter (GSC) was controlled using a second-order sliding mode controller (SOSMC) with an adaptive-gain super-twisting algorithm (STA) to realize the high-quality seamless setting of power injected into the grid, a satisfactory power factor correction, a high harmonic performance of the AC source, and removal of the chatter effect compared to the traditional first-order sliding mode controller (FOSMC). Simulation results showed the superiority of the suggested RVS-P&O over the competing based P&O techniques. The RVS-P&O offered the WT an efficiency of 99.35%, which was an increase of 3.82% over the variable-step P&O algorithm. Indeed, the settling time was remarkably enhanced; it was 0.00794 s, which was better than for LS-P&O (0.0841 s), SS-P&O (0.1617 s), and VS-P&O (0.2224 s). Therefore, in terms of energy efficiency, as well as transient and steady-state response performances under various operating conditions, the RVS-P&O algorithm could be an accurate candidate for MPP online operation tracking.
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The enhancement of Robustness (R) has gained significant importance in Scale-Free Networks (SFNs) over the past few years. SFNs are resilient to Random Attacks (RAs). However, these networks are prone to Malicious Attacks (MAs). This study aims to construct a robust network against MAs. An Intelligent Rewiring (INTR) mechanism is proposed to optimize the network R against MAs. In this mechanism, edge rewiring is performed between the high and low degree nodes to make a robust network. The Closeness Centrality (CC) measure is utilized to determine the central nodes in the network. Based on the measure, MAs are performed on nodes to damage the network. Therefore, the connections of the neighboring nodes in the network are greatly affected by removing the central nodes. To analyze the network connectivity against the removal of nodes, the performance of CC is found to be more efficient in terms of computational time as compared to Betweenness Centrality (BC) and Eigenvector Centrality (EC). In addition, the Recalculated High Degree based Link Attacks (RHDLA) and the High Degree based Link Attacks (HDLA) are performed to affect the network connectivity. Using the local information of SFN, these attacks damage the vital portion of the network. The INTR outperforms Simulated Annealing (SA) and ROSE in terms of R by 17.8% and 10.7%, respectively. During the rewiring mechanism, the distribution of nodes' degrees remains constant.
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Systems are naturally or purposely formed with functional components and connection structures [...].
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In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.
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The real-world data analysis and processing using data mining techniques often are facing observations that contain missing values. The main challenge of mining datasets is the existence of missing values. The missing values in a dataset should be imputed using the imputation method to improve the data mining methods' accuracy and performance. There are existing techniques that use k-nearest neighbors algorithm for imputing the missing values but determining the appropriate k value can be a challenging task. There are other existing imputation techniques that are based on hard clustering algorithms. When records are not well-separated, as in the case of missing data, hard clustering provides a poor description tool in many cases. In general, the imputation depending on similar records is more accurate than the imputation depending on the entire dataset's records. Improving the similarity among records can result in improving the imputation performance. This paper proposes two numerical missing data imputation methods. A hybrid missing data imputation method is initially proposed, called KI, that incorporates k-nearest neighbors and iterative imputation algorithms. The best set of nearest neighbors for each missing record is discovered through the records similarity by using the k-nearest neighbors algorithm (kNN). To improve the similarity, a suitable k value is estimated automatically for the kNN. The iterative imputation method is then used to impute the missing values of the incomplete records by using the global correlation structure among the selected records. An enhanced hybrid missing data imputation method is then proposed, called FCKI, which is an extension of KI. It integrates fuzzy c-means, k-nearest neighbors, and iterative imputation algorithms to impute the missing data in a dataset. The fuzzy c-means algorithm is selected because the records can belong to multiple clusters at the same time. This can lead to further improvement for similarity. FCKI searches a cluster, instead of the whole dataset, to find the best k-nearest neighbors. It applies two levels of similarity to achieve a higher imputation accuracy. The performance of the proposed imputation techniques is assessed by using fifteen datasets with variant missing ratios for three types of missing data; MCAR, MAR, MNAR. These different missing data types are generated in this work. The datasets with different sizes are used in this paper to validate the model. Therefore, proposed imputation techniques are compared with other missing data imputation methods by means of three measures; the root mean square error (RMSE), the normalized root mean square error (NRMSE), and the mean absolute error (MAE). The results show that the proposed methods achieve better imputation accuracy and require significantly less time than other missing data imputation methods.
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In this study, the design of an adaptive terminal sliding mode controller for the stabilization of port Hamiltonian chaotic systems with hidden attractors is proposed. This study begins with the design methodology of a chaotic oscillator with a hidden attractor implementing the topological framework for its respective design. With this technique it is possible to design a 2-D chaotic oscillator, which is then converted into port-Hamiltonia to track and analyze these models for the stabilization of the hidden chaotic attractors created by this analysis. Adaptive terminal sliding mode controllers (ATSMC) are built when a Hamiltonian system has a chaotic behavior and a hidden attractor is detected. A Lyapunov approach is used to formulate the adaptive device controller by creating a control law and the adaptive law, which are used online to make the system states stable while at the same time suppressing its chaotic behavior. The empirical tests obtaining the discussion and conclusions of this thesis should verify the theoretical findings.
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In this paper, a gradient descent algorithm is proposed for the parameter estimation of multi-input and multi-output (MIMO) total non-linear dynamic models. Firstly, the MIMO total non-linear model is mapped to a non-completely connected feedforward neural network, that is, the parameters of the total non-linear model are mapped to the connection weights of the neural network. Then, based on the minimization of network error, a weight-updating algorithm, that is, an estimation algorithm of model parameters, is proposed with the convergence conditions of a non-completely connected feedforward network. In further determining the variables of the model set, a method of model structure detection is proposed for selecting a group of important items from the whole variable candidate set. In order to verify the usefulness of the parameter identification process, we provide a virtual bench test example for the numerical analysis and user-friendly instructions for potential applications.