Fractional finite difference methods are useful to solve the fractional differential equations. The aim of this article is to prove the stability and convergence of the fractional Euler method, the fractional Adams method and the high order methods based on the convolution formula by using the generalized discrete Gronwall inequality. Numerical experiments are also presented, which verify the theoretical analysis.

The finite difference methods for fractional ordinary differential equations

Abstract In this paper, the authors have proposed a Linear Predictive coefficient-based Radial basis function neural network model (LPC-RBF) to solve the system identification problem. A recorded speech signal is considered to develop the model. The objective is to develop a machine learning model with the LPC values of the speech signal. The parameters of a speech signal are directly estimated using linear predictive coefficients. The proposed model is considered as the ARX model and trained with the LPC value of the speech signal. The comparison results are shown in the table.The performance is evaluated through mean square error (MSE). From the result analysis, the superiority of the proposed model is analyzed. The proposed model archives the best final MSE value 0.0027, as compared to the basic RBF model. From the comparison table, it can be seen that LPC-RBF has better performance as compared with the RBF model.

Nonlinear system identification for speech model using linear predictive coefficients based radial basis function

Abstract The propagation of epidemic COVID-19 is a critical subject that can be addressed in the field of science and systems control. Adopting the fractional-order model to represent the behavior of this infectious disease provides a more accurate framework to implement an efficient controller. As for obtaining a control strategy to tackle the problem, a novel fractional-order feedback linearization is proposed in this paper. Investigating the situation by counting the number of endangered people, as the output of the model, and giving feedback to the system input, the control policy is obtained to decrease the number of exposed and infected individuals. In this paper, the feedback linearization method is proposed to provide the government to tackle the problem with a robust control policy as non-pharmaceutical interventions (NPI). To evaluate the suggested methodology, the open-loop controller is compared with the closed-loop controller.

A novel fractional-order feedback management of COVID-19 prevalence

Due to the feasibility of the gray model for predicting time series with small samples, the gray theory is well investigated since it is presented and is currently evolved in an important manner for forecasting small samples. This study proposes a new gray prediction criterion based on the neural ordinary differential equation, which is named the neural ordinary differential gray mode. This neural ordinary differential gray mode permits the forecasting model to be learned by a training process which contains a new whitening equation. It is needed to prepare the structure and time series, compared with other models, according to the regularity of actual specimens in advance, therefore this model of neural ordinary differential gray mode can provide comprehensive applications as well as learning the properties of distinct data specimens. To acquire a better model which has highly predictive efficiency, afterward, this study trains the model by neural ordinary differential gray mode using the Runge–Kutta method to obtain the prediction sequence and solve the model. The controller establishes an advantageous theoretical foundation in adapting to novel wheels and comprehensively spreads the utilize extent of mechanical elastic vehicle wheel.

Neural ordinary differential gray algorithm to forecasting models of controlled systems

This paper proposes a composite design of fuzzy adaptive control scheme based on TMD RC structural system and the gain of two-dimensional fuzzy control is controlled by parameters. Monitoring and learning in LMI then produces performance indicators with a weighting matrix as a function of cost. It allows to control the trade-off between the two efficiencies by adjusting the appropriate weighting matrix. The two-dimensional Boost control model is equivalent to the LMIconstrained multi -objective optimization problem under dual performance criteria. By using the proposed intelligent control model, the fuzzy nonlinear criterion is satisfied. Therefore, the data connection can be further extended. Evaluation of controller performance the proposed controller is compared with other control techniques. This ensures good performance of the control routines used for position and trajectory control in the presence of model uncertainties and external influences. Quantitative verification of the effectiveness of monitoring and control. The purpose of this article is to ensure access to adequate, safe and affordable housing and basic services. Therefore, it is assumed that this goal will be achieved in the near future through the continuous development of artificial intelligence and control theory.

RC Structural System Control Subjected to Earthquakes and TMD

Due to the feasibility of the gray model for predicting time series with small samples, the gray theory is well investigated since it is presented and is currently evolved in an important manner for forecasting small samples. This study proposes a new gray prediction criterion based on the Neural Ordinary Differential Equation (NODE), which is named the NODGM (Neural Based Ordinary Differential gray Mode). This mode permits the forecasting approximation to be learned by a training process which contains a new whitening equation. It is needed to prepare the structure and time series, compared with other models, according to the regularity of actual specimens in advance, therefore this model of NODGM can provide comprehensive applications as well as learning the properties of distinct data specimens. In order to acquire a better model which has highly predictive efficiency, afterwards, this study trains the model by NODGM meanwhile using the Runge-Kutta method to obtain the prediction sequence and solve the model. The controller establishes an advantageous theoretical foundation in adapting to novel wheels and comprehensive spreads the utilize extent of Mechanical Elastic Vehicle Wheel (MEVW). 

Neural ordinary differential gray algorithm to forecasting nonlinear systems

The point of the article is to plan a productive mathematical technique to illuminate a class of time partial ideal control issues. In this issue definition, the fragmentary subordinate administrat...

A new fractional model and optimal control to model chaotic problems


Because of the advantage of the gray theory for forecasting small sample time data, gray algorithm theory has definitely been extensively utilized since it has been proposed and is currently being widely developed for predicting frames particularly in small sample problems. This article presented a viewpoint called gray algorithm by neuron- based ordinary-differential equation (NODE), called NODGM (neuron-based ordinary-differential gray-mode). In this type, we learn prediction methods through a training process that includes whiting equations. Compared with other models, the structure and time series via the regularity of real-samples are required in advance, so this NODGM design can have a better feasibility of applications and also study the origins of data according to different samples. The purpose is obtaining a better design with high forecast effectiveness, this study uses NODGM to train the model, while Runge-Kutta method is used to have the forecast set and solve numerical framwork. This algorithmic design creates a favorable theoretical basis for the installation of new process and distributes the numerical dimensions of completely mechanically elastic vehicle wheels (MEVW) in practical simulations.


Neural ordinary differential grey algorithm to forecasting MEVW systems

Neural Based Grey Nonlinear Control for Real-World Example of Mechanical Systems

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