Neural ordinary differential gray algorithm to forecasting models of controlled systems

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.