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

To ensure the asymptotic stability and improve the ride comfort of vehicles, this paper develops a fuzzy neural network (NN) based evolved bat algorithm (EBA) to design adaptive backstepping controllers with grey signal predictors. The Lyapunov theory and backstepping method were employed to evaluate the nonlinearity of controlled systems and derive the evolved control law for the signal tracking. The discrete grey model DGM (2,1) is utilized to obtain future movement of the nonlinear system, so that the command controller can prove the Lyapunov stability and feasibility of the entire scheme through the Lyapunov-like lemma. The controller design criterion is demonstrated in the range of mechanical elastic wheel (MEW) and lays a feasible mathematical framework for the matching of new wheels.

Grey signal predictor and FNN evolved control for practical nonlinear systems

A novel discrete GM(2,1) model with a polynomial term for forecasting electricity consumption

This article develops an evolutionary bat algorithm (EBA) based fuzzy neural network (NN), which is applied to the adaptive controller in a plant, for the purpose of ensuring the asymptotic stability and heightening the stability of the vehicle. With a gray signal predictor, the Lyapunov theory as well as the backstepping method are adopted to ensure the non-linearity of the controlled system and derive the evolutionary control law of the signal tracking. The discrete gray model (DGM) (2,1) is used to predict the future motion of the nonlinear system, so that the fuzzy controller can ensure the Lyapunov stability and the feasibility of the parallel distributed compensation (PDC) scheme through the Lyapunov type lemma. The controller design is demonstrated in practical nonlinear systems, for a mechanical elastic wheel (MEW), as a feasible mathematical framework for the matching of this circular object revolving on an axle. 

NN model-based evolved control by DGM model for practical nonlinear systems

Grey Signal Predictor and Evolved Control for Practical Nonlinear Mechanical Systems

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Grey Signal Predictor and Evolved Control for Practical Nonlinear Mechanical Systems