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The robot dynamic model is often rarely known due to various uncertainties such as parametric uncertainties or modeling errors existing in complex environments. It is a key problem to find the relationship between the changes of neural network structure and the changes of input and output environments and their mutual influences. Firstly, this paper defined the conceptions of neural network solution, neural network eigen solution, neural network complete solution, and neural network partial solution and the conceptions of input environments, output environments, and macrostructure of neural networks. Secondly, an eigen solution theory of general neural networks was proposed and proven including consistent approximation theorem, eigen solution existence theorem, consistency theorem of complete solution, the partial solution, and none solution theorem of neural networks. Lastly, to verify the eigen solution theory of neural networks, the proposed theory was applied to a novel prediction and analysis model of controller parameters of grinding robot in complex environments with deep neural networks and then build prediction model with deep learning neural networks for controller parameters of grinding robot. The morphological subfeature graph with multimoment was constructed to describe the block surface morphology using rugosity, standard deviation, skewness, and kurtosis. The results of theoretical analysis and experimental test show that the output traits have an optional effect with joint action. When the input features functioning in prediction increase, higher predicted accuracy can be obtained. And when the output traits involving in prediction increase, more output traits can be predicted. The proposed prediction and analysis model with deep neural networks can be used to find and predict the inherent laws of the data. Compared with the traditional prediction model, the proposed model can predict output features simultaneously and is more stable.

In this article, a partial synchronization scheme is proposed based on Lyapunov stability theory to track the signal of the delay hyperchaotic Lu system using the Coullet system based on only one single controller. The proposed tracking control design has two advantages: only one controller is adopted in our approach and it can allow us to drive the hyperchaotic system to a simple chaotic system even with uncertain parameters. Numerical simulation results are given to demonstrate the effectiveness and robustness of the proposed partial synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity, 2014