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

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Abstract

Due to the feasibility of the gray model for predicting time series with small samples, the grey 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 grey prediction criterion based on the neural ordinary differential equation, which is named the NODGM (neural based ordinary differential grey mode). The new idea or new consideration which have not been proposed in any other literature is that the proposed grey prediction criterion has been combined with the artificial control schemes for the real-world application in mechanical systems. 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 control application.

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Acknowledgements

The authors are grateful for the research grants given to Ruei Yuan Wang from the Projects of Talents Recruitment of GDUPT, Peoples R China under Grant NO. 2019rc098, and the research grants given to ZY Chen from the Projects of Talents Recruitment of GDUPT (NO. 2021rc002) in Guangdong Province, Peoples R China. as well as to the anonymous reviewers for constructive suggestions.

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Authors and Affiliations

  1. School of Science, Guangdong University of Petrochem Technol, Kuan-Du Avenue, No. 139, Maoming City, 525000, People’s Republic of China

    Z. Y. Chen, Y. H. Meng & Ruei-Yuan Wang

  2. Caltech, CA, 91125, USA

    Timothy Chen

Authors
  1. Z. Y. Chen
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  2. Y. H. Meng
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  3. Ruei-Yuan Wang
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  4. Timothy Chen
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Contributions

Prof. ZYC contributed to this review by conducting an extensive literature review on the above issues. He is also involved in writing reviews and comparing different artificial algorithmic intelligent technologies and approaches. The first draft of the manuscript was by Dr. ZYC and all authors commented and participated in amending versions of the manuscript. The final manuscript was read and accepted by all authors. Dr. Wang also participated in this work and demonstrated the work of Dr. ZYC, confirming that the submitted literature review is sufficiently up-to-date and informative for the journal readers in the field. In addition, Professor R-YW excellent understanding of various control techniques helps provide insightful, easy-to-understand explanations. Prof. TC involved in discussions on various mechanical nonlinear architectures. His experience in mechanical engineering allows him to find feasible structures that meet the most desirable requirements of today. The last but not the least, Dr. YHM contribution is to propose algorithm which is with fast convergence speed, easy parameter setting and memory ability. Therefore, the grey evolved neural networks learns the way of wolves foraging, randomly generates initial values in the solution space to simulate the location of the wolves, and uses the formula of encirclement and attack to approach the optimal solution. The improved grey neural network linear differential scheme-algorithm modifies the convergence coefficient to increase the proportion of global search, avoids falling into the best solution in the region, adds memory capabilities, improves convergence efficiency, adds weights for different positions, makes the search direction clearer, and uses greed Strategies to avoid excessive unnecessary searches. The novel NODGM combines the neural network linear differential scheme and the Lyapunov stabilization approach for nonlinear suspension system.

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Correspondence to Y. H. Meng, Ruei-Yuan Wang or Timothy Chen.

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The authors would like to state that they have no conflict of interest in the publication of this article. All data and measurements analyzed not only in illustration but also the examples during this study are included within the article and the application of the methodology in this paper is original without submitting other journals for publication.

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Chen, Z.Y., Meng, Y.H., Wang, RY. et al. Neural Based Grey Nonlinear Control for Real-World Example of Mechanical Systems. Neural Process Lett 55, 5745–5761 (2023). https://doi.org/10.1007/s11063-022-11109-9

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