Abstract
A new kind of fuzzy modeling method to construct an approximate solution to a differential equation is proposed in this paper. The proposed method is based on the interpolation mechanism of rectangular pyramid fuzzy system and ends up with a solution to a nonlinear differential equation with variable coefficients. The proposed fuzzy modeling method is applied to model time-invariant second-order freedom movement systems, so a new input–output model and a new state-space model are constructed, respectively. Simulation results show that the proposed modeling method is effective in approximating the original system.
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Acknowledgements
The authors would like to thank the Editor-in-Chief, the Associate Editor and anonymous reviewers for their constructive comments, which helped greatly improve the presentation of this paper. This work was supported by National Science Foundation of China (No. 61473327).
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Jiang, M., Er, M.J. & Yuan, X. Fuzzy Modeling Method Based on Rectangular Pyramid Fuzzy System. Int. J. Fuzzy Syst. 19, 1731–1738 (2017). https://doi.org/10.1007/s40815-017-0329-7
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DOI: https://doi.org/10.1007/s40815-017-0329-7