Abstract
Look-up table (LUT) controllers are among the most widely utilized control tools in engineering practice. The reasons for their popularity include simplicity, easy to use, inexpensive hardware implementation, and strong nonlinearity and multimodal behaviors that can be formalized, in many cases, only by experimentally measured data. In a previous paper, we showed that the two-dimensional (2D) LUT controllers and one special type of two-input Mamdani fuzzy controllers are connected in that they have the identical input-output mathematical relation. We also demonstrated how to represent the LUT controllers by the fuzzy controllers. Finally, we showed how to determine the local stability of the LUT control systems. In the present work, we extend these results to the n-dimensional LUT controllers and the special type of the n-input Mamdani fuzzy controllers.
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Filev, D., Ying, H. (2017). The Multiple Facets of Fuzzy Controllers: Look-up-Tables—A Special Class of Fuzzy Controllers . In: Kacprzyk, J., Filev, D., Beliakov, G. (eds) Granular, Soft and Fuzzy Approaches for Intelligent Systems. Studies in Fuzziness and Soft Computing, vol 344. Springer, Cham. https://doi.org/10.1007/978-3-319-40314-4_10
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