Abstract
This article presents a mathematical framework for studying the existence of optimal feedback control based on IF-THEN fuzzy rules through approximate reasoning, and introduces the notion of an admissible fuzzy controller. The framework consists of two propositions: To guarantee the convergence of optimal solution, a set of fuzzy membership functions (admissible fuzzy controller) which are selected out of L 2 space is convex and compact metrizable for the weak topology. And assuming approximate reasoning to be a functional on the set of membership functions, its continuity is proved. Then, we show the existence of a fuzzy controller which minimize (maximize) the integral performance function of the nonlinear feedback system.
The paper was supported in part by Grant-in-Aid for Young Scientists (B) #19700225 from Japan Society for the Promotion of Science (JSPS).
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© 2008 Springer-Verlag Berlin Heidelberg
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Mitsuishi, T., Shidama, Y. (2008). Admissible Fuzzy Controller in L 2 Space . In: Nguyen, N.T., Borzemski, L., Grzech, A., Ali, M. (eds) New Frontiers in Applied Artificial Intelligence. IEA/AIE 2008. Lecture Notes in Computer Science(), vol 5027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69052-8_7
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DOI: https://doi.org/10.1007/978-3-540-69052-8_7
Publisher Name: Springer, Berlin, Heidelberg
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