Abstract
The nonlinear feedback control whose feedback law is constructed by the SIRMs method is structured and presented mathematically. The set of SIRMs formed from the membership functions, important degrees and some parameters is compact by considering it to be a family of them. And by considering the fuzzy inference calculations as a composite functional on the family of the membership functions, its continuity is proved in functional analysis. Then, the existence of optimal solution of fuzzy feedback control using SIRMs method is derived from these facts.
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References
Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)
Zadeh, L.A.: Fuzzy algorithms. Information and Control 12, 94–102 (1968)
Mamdani, E.H.: Application of fuzzy algorithms for control of simple dynamic plant. Proc. IEE 121(12), 1585–1588 (1974)
Akiyama, T., Takaba, T., Mizutani, K.: Fuzzy Travel Behaviour Analysis for Navigation. Journal of Japan Society for Fuzzy Theory and Systems 11(2), 21–30 (1999)
Yubazaki, N., Yi, J., Hirota, K.: A Proposal of SIRMs (Single Input Rule Modules) Connected Fuzzy Inference Model for Plural Input Fuzzy Control. Journal of Japan Society for Fuzzy Theory and Systems 9(5), 699–709 (1997)
Seki, H., Mizumoto, M., Yubazaki, N.: On the Property of Single Input Rule Modules Connected Type Fuzzy Reasoning Method. The Transactions of the Institute of Electronics, Information and Communication Engineers (A) J89-A(6), 557–565 (2006)
Ishibuchi, H., Nii, M.: Generating Fuzzy Classification Rules from Trained Neural Networks. Journal of Japan Society for Fuzzy Theory and Systems 9(4), 512–524 (1997)
Nomura, H., Wakami, N.: A Method to Determine Fuzzy Inference Rules by a Genetic Algorithm. The Transactions of the Institute of Electronics, Information and Communication Engineers (A) J77-A(9), 1241–1249 (1994)
Gonda, E., Miyata, H., Ohkita, M.: Self-Tuning of Fuzzy Rules with Different Types of MSFs. Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 16(6), 540–550 (2004)
Shidama, Y., Yang, Y., Eguchi, M., Yamaura, H.: The compactness of a set of membership functions and its application to fuzzy optimal control. The Japan Society for Industrial and Applied Mathematics 6(1), 1–13 (1996)
Mitsuishi, T., Wasaki, K., Ohkubo, K., Kawabe, J., Shidama, Y.: Fuzzy Optimal Control Using Simple Inference Method and Function Type Inference Method. In: Proc. American Control Conference 2000, pp. 1944–1948 (2000)
Mitsuishi, T., Kawabe, J., Wasaki, K., Shidama, Y.: Optimization of Fuzzy Feedback Control Determined by Product-Sum-Gravity Method. Journal of Nonlinear and Convex Analysis 1(2), 201–211 (2000)
Mitsuishi, T., Endou, N., Shidama, Y.: Continuity of Nakamori Fuzzy Model and Its Application to Optimal Feedback Control. In: Proc. IEEE International Conference on Systems, Man and Cybernetics, pp. 577–581 (2005)
Watanabe, S., Seki, H., Ishii, H.: Application for Discriminant Analysis by Kernel Type SIRMs Connected Fuzzy Reasoning Method. In: Proc. The 2008 Fall National Conference of Operations Research Society of, Japan, pp. 332–333 (2008)
Miller, R.K., Michel, A.N.: Ordinary Differential Equations. Academic Press, New York (1982)
Riesz, F., Sz.-Nagy, B.: Functional Analysis. Dover Publications, New York (1990)
Dunford, N., Schwartz, J.T.: Linear Operators Part I: General Theory. John Wiley & Sons, New York (1988)
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Mitsuishi, T., Kawakatsu, H., Shidama, Y. (2010). Existence of Single Input Rule Modules for Optimal Fuzzy Logic Control. In: Setchi, R., Jordanov, I., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based and Intelligent Information and Engineering Systems. KES 2010. Lecture Notes in Computer Science(), vol 6278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15393-8_32
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DOI: https://doi.org/10.1007/978-3-642-15393-8_32
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