Adaptive fuzzy controllers based on variable universe. (English) Zbl 0935.93042

The interpolation mechanism for fuzzy control, previously introduced by the same author [ibid. 41, No. 3, 312-320 (1998; Zbl 0916.93041)], is exploited in the construction of adaptive control architectures. The approach relies on the concept of monotonicity of control rules, which is proved equivalent to the monotonicity of interpolation functions of fuzzy control. The structure of contraction-expansion factors of variable universe is used to develop and study three types of adaptive fuzzy controllers called “with potential heredity”, “with obvious heredity” and “with successively obvious heredity”, respectively.


93C42 Fuzzy control/observation systems
93C40 Adaptive control/observation systems


Zbl 0916.93041
Full Text: DOI


[1] Li Hongxing, To see the success of fuzzy logic from mathematical essence of fuzzy control,Fuzzy Systems and Mathematics (in Chinese), 1995, 9(4): 1.
[2] Li Hongxing, The mathematical essence of fuzzy controls and fine fuzzy controllers, inAdvances in Machine Intelligence and Soft-Computing (ed. Wang, Paul P.), Vol. IV, Durham: Bookwrights Press, 1997, 55–74.
[3] Li Hongxing, Interpolation mechanism of fuzzy control,Science in China, Ser. E, 1998, 41(3): 312. · Zbl 0916.93041 · doi:10.1007/BF02919442
[4] Zhang Naiyao, Structure analysis of typical fuzzy controllers,Fuzzy Systems and Mathematics (in Chinese), 1997, 11 (2): 10. · Zbl 0925.93495
[5] Wang Guojun, On the logic foundation of fuzzy reasoning,Lecture Notes in Fuzzy Mathematics and Computer Science, Omaha: Creighton Univ., 1997, 4: 1. · Zbl 0894.54010
[6] Chen Yongyi,Fuzzy Control Technique and Its Applications (in Chinese), Beijing: Beijing Normal University Press, 1993.
[7] Liu Xihui, Wang Haiyan,Networks Fuzzy Analysis Methods (in Chinese), Beijing: Electronic Industry Press, 1991.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.