A theoretical justification for nonlinear control property of a class of fuzzy logic controllers

In Sayyarrdsari, Homaifar, and Hogans (1993), a hybrid implementation of fuzzy and conventional PID controller was introduced and its application to a 2 degree of freedom robot manipulator arm was examined. A theoretical justification for that approach, based on the fact that “fuzzy systems are universal approximators” is presented in this paper.

[1]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[2]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[3]  Chuen-Chien Lee,et al.  Fuzzy logic in control systems: fuzzy logic controller. II , 1990, IEEE Trans. Syst. Man Cybern..

[4]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[5]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  J. Buckley Sugeno type controllers are universal controllers , 1993 .

[7]  Jerry M. Mendel,et al.  Back-propagation fuzzy system as nonlinear dynamic system identifiers , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[8]  J. Buckley,et al.  Fuzzy input-output controllers are universal approximators , 1993 .

[9]  Fuzzy Logic in Control Systems : Fuzzy Logic , 2022 .

[10]  Abdollah Homaifar,et al.  Fuzzy controller for robot arm trajectory , 1994 .

[11]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[12]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[13]  L. Wang,et al.  Fuzzy systems are universal approximators , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.