T-S fuzzy model with linear rule consequence and PDC controller: a universal framework for nonlinear control systems

We present two results concerning the fuzzy modeling and control of nonlinear systems. The first result is on the approximation of smooth nonlinear dynamical systems using linear Takagi-Sugeno (T-S) fuzzy models. The second result is on the approximation of smooth nonlinear state-feedback controllers using the so-called parallel distributed compensation (PDC) controller. Both results are based on the effectiveness of using linear Takagi-Sugeno systems to approximate nonlinear function, which is also proved in this paper.

[1]  Jing Li,et al.  Robust tracking for high-rise/high-speed elevators , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[2]  Juan Miguel Medina,et al.  Towards the implementation of a generalized fuzzy relational database model , 1995, Fuzzy Sets Syst..

[3]  Hannu Toivonen,et al.  Efficient discovery of functional and approximate dependencies using partitions , 1998, Proceedings 14th International Conference on Data Engineering.

[4]  Kazuo Tanaka,et al.  A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer , 1994, IEEE Trans. Fuzzy Syst..

[5]  B. Buckles,et al.  A fuzzy representation of data for relational databases , 1982 .

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

[7]  R. Gorez,et al.  Fuzzy gain scheduling controllers based on fuzzy models , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[8]  James J. Buckley,et al.  Universal fuzzy controllers , 1992, Autom..

[9]  M. Sc,et al.  Sufficient Conditions on Uniform Approximation of Multivariate Functions by General Takagi-Sugeno Fuzzy Systems with Linear Rule Consequent , 1998 .

[10]  Soumitra Dutta,et al.  Approximate reasoning by analogy to answer null queries , 1991, Int. J. Approx. Reason..

[11]  M. Spivak.  A comprehensive introduction to differential geometry , 1979 .

[12]  Xiao-Jun Zeng,et al.  Approximation theory of fuzzy systems-SISO case , 1994, IEEE Trans. Fuzzy Syst..

[13]  Kazuo Tanaka,et al.  Parallel distributed compensation of nonlinear systems by Takagi-Sugeno fuzzy model , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[14]  Henri Prade,et al.  Lipski's approach to incomplete information databases restated and generalized in the setting of Zadeh's possibility theory , 1984, Inf. Syst..

[15]  Juan Luis Castro,et al.  Fuzzy logic controllers are universal approximators , 1995, IEEE Trans. Syst. Man Cybern..

[16]  Liu Xuecheng,et al.  Entropy, distance measure and similarity measure of fuzzy sets and their relations , 1992 .

[17]  Sujeet Shenoi,et al.  Proximity relations in the fuzzy relational database model , 1999 .

[18]  Arun K. Majumdar,et al.  Fuzzy Functional Dependencies and Lossless Join Decomposition of Fuzzy Relational Database Systems , 1988, ACM Trans. Database Syst..

[19]  Sujeet Shenoi,et al.  Analyzing FD Inference in Relational Databases , 1996, Data Knowl. Eng..

[20]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[21]  N. W. Rees,et al.  Fuzzy control of nonlinear continuous-time systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[22]  M. G. Singh,et al.  Approximation theory of fuzzy systems , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[23]  Geuntaek Kang,et al.  Design of TSK fuzzy controller based on TSK fuzzy model using pole placement , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[24]  R. Rovatti,et al.  On the approximation capabilities of the homogeneous Takagi-Sugeno model , 1996, Proceedings of IEEE 5th International Fuzzy Systems.