Sufficient conditions for monotonically constrained functional-type SIRMs connected fuzzy systems

Monotonic input-output relationship is common in many physical systems. When modeling a physical system whose input-output relationship is monotonic, it is desired for a model to have the monotonicity. In this paper, we construct a model with single input rule modules (SIRMs) connected fuzzy system to solve “the curse of dimensionality”, and propose sufficient conditions for the constructed fuzzy system to have monotonic input-output relationship. The conditions are obtained by restricting the first derivative of the fuzzy system to be nonnegative. The derived conditions can be classified into two parts: the condition on the consequent part parameters of fuzzy rules and the condition on the input membership functions. The simulation results show the validity of the derived conditions.

[1]  Hiroaki Ishii,et al.  On the Monotonicity of Single Input Type Fuzzy Reasoning Methods , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[2]  Jianqiang Yi,et al.  A new fuzzy controller for stabilization of parallel-type double inverted pendulum system , 2002, Fuzzy Sets Syst..

[3]  Cheng-Juei Wu,et al.  A general purpose fuzzy controller for monotone functions , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[4]  Jianqiang Yi,et al.  A proposal of SIRMs dynamically connected fuzzy inference model for plural input fuzzy control , 2002, Fuzzy Sets Syst..

[5]  Hiroaki Ishii,et al.  On the monotonicity of functional type SIRMs connected fuzzy reasoning method and T-S reasoning method , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[6]  N. Yubazaki.  SIRMs dynamically connected fuzzy inference model and its applications , 1997 .

[7]  Jianqiang Yi,et al.  Upswing and stabilization control of inverted pendulum and cart system by the SIRMs dynamically connected fuzzy inference model , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[8]  C. J. Wu,et al.  Guaranteed accurate fuzzy controllers for monotone functions , 1997, Fuzzy Sets Syst..

[9]  Li-Xin Wang,et al.  A Course In Fuzzy Systems and Control , 1996 .

[10]  Jinwook Kim,et al.  Monotonic Fuzzy Systems As Universal Approximators For Monotonic Functions , 2012, Intell. Autom. Soft Comput..

[11]  Sang Y. Park,et al.  Automatic current control of magnet cranes for steel plate yard automation , 1998 .

[12]  Jin S. Lee,et al.  Parameter conditions for monotonic Takagi-Sugeno-Kang fuzzy system , 2002, Fuzzy Sets Syst..

[13]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[14]  Hailiang Zhao,et al.  Monotone fuzzy control method and its control performance , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[15]  Jianqiang Yi,et al.  Stabilization fuzzy control of parallel-type double inverted pendulum system , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[16]  Lennart Ljung,et al.  Ensuring monotonic gain characteristics in estimated models by fuzzy model structures , 2000, Autom..

[17]  Yannis A. Phillis,et al.  On the monotonicity of hierarchical sum-product fuzzy systems , 2009, Fuzzy Sets Syst..