By Jacek Kluska

ISBN-10: 354089926X

ISBN-13: 9783540899266

ISBN-10: 3540899278

ISBN-13: 9783540899273

This publication is concentrated on mathematical research and rigorous layout tools for fuzzy regulate platforms in accordance with Takagi-Sugeno fuzzy types, often referred to as Takagi-Sugeno-Kang types. the writer provides a slightly basic analytical thought of tangible fuzzy modeling and keep an eye on of continuing and discrete-time dynamical platforms. major cognizance is paid to usability of the implications for the keep watch over and machine engineering group and accordingly easy and simple knowledge-bases for linguistic interpretation were used. The method relies at the author’s theorems referring to equivalence among known Takagi-Sugeno platforms and a few type of multivariate polynomials. It combines the benefits of fuzzy approach conception and classical keep watch over concept. Classical keep watch over idea might be utilized to modeling of dynamical crops and the controllers. they're all comparable to the set of Takagi-Sugeno style fuzzy ideas. The technique combines the easiest of fuzzy and traditional keep an eye on conception. It allows linguistic interpretability (also referred to as transparency) of either the plant version and the controller. relating to linear structures and a few category of nonlinear structures, engineers can in lots of circumstances at once follow recognized classical instruments from the regulate idea either for research, and the layout of closed-loop fuzzy keep watch over structures. as a result the most goal of the ebook is to set up accomplished and unified analytical foundations for fuzzy modeling utilizing the Takagi-Sugeno rule scheme and their purposes for fuzzy keep watch over, identity of a few classification of nonlinear dynamical strategies and type challenge solver design.

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Extra resources for Analytical Methods in Fuzzy Modeling and Control

Sample text

It is complete and noncontradictory. This case is simple and does not need a comment. 1 b). Observe that there is no consequent for the antecedent “z1 is N1 and z2 is P2 ”. This system is noncomplete and noncontradictory. 8) ⎫ R1 : If z1 is N1 and z2 is N2 , then S = q1 , ⎪ ⎪ ⎪ ⎪ R1 : If z1 is N1 and z2 is P2 , then S = q1 , ⎬ R2 : If z1 is P1 and z2 is N2 , then S = q2 , R3 : If z1 is N1 and z2 is P2 , then S = q3 . ⎪ ⎪ ⎪ ⎪ ⎭ Although there are four single rules, there is no consequent for the antecedent “z1 is P1 and z2 is P2 ”.

In ) are real numbers. 26). 26) is given. 1 . 1 ]T ∈ R2 , T g (z) = [1, . . , (z1p1 · · · znpn ) , . . 28) with pk ∈ {0, 1} for k = 1, . . , n. For a given z, the vector g (z) we will call a generator. 0 , . . ,pn , . . 1 . The generator g = g (z1 , z2 , . . , zn ) contains 2n components of the form “zi1 zi2 . . zik ” being elements of the polynomial “(1 + z1 ) × · · · × (1 + zn )” written in the expanded additive form, when substituting in the monomials of this polynomial all coefficients by “1”.

Nk Pk+1 q2k +2 /Dk+1 + . . + P1 P2 . . Pk Pk+1 q2k+1 /Dk+1 ) = Nk+1 (N1 N2 . . Nk q1 + . . + P1 P2 . . Pk q2k ) /Dk+1 + Pk+1 (N1 N2 . . Nk q2k +1 + . . + P1 P2 . . Pk q2k+1 ) /Dk+1 , where the denominator Dk+1 = Dk = 1 for k = 1, 2, . . 14) (Ni (zi ) + Pi (zi )) = 1. Knowing that Sk (z1 , . . , zk | q1 , . . , q2k ) = N1 N2 . . Nk q1 + P1 N2 . . Nk q2 + . . + P1 P2 . . 3 Recursion in More General TS Systems with Two Fuzzy Sets 33 and Sk (z1 , . . , zk | q2k +1 , . . , q2k+1 ) = N1 N2 .

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Analytical Methods in Fuzzy Modeling and Control by Jacek Kluska


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