Analytical Methods in Fuzzy Modeling and Control (Studies in by Jacek Kluska

By Jacek Kluska

This booklet is concentrated on mathematical research and rigorous layout equipment for fuzzy keep watch over platforms in keeping with Takagi-Sugeno fuzzy versions, also known as Takagi-Sugeno-Kang models.

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Additional info for Analytical Methods in Fuzzy Modeling and Control (Studies in Fuzziness and Soft Computing)

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The inputs. The inputs of the MIMO TS system which should model a nonlinear dynamical system, are quantities zk (t) constituting the vecT tor z (t) = [z1 (t) , .

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”. The equation f0 (z1 , . . , zn ) = θT g (z1 , . . , zn ) must be satisfied for all points in the hypercuboid Dn , especially in its vertices. Thus, the following 2n linear equations θ T g (γ v ) = qv , must be satisfied, or equivalently v = 1, 2, . . 4 Crisp Output of the Zero-Order MISO P1-TS System q = ΩT θ, Ω = g (γ 1 ) , .

Q2n−1 ) + Pn (zn ) Sn−1 (z1 , . . , zn−1 | q2n−1 +1 , . . 10) where • Sn (z1 , . . , zn | q1 , . . 7), with input variables (z1 , . . 12), • Sn−1 (z1 , . . , zn−1 | q1 , . . 8), with the inputs (z1 , . . , zn−1 ) ∈ Dn−1 T and the consequents of the rules constituting the vector [q1 , · · · , q2n−1 ] , 30 3 Recursion in TS Systems with Two Fuzzy Sets for Every Input • Sn−1 (z1 , . . , zn−1 | q2n−1 +1 , . . 8), with input variables (z1 , . . , zn−1 ) ∈ T Dn−1 , replacing its consequents with [q2n−1 +1 , .

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