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.
Read or Download Analytical Methods in Fuzzy Modeling and Control (Studies in Fuzziness and Soft Computing) PDF
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Additional info for Analytical Methods in Fuzzy Modeling and Control (Studies in Fuzziness and Soft Computing)
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 , .