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A design for a fuzzy logic controller. (English) Zbl 0662.93004
[For the entire collection see Zbl 0648.00013.]
The paper deals with the problem of designing a control algorithm realized on the basis of a set of linguistic control rules. The rules express relationships between variables \(x_1,x_2,\ldots,x_ p\) of the system under control and an appropriate control action \(y\), say \[ \begin{aligned} \text{---if }x_1 \text{ is }A&_{11} \text{ and }x_2 \text{ is } A_{12} \text{ and \quad \dots and }x_ p \text{ is }A_{1p} \text{ then }y \text{ is }f_1(x_1,x_2,\ldots,x_ p),\\ &\vdots\\ \text{---if }x_1 \text{ is }A&_{n1} \text{ and }x_2 \text{ is } A_{n2} \text{ and \quad \dots and }x_ p \text{ is }A_{np} \text{ then }y \text{ is }f_ n(x_1,x_2,\ldots,x_ p), \end{aligned} \] The \(A_{ij}\)’s standing in the above rules are fuzzy sets describing consecutive system variables. The \(f_ i's\) are functions giving rise to values of the control variable \(y\). The control \(y\) is calculated on the basis of all rules by determining degrees of activation (firing) of their antecedents and aggregating results coming from the individual rules, namely \[ \sum^{n}_{i=1} g_ i (A_{i1}(x^*_ 1), A_{i2}(x^*_2),\ldots, A_{ip}(x^*_ p)) f_ i(x^*_1,x^*_2,\ldots,x^*_ n) / \sum^{n}_{i=1} g_ i(A_{i1}(x^*_1), A_{i2}(x^*_2), \ldots, A_{ip}(X^*_ p)) \] with \(x^*_1, x^*_2, \ldots, x^*_ p\) being actual values of the system variables. Assuming the functions \(f_ i\) to be linear with regard to their arguments, \(f_ i = \sum^{p}_{j=1} a_{ij}x_ i\), their parameters are estimated using the standard least squares error method.
Reviewer: W.Pedrycz

93A99 General systems theory
93B30 System identification
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text: DOI
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