# zbMATH — the first resource for mathematics

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

##### MSC:
 93A99 General systems theory 93B30 System identification 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text:
##### References:
 [1] Akaike, H., A new look at statistical model identification, IEEE trans. automat. control, AC-19, 6, 716-723, (1974) · Zbl 0314.62039 [2] Businger, P.; Golub, G.H., Linear least squares solutions by Householder transformations, Numer. math., 7, 269-276, (1965) · Zbl 0142.11503 [3] Mamdani, E.H., Application of fuzzy algorithm for control of simple dynamic plant, (), 1585-1588, (12) [4] Murakami, S.; Maeda, M., Automobile speed control system using a fuzzy logic controller, (), 105-123 [5] Sugeno, M.; Murakami, K., An experimental study of fuzzy parking control using a model car, (), 125-138 [6] Yasunobu, S.; Miyamoto, S., Automatic train operation system by predictive fuzzy control, (), 1-18
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.