Fuzzy Modeling and Fuzzy Control (Control Engineering) by Huaguang Zhang

By Huaguang Zhang

Fuzzy common sense method has confirmed potent in facing complicated nonlinear structures containing uncertainties which are another way tough to version. know-how in accordance with this system is appropriate to many real-world difficulties, in particular within the sector of purchaser items. This publication provides the 1st entire, unified remedy of fuzzy modeling and fuzzy keep watch over, offering instruments for the keep an eye on of advanced nonlinear platforms. insurance contains version complexity, version precision, and computing time. this is often a very good reference for electric, desktop, chemical, business, civil, production, mechanical and aeronautical engineers, and likewise precious for graduate classes in electric engineering, machine engineering, and laptop technological know-how.

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The one with the smallest PER is selected. Its PER and premise structure are denoted as PER(i) and STR(i), respectively. (5) If either of the following criteria is satisfied the search will be stopped and the optimum premise structure for the model is obtained as STR(i). Otherwise, go to Step 4. - With a predetermined small value e > 0, we have PER(i) - PER(2 - 1) < e. PER(i) - The number of rules exceeds a predetermined number. If the number of input variables is rather large, the number of possible premise structures at each step becomes combinatorially large.

To conduct inferences like this one, we will have to use the "rules of replacement" with which we can change the original forms of our premises so that our basic inference rules can be applied to them. 3, shows a set of rules of replacement. Returning to our inference above, we can see that the first premise -(pvg) may be rewritten as its logically equivalent (synonymous) expression -ip A ^q and the inference now proceeds easily. Before we start a survey on the various inference rules in fuzzy reasoning, we will make some remarks about knowledge representation.

2) A fuzzy model consisting of two fuzzy rules is constructed by first dividing the range of xi into {small} and {large} fuzzy subspaces: R^\ IF xi is {small}, THEN • • • ; R^\ IF xi is {large}, THEN • • •. Then, the premise parameters and the consequent structure and parameters are identified, and the PER of the model is calculated. Similarly, a fuzzy model dividing the range of each xi^i = 2, 3 , . . , m, is identified, and its PER is calculated. Among the m models, the one with the smallest PER is determined.

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