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Monitoring and Control of Information-Poor Systems: An Approach Based on Fuzzy Relational Models by Arthur L. Dexter

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10

Online Model Identification in Information-Poor Environments

10.1 Online Fuzzy Identification Schemes

A number of online fuzzy identification schemes have been proposed but few of them can be used to identify FRMs that are capable of generating a fuzzy output (Xu and Lu, 1987; Shaw and Kruger, 1992; Chen et al., 1994; Bourke and Fisher, 2000). The two main approaches to identifying fuzzy FRMs online are recursive fuzzy least-squares and variants of the recursive RSK identification scheme (see also Section 5.3).

10.1.1 Recursive Fuzzy Least-Squares

The rule confidences of a fuzzy FRM that minimize a fuzzy cost function of the form (see Section 5.3)

Unnumbered Display Equation

can be estimated using a recursive least-squares parameter estimator (Wong et al., 2000; Campello and Amaral, 2001, 2003).

Example 10.1

Consider the online identification of the fuzzy FRM of a first-order dynamic system:

(10.1) Numbered Display Equation

Let the difference between the kth element of the output data at the (n+1)th sample time and the kth element of the fuzzy prediction generated by the FRM be  , defined

(10.2) Numbered Display Equation

Note that is only a function of the ...

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