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)
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) 
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) 
Note that is only a function of the ...
