Dynamic Extensions of PLS

If the f/ block contains past values of the process inputs and outputs, the PLS model would be a dynamic model of e form  

Kaspar and Ray (1992, 1993) developed dynamic PLS models by filtering the process inputs and subsequent application of the standard PLS algorithm. Lakshminarayanan (1997) and Patwardhan (1998) proposed the modification of the PLS inner relation to be able to identify dynamic models. Instead of using the input scores i, and output scores m a dynamic ARX model G, (see chapter 24) was used. The general ARX model stracture can be described by  

is the measure of the Y space that is explained by the i-th PLS dimension. The matrix G is a diagonal matrix, comprising the dynamic elements identified at each of the n PLS dimensions  

Lakshnrirrarayatran (1997) also shows the procedure to apply PLS to Harmnerstein models, which describe a process in terms of a non-linear static element and a linear dyiramic ele-merrt. 

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