FILTERED REFERENCE AND FILTERED ERROR LMS ALGORITHMS FOR ADAPTIVE FEEDFORWARD CONTROL

A unified and consistent formulation is developed for both filtered re ference and filtered error forms of the instantaneous steepest descent , or LMS, algorithm when used to adapt FIR feedforward controllers. Bo th algorithms minimise the mean-square value of the same, output, erro r function. The two algorithms are first formulated for single-input s ingle-output linear plants. It is argued that since the behaviour of t he two algorithms is equivalent in the case of slow adaptation, the co nditions on the accuracy of the plant model for stability should also be the same in both cases. This is expressed as a bound on the unstruc tured multiplicative uncertainty of the plant. Filtered reference and filtered error algorithms are also derived for multiple-input multiple -output (MIMO) linear systems, although the filtered reference algorit hm is found not to have a simple block diagram interpretation. In the MIMO case, the filtered error form of the algorithm can have considera ble computational advantages over the filtered reference form. Finally the two algorithms are extended to the case of non-linear plants and/ or controllers which are modelled as feedforward neural networks. In t he non-linear case the two formulations of the LMS algorithm reduce to two forms of the widely used backpropagation algorithm. (C) 1998 Acad emic Press.