On a general structure for adaptation/learning algorithms - stability and performance issues
Abstract
The paper introduces a general structure for parameter adaptation/learning algorithms (PALA). This
structure is characterized by the presence of an embedded ARMA (poles-zeros) filter in the PALA. The
key question is how to select the coefficients of this
filter in order, on the one hand, to guarantee the stability of the parameter estimator for any (positive)
value of the adaptation gain/learning rate and for any
initial conditions and on the other hand to accelerate
the adaptation transient. In order to achieve this, it
is shown that on one hand the embedded ARMA filter should be characterized by a positive real transfer
function and on the other hand the filter acting on
the correcting term (the dynamic adaptation gain)
should be characterized by a strictly positive real
transfer function. Specic conditions for the design
of a second order ARMA embedded filter (ARIMA2
algorithm) are provided.
It is shown in the paper that many parameter adaptation/learning algorithms (PALA) used in
adaptive control, system identication and neural networks (Nesterov, Conjugate gradients, Momentum back propagation, Averaged gradient, Integral+proportional+derivative, ...) are particular
cases of the PALA structure introduced in this paper and specic conditions for the stable operation of
these algorithms are given.
Performance of the ARIMA2 algorithm as well as of
the other algorithms reviewed in the paper will be
comparatively evaluated by simulations and experimental results obtained on an active noise control
system.
Origin : Files produced by the author(s)