Digital Signal Processing Reference
In-Depth Information
where
(m,n)
kT
=
Cell coordinates,
= Sampling instant
= Learning parameter,
= Momentum parameter,
= Reference input at step
k,
=
Plant output at step
k,
closed-loop error,
N
= Neighborhood parameter,
= Distance from cell located at (
m,n
) to cell
(i, j)
=
Variance of Gaussian distribution,
= Contents of MCMAC cell located at
m, n
at step
k,
and
= Quantization function defined by equation (1).
It is worth noting that the original CMAC and the proposed MCMAC
configurations attempt to model the characteristics of the plant on the basis
of input indices. The difference between the two is that the former system
learns from the plant input
x(kT)
and the output while the latter
one employs the closed loop error and the plant output in
their respective learning modes. Hence, the MCMAC does not require an
inverse model of the plant and there is no need for the classical controller to
be operational during the learning phase. This has an added advantage in the
determination of the training trajectory through the control of the reference
input
