Traditional Problem Definition - Computational Intelligence in Time Series Forecasting - page 69

G

ut () yt () .

BF

2.10.6 General Predictive Control

General predictive control (Hueseyin and Karasu, 2000) is based on the CARIMA
model

Bz ()

1

C z ()

1

yt () ut ( ' 1) et () , (2.21)

1 1

Az () Az ()

where,

'

1.

z

Introducing the term

et ()

[ () t

1

Cz ()

and presuming that

Cz

()1

,

the CARIMA model (2.21) takes the form

1 1
()() ()( ) ( / Az yt Bz ut [ t ' . (2.22)

Based on this model, the predictive control (Camacho and Bordons, 1999; Clarke
et al. , 1987) is implemented through the following steps and should be repeated for
every sample instant:

x prediction of output value using the CARIMA model and the observation
data collected up to time t
x determination of control signal value that produces the future output value
close to the predicted output value
x closing the control loop using the above results.
To determine a d -step predictor for y ( t ), i.e . y ( t+d ) using the Equation (2.22), the
Diophantine equation

1 1 d 1

Pz Az ()() ' z Q z ()1

d d