Page 158 - Control Theory in Biomedical Engineering

142 Control theory in biomedical engineering

100
Estimated
Desired
80

60
y
40

20

0
20 40 60 80 100 120
x
Fig. 7 The response of cross-validation of the model (4): Arabic letter SIN.

following question: How can we model different kinds of graphic traces without
adjustment of the model parameters?
To answer this question, we propose, in this section, an interval observer
to estimate manuscript coordinates in the two-dimensional plane, using the
parametric model (Eq. 2). This estimator is based on two Luenberger
observers, which contain two parameter intervals, upper and lower. Indeed,
we studied parameter variation of different models characterizing the letters
“SIN” and “HA” (Ito and Dinh, 2018; Chihi et al., 2018). This study led us
to show a significant difference between parameter intervals even if it is
computed to characterize the same kind of letter written by the same writer.
Besides, this study allowed classifying the model parameters according to
two intervals, upper and lower (see Table 2). In order to explain the pro-
posed approach, we start by studying parametric variations of two Arabic
letters “HA” and “SIN.” These writings are different; the letter “SIN” is
constituted by three primitives, similar to arcs of a circle, two small and
one bigger. The second letter “HA” is composed of two primitives, a line
quasihorizontal (left/right) and a large arc as shown in Figs. 9 and 10.
As already mentioned, each participant wrote each graphic form many
times. For three writers, we study, in a first step, the parametric variations
of two letters (“HA” and “SIN”) estimated using model (2).