Page 160 - Control Theory in Biomedical Engineering

144 Control theory in biomedical engineering

80
70
60
50
y 40
30
20
10
0
30 40 50 60 70 80 90 100 110 120
x
Fig. 9 Letter “HA”—one-writer validation: desired response and interval observer
response.

100

80

60
y
40
20

0
20 30 40 50 60 70 80 90 100 110 120
x
Fig. 10 Letter “SIN”—multiwriter validation: desired response and interval observer
response.

estimator. Cross-validation of the proposed approach is presented in Figs. 9
and 10 with considerable accuracy of the handwriting structure using the
principle of the interval observer.
In order to obtain a better estimation accuracy, we developed the interval
observer, deduced from two observers—upper and lower—that contains
superior and inferior variations of the parameters (Ito and Dinh, 2018, Chihi
et al., 2018).
• Upper observer e X:

8
e Xk +1ð Þ ¼ A s XkðÞ + B s UkðÞ + K s Y e Y
< e
(10)
:
e YkðÞ ¼ C s XkðÞ
e