Information Technology Reference
In-Depth Information
a
b
5
5
10
0
0
0
−5
−5
5
10
15
20
25
30
35
40
0
10
20
30
40
0
10
20
30
40
time
time
time
1
2
5
0
0
0
−1
−2
5
10
15
20
25
30
35
40
0
10
20
30
40
0
10
20
30
40
time
time
time
1
0.5
5
0
0
0
−1
−0.5
5
10
15
20
25
30
35
40
0
10
20
30
40
0
10
20
30
40
time
time
time
Fig. 5.5
Test 3: (
a
) Synchronization of state variables x
i
(i D 1;4: frq mRNA concentration,
i D 2;5: FRQ protein concentration in cytoplasm, i D 3;6: FRQ protein concentration in nucleus)
between the two circadian cells (
red continuous line
denotes concentration in cell 1 whereas the
dashed blue line
denotes concentration in cell 2) (
b
) Estimation of disturbance inputs and of their
derivatives (
blue lines
) with the use of the Derivative-free nonlinear Kalman Filter
a
b
5
2
10
0
0
5
0
−5
−2
5
10
15
20
25
30
35
40
0
10
20
30
40
0
10
20
30
40
time
ti
m
e
ti
m
e
1
2
4
2
0
0
0
−1
−2
5
10
15
20
25
30
35
40
0
10
20
30
40
0
10
20
30
40
time
time
time
0.5
0.2
4
0
0
2
0
−0.5
−0.2
5
10
15
20
25
30
35
40
0
10
20
30
40
10
20
30
40
time
time
time
Fig. 5.6
Test 4: (
a
) Synchronization of state variables x
i
(i D 1;4: frq mRNA concentration,
i D 2;5: FRQ protein concentration in cytoplasm, i D 3;6: FRQ protein concentration in nucleus)
between the two circadian cells (
red continuous line
denotes concentration in cell 1 whereas the
dashed blue line
denotes concentration in cell 2) (
b
) Estimation of disturbance inputs and of their
derivatives (
blue lines
) with the use of the Derivative-free nonlinear Kalman Filter
In Figs.
5.3
b,
5.4
b,
5.5
b,
5.6
b,
5.7
b, and
5.8
b the estimates of the disturbance
inputs affecting the model of the coupled circadian oscillators are presented. The
real value of the disturbance variable is denoted with the red line while the estimated
value is denoted with the blue line. The disturbance terms affecting the inputs of the
model are variables
z
7
and
z
10
. Their first and second order derivatives are variables
z
8
,
z
9
and
z
11
,
z
12
, respectively. It can be noticed that the Kalman Filter-based
observer provides accurate estimates about the non-measurable disturbances and
this information enables the efficient compensation of the perturbations' effects.
