Information Technology Reference
In-Depth Information
0
@
1
A
0
@
1
A
0
@
1
A
0
@
1
A
z
1
z
2
z
3
z
4
z
5
z
6
010000
001000
000000
000010
000001
000000
z
1
z
2
z
3
z
4
z
5
z
6
00
00
10
00
00
01
v
1
v
2
D
C
(5.77)
0
1
z
1
z
2
z
3
z
4
z
5
z
6
@
A
z
m
1
z
m
2
100000
000110
D
(5.78)
The control law that allows FRQ protein concentration converge to desirable levels
is given by
v
1
D x
.3/
1;d
K
1
.x
1
x
1
/ K
2
.x
1
x
1
/ K
3
.x
1
x
1
/
v
2
D x
.3/
(5.79)
1;d
K
1
.x
4
x
4
/ K
2
.x
4
x
4
/ K
3
.x
4
x
4
/
By knowing the control inputs .
v
1
;
v
2
/
T
one can compute the control inputs .
u
1
;
u
2
/
T
that are finally applied to the system of the coupled circadian neurons. By setting
f
A
.y
1
; y
1
;y
2
; y
2
/
f
B
.y
1
; y
1
;y
2
; y
2
/
g
A
1
.y
1
; y
1
;y
2
; y
2
/g
A
2
.y
1
; y
1
;y
2
; y
2
/
g
B
1
.y
1
; y
1
;y
2
; y
2
/g
B
2
.y
1
; y
1
;y
2
; y
2
/
(5.80)
f D
G D
f C G
u
)
u
D G
1
.
v
f/.
It holds
v
D
5.7
State Estimation and Disturbances Compensation
with the Derivative-Free Nonlinear Kalman Filter
The parametric uncertainty terms and the external disturbance terms affecting
x
.3/
d. In that case the dynamics of
v
or y
.3/
D
D
v
are denoted with variable
the coupled circadian oscillators takes the form
y
.3/
1
d
1
y
.3/
d
2
(5.81)
D
v
1
C
D
v
2
C
2
It is also assumed that the dynamics of the disturbance and model uncertainty terms
is described by the associated n-th order derivative, where without loss of generality
here it is assumed that n D 3
