Wireless Sensor and Actuator Networks for Lighting Energy ...

E =
e 11
e m1
e 12
e m2
e 1n
e mn
1
l 11
1
l
m1
1
l
12
| | |
= l 1 l 2
l
K 1
d=
l m2
| | |
1
l
1n
1
l
mn
2
l 11
2
l m1
2
l 12
2
l m2
2
l 1n
12
l mn
K
l 11
K
l
m1
K
l
12
K
l m2
l 1n
K
K
l mn
d a
d b
d l
Ld (6.3)
The objective is to find an optimal set of light output levels d so as to result in a
properly illuminated room E that satisfies each occupant’s lighting preference. The
occupants’ lighting preferences are also specified in correspondence with the small
squares in the grid of discretized room, which are the locations of their workplanes.
Since the personally specified points of interest are most likely confined to a small area
rather than the entire room, it is unrealistic and unnecessary to artificially generate the
entire E for finding the optimal light setting. Therefore, the reduced-order vector E sub
,
which contains only the specified illuminances at the points of interest, is considered.
Likewise, the order of the operator L is reduced to obtain the corresponding matrix L sub
and (6.3) is then condensed to (6.4), where e pq ,e rs ,…,e xy are the desired illuminances at
the specified locations. The goal then becomes finding the optimal set of light output
levels d that satisfy the occupants’ lighting preferences E sub
.
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