Thermostats; What is a goal?; Saccades

[From Bill Powers (931217.0930 MST)]

Hans Blom (931217) --

Actually, the predictive controller you describe will result in
worse fuel economy, not better.

In the first place, the practice of turning the thermostat higher
than the desired set point has no effect at all on how rapidly
the house warms up, unless you have a proportional-output furnace
(which I doubt). The furnace simply remains on as long as the
sensed temperature is lower than the reference temperature. It
doesn't matter how much lower. So you waste no fuel by turning
the thermostat up to 120 F until the house reaches the
temperature you like, then reducing the setting to the desired
temperature. If the inside temperature is 60 F, and you set the
thermostat to 65, the furnace burns fuel at the same rate as when
you set the thermostat to 120.

To see why the fuel economy is worse if you turn the furnace on
earlier in the morning, all you have to do is consider the heat
losses from the house. Those losses are proportional to the
difference between outside and inside temperature. If you begin
heating the house earlier (as the predictive controller you
describe does), then this temperature difference begins to
increase earlier. Therefore the heat losses begin to increase
earlier, too. The only advantage of the predictive thermostat is
human comfort; the house is brought to the desired temperature at
the desired time, rather than just beginning to warm up at the
desired time.

As you say, this could be called a predictive control system. It
could also be seen as a sampled control system, in that the
controlled variable is sampled at a specific time each day, and
the turn-on time is varied to make that sampled temperature be at
the set point at the time of sampling. As in any sampled control
system, it's necessary to sense the variable through a low-pass
filter to avoid trying to control the fluctuations between
samples. That's what the 10-day running average does.

You'll note that this is also a hierarchical control system, with
the lower level being the normal thermostat, and the higher level
being the "predictive" or "sampled" system that controls for
reaching the desired temperature at a specified time. A "when"
controller is using a "how much" controller as its output
function.

Another design that would work would be to sample the time at
which the temperature reaches the desired set-point, and vary the
turn-on time to make the sampled time match a reference time.

ยทยทยท

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Osmo Eerola (931215.0930) --

In seeing Tom's replies, I notice that you are using the term
"goal" quite a lot. Could you explain your concept of a goal, and
how a goal can affect behavior?
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Gary Cziko (931217.0322 GMT) --

The abbreviation "SC" in the quote about the monkey experiment
means "Superior colliculus", not "saccade." Wolfgang Zocher now
has my materials on my model of the oculomotor control systems,
so he would be in a better position to go into details here. In
brief, I have proposed that a saccade results from (a) setting
the reference direction for looking to a point in the visual
field away from the fovea, and (b) momentarily blanking the
pursuit control system. Normally the pursuit system holds the eye
locked onto a scene, moving or stationary. One can attend to
places off the fovea without moving the eye. In my model, this
alters the reference signal for direction of looking, but in a
way that the pursuit system can override. Momentarily gating the
pursuit control system off allows the other control system to
snap the off-foveal fixation point to the fovea (or from the
external point of view, snap the eye to a position aimed at the
selected target). Then pursuit tracking immediately takes over
again. This model appears to explain all reported phenomena,
including the effects of mechanical disturbances and various
phenomena involving changing the fixation point on moving or
stationary targets.

As to the "reafference" concept of control used here, I can't
really comment without working out the details in my model. The
model doesn't use reafference, but I can't say from memory
whether it would be required in the conditions you describe. The
existence of kinesthetic feedback about eyeball position is
problematic, in that although some spindle cells have been found
in human eye muscle, nobody has shown the existence of a stretch
reflex there. My model assumes it, but also shows why a stretch
reflex (of normal size) would not be observed.

Malpeli's explanation (I suppose it's really the authors') is
that the brain keeps track of where the eyeball is by
integrating the velocity command signal.

This is not a practical explanation unless it's limited to very
short periods of time. Neural integration is an analog process
and must lose accuracy rapidly.

Wolfgang, if you're listening, you never told me whether you
received the reference materials I sent you.
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Best to all,

Bill P.