Comments on Hans' model

[From Bill Powers (931127.1230 MST)]

Hans Blom (931124b) --

Some added thoughts about your model-based control model:

       -------------- organism . world
goal | | .
------>| | u .
       > controller |----------------------------
    -->| | | . |
    > > > \|/ . \|/
    > -------------- ---------- . ----------
    >W^ = knowledge about W | | . | |
    ------------------------| ^ | . | |
                            > W | . | W |<-"system
                    ------->| | . | | noise"
                    > > > . | |
                    > ---------- . ----------
                    >adjust | . \|/
                    > > . ------
                --------- x | . | + |<-"obser-
                > ><-------- . ------ vation
                >compare> y ----- | noise"
                > ><------------| M |<-----
                --------- -----
                                        .

There is a tradeoff here between control that can actually oppose
unpredictable disturbances from the environment ("system noise"),
and control that can continue over a brief interruption of the
feedback signal y.

If the adjustment is fast enough to keep up with changes in y
caused by unpredictable disturbances, then loss of feedback will
cause a rapid adjustment and actions that are inappropriate for
controlling W. If the adjustment is slow in comparison with the
duration of transient disturbances, then loss of feedback will
not cause loss of control but short-term disturbances will not be
resisted.

If it's important to oppose transient disturbances, then this is
not the form of model that would be best. However, the simple
control model that would be suitable would be vulnerable to loss
of feedback. This appears to be the case for the lower-level
control systems in the HPCT model (and the real organism).

On the other hand, when the kind of variable being controlled is
of a more general or abstract nature, disturbance capable of
altering the perceptions are fewer and slower; rapid disturbances
are largely cancelled by the fast lower-level systems. This means
that model-based control might well be appropriate as the main
mode of operation of higher-level systems.

To adapt your diagram for a hierarchical system, the main change
that's needed is to make the controller output act via lower-
level control systems instead of affecting W directly. If the
higher-level behavior is carried out by altering the direction,
speed, and duration of walking, then the controller output would
supply reference signals to lower-level control systems concerned
with controlling those aspects of walking, and those systems in
turn would manipulate reference signals for joint angle velocity
and position control and so on to control of muscle tension. The
model at the highest level would then represent the overall
effects of sending these reference signals to lower systems,
rather than just an external environmental effect. With lower-
level systems taking care of the details such as limb and body
dynamics, the model at the higher level could be much simpler
than otherwise. The lower control systems greatly reduce the
dimensionality of the highest-level control problem.

Now we could understand how feedback to the highest level might
be lost without disrupting the selection of direction, speed, and
duration of walking, while loss of feedback at lower levels would
result in immediate loss of coordination. This would seem to fit
the facts of real behavior better than a single-unit model can
do.

···

---------------------
Incidentally, in your model, what determines the setting of the
reference signal (the goal)?
-------------------------------------------------------------
Best,

Bill P.