[Martin Taylor 950113 16:15]

Avery Andrews, Joel Judd, Bruce Nevin

If you have a bunch of control loops that share common pathways (or even

if they don't--the trivial case), there is a maximum number of independently

controllable degrees of freedom. The classic "conflict" comes about because

there are two independent perceptual signals, but at one point in the two

loops, the pathways share one single degree of freedom, the common CEV.

You have been talking about a set of control systems in which the "bottleneck"

(the point of minimum number of degrees of freedom) is the set of perceptual

signals to be controlled. If the output degrees of freedom (say, muscles)

are fewer than the number of perceptual signals, then you can manage the

control only by time multiplexing--shifting the commitment of some part of

the bottleneck from one control loop to another at a rate fast enough

that control can be maintained over a set of sufficiently slowly changing

perceptions.

But then, the actual degrees of freedom involved DO include considerations

of the bandwidths of various parts of the channels, and what you are doing

is trading off available temporal degrees of freedom for the lacking

spatial degrees of freedom. Roughly speaking, the temporal degrees of

freedom for a signal can be considered as having a rate of 2/bandwidth;

that's the number of "statistically independent" samples in the signal.

So, if you have one output signal that can be varied with a bandwidth of

10 Hz, you can (in principle--it never works in practice) use it to control

two perceptions for which the disturbance varies with a bandwidth of 5Hz.

But you can't use it to control accurately two signals for which the

bandwidth of the disturbances total more than 10 Hz.

Bottom line--there's no problem with parts of the control loop where a bunch

of control systems share a larger number of degrees of freedom than the

number of degrees of freedom to be controlled, but there is a problem

when the output or the environmental feedback path (or the sensor systems)

have fewer degrees of freedom, totalled over time, than the number of

degrees of freedom for which control is attempted.

Martin

PS. If I don't answer some message, it may be because our mail system

garbled it. One of Bill Powers' messages was garbled, but I got the sense

of it (I think). My response was trashed before I could send it, so I'm

rewriting it off-line. There may well have been other messages with

missing parts, as I suspect happened to Bruce Nevin's message of yesterday

about tweaking speech synthesis.