[From Bill Powers (2003.12.15.1503 MST)]
Bruce Gregory (2003.12.15.1635)--
Would it be fair to say that the spreadsheet represents an equilibrium
solution to hierarchical control? The conclusion that two higher-order
levels cannot control the same lower-level perception without control
being lost describes an equilibrium configuration.
I won't speak for Rick, but I believe that what happens when conflict
occurs in any model depends greatly on the values of parameters like loop
gain, whether the output functions are proportional amplifiers or
integrators, and whether there are limits placed on the amount of output
that can be generated.
A collection of proportional-output systems with low gain and conflict will
simply come to some overall equilibrium condition with the uncorrected
error being distributed among the different systems. Nothing dramatic will
happen becvause of conflicts, other than a degradation in the abilities of
the subsystems to resist disturbances. The most dramatic effects will occur
when there are high-gain systems in conflict, and the outputs of the
systems reach limits. Then there can be complete loss of the ability to
counteract disturbances or make perceptual signals match reference signals.
This might still be called an equilibrium system, but the behavior in the
presence of disturbances would be much different from that of the low-gain
The Traffic story
describes a transient non-equilibrium state during which two higher
level systems attempt to control the same lower-level perception, and
the one with the greatest error prevails.
This is a reasonable description, but it's more the system with the highest
gain that prevails. Well, even that ... the problem is that there are
several factors that contribute: loop gain, degree of disturbance, and the
nature of the environmental feedback function. The latter is important in
your traffic case. Bill Williams suggests several other factors that can
influence the outcome.
Consider the speed control dimension. When local problems arise, the
avoidance system sees an error that varies rapidly with position -- twenty
feet of movement can double the error, for example, if you're 40 feet from
an obstacle and moving toward it. But the same 20 feet of movement will
change your distance from the destination, some blocks or even miles away,
by only a very tiny percentage. Martin Taylor already said something like
this. Therefore we would expect a slowdown to cause very large change in
the perceptions of the obstacle avoidance system, but a hardly detectable
change in the perceptions of the destination-seeking system. The
destination-seeking system is therefore much less affected by a brief local
delay than the collision-avoidance system is, because of the nature of the
environmental feedback functions involved. The destination-seeking system,
experiencing less error, will produce less output to correct it than the
collision-avoidance system will produce.
The directional control systems conflict more, because the direction error
relative to the destination and the direction error relative to the local
obstacle, both measured from the direction of travel, are equally affected
by changes in the direction of travel. We might predict that drivers would
suffer less conflict from needing to slow down or speed up to avoid
collisions than they would from needing to change direction.