Dynamical systems vs. control systems

Cliff Joslyn (931117.1300), I guess? I still haven't mastered your
quotation system here. Down below I can't tell who's Rick and who's
Martin.

[From Rick Marken (931116.1300)]

Martin Taylor (931116 12:00) --

>A control system is the type of dynamical system that resists
>disturbances. There are others. A marble in a bowl resists disturbances
>to its resting position in the bottom of the bowl, but is not a control
>system.

I can't believe you claim this? What kind of marbles have they got
up there in Canada? So when you gently push on a marble at the bottom
of a bowl the marble pushes back with a force that is nearly equal and
opposite to the applied force -- resulting in a stationary marble?
I'd love to see THAT! Is it in the design of the marble or the bowl?

There's a confusion about what a dynamical system is. According to the
technical definition, a dynamical system is ANY system which can be
described by deterministic equations, so that future states can be
predicted from current states. This is true even of systems with
input, even if the input is unknown (a disturbance, or to be very
clear an external factor which affects the PV in some way which may or
may not be perceived as a fluctuation of the PV), as long as the
effects of the input can be predicted deterministically once the input
becomes known.

So clearly the simple kinds of control systems as in the appendix of
BCP are dynamical systems.

But also of course not all dynamical systems are control systems. Only
those dynamical systems which are wired up in such a way as to have
negative feedback are control systems.

Now concerning the marble at the bottom of the bowl, in my
terminology, this is a dynamical system with stability but without
control. Good control is a sufficient, but not necessary, condition
for stability. The CAUSE of the stability in the marble is the
friction of the concave walls interacting with gravity. Thus the
marble will act in such a way as to DISSIPATE disturbances, but not
RESIST them in the sense of taking appropriate actions for a given
diturbance. IMPULSE disturbances can be dissipated, but CONTINUAL
disturbances cannot. This was the point of Marken's "Nature of
Behavior" (Rick: which side are you arguing above?).

O----------------------------------------------------------------------------->

Cliff Joslyn, Cybernetician at Large, 327 Spring St #2 Portland ME 04102 USA
Systems Science, SUNY Binghamton NASA Goddard Space Flight Center
cjoslyn@bingsuns.cc.binghamton.edu joslyn@kong.gsfc.nasa.gov

V All the world is biscuit shaped. . .