Re: Discrete Controls

[glen e. p. ropella]

Mark P. Line writes:
 > >   xi is-a-member-of X defined-as a set of interacting elements
 > 
 > ... some of which must be control elements, if you're saying your system
 > has some control elements.
 > 
 > Maybe I don't understand the problem. :)

Well, after speaking with Barry and Tim (Tim's our sysadmin, here),
I've come to the conclusion that my post didn't state my real
question.  So, it wouldn't surprise me at all if what I was trying to
say failed to get out in a coherent way. [grin]

But, no, I'm not explicitly saying that some of the members of X are
elements whose only goal is to control the other parts of the system.
That certainly could be the case; but, I wasn't assuming it.

I was trying to formulate a generic discrete (possibly, I should use
the term "object-based" instead of "discrete") system to which normal
control theory results could be applied.  And the first step in doing
that is to cast our type of modelling (ABM's) in a control theory
framework.  Now, as I see it, the formulation of a problem in a
classical control theory framework involves a very close tie between
the state space (which includes a set of states and a metric defined
on that set) and the dynamics of the state transitions (which are
usually based on the metric for that space).

This is not necessarily true for the generic discrete model.
I.e. there is no obviously characterizable metric defined on
the set of heatbugs (like there is for the real line, say). 
The metric is completely dependent on the rules that govern
the behaviour of the bugs and, thus, the dynamic that
governs the behaviour of the system is completely dependent
on those rules.  Now, granted, those dynamics are completely
embodied in the objective-C code that is heatbugs.... [grin]
But, the characterization of the dynamic in a system like
heatbugs is not in a form that is amenable to analysis.

So! [whew] What I'm trying to get at with all this is that
we *may* be able to use control theoretic techniques on 
some of these models IF we can either find ways to characterize
these ugly dynamics and apply the analytic techniques to the
ones for which our control theory theorems apply... OR maybe
we can find ways to divide up our agents, objects, and methods
so that we can get ideas about how to control these systems
just by formulating them in ways that are analogous to classical
control theoretical problem formulations.

Now, one of the things Barry and Tim tried (in vain [grin]) to
point out to me is that the dynamic for heatbugs is *probably*
nonlinear, and so, alot of the classical control theory results
don't apply.  And if all I were worried about was heatbugs, then
I'd say, "Ahhh, you're probably right" and walk away.  But, what
I'm really after is a *method* for characterizing the dynamic in
these ugly systems that is more formal than sprawling source
code.  And then, on top of that, it would be nice if that
characterization were amenable to analysis so that we could 
*prove* whether the dynamics were nonlinear, and if they were,
then maybe we could even salvage some of the specialty maths
that do address nonlinear systems.

But, even if that is too hard, it would still be nice to have
a discrete formalization of control theoretic problems so that
we could begin to talk about control-type issues on these ugly
systems.  I want to answer questions like, "Can I make the 
heatbugs cluster within certain bounds by adding a control
object or some special control methods to the existing bugs?"

Any clearer?

glen
-- 
{glen e. p. ropella <address@hidden> |                                  }
{Hive Drone, SFI Swarm Project         |            Hail Eris!            }
{http://www.trail.com/~gepr/home.html  |               =><=               }


                  ==================================
   Swarm-Modelling is for discussion of Simulation and Modelling techniques
   esp. using Swarm.  For list administration needs (esp. [un]subscribing),
   please send a message to <address@hidden> with "help" in the
   body of the message.
                  ==================================