| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
03 Aug 2006 11:54:17 PM |
| Object: |
Tightly coupled dynamics in physical systems? |
Hello,
I am studying a problem in computer science domain which has led to two
interacting dynamical systems as follows:
The problem consists of a set of state vectors which start from a given
initial condition and evolve in such a way to (locally) minimize an
energy function. This process forms the first dynamical system. The
energy function is smooth, but nonlinear and expressed in parametric
form where its parameters change over time, hence realizing the second
dynamical system. The dynamics of the energy parameters is in such a
way that minimizes the distance/norm between the current location of
each state vector and a given goal state for that vector, hence
coupling the two processes within a tight loop..
In other words, each state vector is associated with a corresponding
goal vector which is fixed and known. The system starts from an initial
condition and tries to push each state vector toward the corresponding
goal indirectly, through the energy function.
I was wondering what is the closest physical phenomenon to this kind of
behavior? This would hopefully provide useful pointers for me to better
understand this behavior and possibly analyze the esistence of
solution, getting stuck in local minima (i.e. not being able to take
all states to their goals), and stability issues.
Thank you for your valuable help in advance.
H.M.
.
|
|
| User: "Edward Green" |
|
| Title: Re: Tightly coupled dynamics in physical systems? |
10 Aug 2006 01:12:33 PM |
|
|
wrote:
I am studying a problem in computer science domain which has led to two
interacting dynamical systems as follows:
The problem consists of a set of state vectors which start from a given
initial condition ...
To a physicist, "state vector" is liable to mean a quantum mechanical
state; I take it you just mean "arrays of numbers labeling a state".
and evolve in such a way to (locally) minimize an energy function.
This process forms the first dynamical system. The
energy function is smooth, but nonlinear and expressed in parametric
form where its parameters change over time, hence realizing the second
dynamical system. The dynamics of the energy parameters is in such a
way that minimizes the distance/norm between the current location of
each state vector and a given goal state for that vector,
I don't follow this. Do you mean the energy minimum moves in order to
put itself as close as possible to the goal state?
hence coupling the two processes within a tight loop..
In other words, each state vector is associated with a corresponding
goal vector which is fixed and known. The system starts from an initial
condition and tries to push each state vector toward the corresponding
goal indirectly, through the energy function.
I was wondering what is the closest physical phenomenon to this kind of
behavior? This would hopefully provide useful pointers for me to better
understand this behavior and possibly analyze the esistence of
solution, getting stuck in local minima (i.e. not being able to take
all states to their goals), and stability issues.
I must not understand the problem. Move the energy minima on top of
the goal states, and let the first algorithm move the state vectors --
put the depression in the surface over where you would like the ball to
end up. Where is the problem? Is the second algorithm chasing the
ball? This would be the central control problem of statistical quality
control, whose solution is to prescribe monitoring only, moving action
outside of the inner algorithm, and into the hands of an undefined
intelligent observer.
<If you can't beat them, join them>
I have the prior that you have no idea what you are talking about, will
reject all useful advice (should you receive any) without discussion,
and shortly disappear back into the sea of idiot twaddle that passes
for the "the net". Only fools waste their time here.
.
|
|
|
|
|
Related Articles |
|
|
