# Systems (under control) which constantly go from stable to unstable states.

1. Jul 31, 2012

### manuka

Hi. I would appreciate if some one could help me with my question. But first some background:

There is a classical problem of inverted pendulum under control.
Pendulum can be put to UNSTABLE equlibrium and (if no control applied) it can put itself to STABLE equlibrium.
So system under control goes from MAXIMUM potential Energy to its MINIMUM potential energy. So keeping system in ONE state forever is the goal of the problem.
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The QUESTION:
Are there models\systems (under control and without one) which are sole purpose to continuously go from Stable to Unstable equlibriums i.e. continiously switch states (and do so in optimal way) and not trying to keep just one of them forever.

thanks.

2. Jul 31, 2012

### pgardn

I dont think this fits the bill but its cool anyways. Another poster found this.

Spends most of its time unstable but still amazing I think.

Last edited by a moderator: Sep 25, 2014
3. Jul 31, 2012

### manuka

thanks.> i've never seen this one. funny thng. but that is not in my list! :)

Maybe i would hint others about such systems. The ONE i can imagin is:

Wolf foraging. Wolf sits "stable" in one area(patch) where game is plentiful, but when pray becomes scares he should move to other patch of the forest.

His objective function is to conserve energy.

When energy spent of hunting for food in old patch exceeds energy needed to travel to the fresh patch he "switches" to UNSTABLE mode (walking between patches) and when he reaches one he "stablizes" for a time.

So whole his life is made of a long serie of switching between Stable-Unstable states.

4. Jul 31, 2012

### Studiot

What you have asked for is logically inconsistent.

By definition there is no tendency of a system to leave a stable state so it will never switch of its own accord.

However you might like to google 'multivibrator'. (Electronic engineering)

There are three types.

Bistable - has two stable states but can be externally switched between them. Once switched it will remain in that state until externally switched again.

Astable - has two metastable states and switches continuously between them of its own accord

Monostable - has one stable and one metastable state. Can only be switched from the stable to the metastable state externally. Once in the metastable state it will switch back to the stable state of its own accord.

There are mechanical equivalents of the electronic circuits.

5. Jul 31, 2012

### manuka

thanks i'll look at it.

does the example with "wolf foraging" is inconsistent too? could you explain a little bit more. Or do you think this example does not undergo "optimal switching between states" at all?

maybe i was wrong to use word SYSTEM... Maybe systems really do not "want" to leave stable states. In this case let me use word "Model of Control". There is a "system" - wolf body which needs energy. and there is a CONTROL - wolf's brain which governs the body to STAY or to MOVE depending on what is optimal right now.

6. Jul 31, 2012

### mikeph

I think your example is fine, but I'd like to point out a possible source of confusion over what exactly you mean by "state". In your example the system state is defined as the location of the wolf- but in someone else's opinion, the system state might be defined as the migratory habit of the wolf, which may follow the same yearly cycle, for example, and may therefore be constant over the life of the wolf.

This labelling can happen everywhere. For example, if someone looks at the sun, they may deduce that the system switches between two stable states of "night" and "day", or "summer" and "winter" (particularly in the polar regions!), but an impartial observer from a satellite might recognise that there is only one stable state - the mutual orbit of the two bodies around a common centre of mass, with each one conserving its own angular momentum about a central axis.

So the definition of what is specifically meant by the word "state" is really important before you can say whether it's stable or not, and I think that's where some confusion is arising, because your initial post asks a very broad question.

7. Jul 31, 2012

### Studiot

However you measure 'state' the term 'stable state' has a precise meaning which you should use to avoid confusion.

8. Jul 31, 2012

### manuka

Well, how should I put it. At the first post i gave an example of inverted pendulum. "State" there is a word which describes position of a pendulum here. One is stable the other is unstable. It is clean and simple model. But it lacks desired dynamics: i can not find an objective function for the CONTROL which will lead the WHOLE model to suffer from constatly changing "states" (points) as a byproduct.

I used a "wolf's analogy" only to show the desired direction of a topic. I personally don't like it (you have mentioned the very reasons of my concerns) that is why i ask for help.

hope i'm clear.

p.s. i have a very basic understanding of physics, be merciful :)

p.p.s
As far as my knoledge of English goes i see the "problem" with the "of its own accord" words.
That's what I what to know ----- physical/engeneering problems under CONTROL, under rule if you will. The System WILL never leave stable state by it's OWN but under CONTROL it will!

9. Jul 31, 2012

### Studiot

Your definitions of state will do for now.

'change state of its own accord' means that the system will change state by itself with no external influence. It will attempt to change state and you would have to do something active to stop it.

The alternative is that the system will change state , if given a slight initial push.

If at all times you have externally forced the condition of the state and it has no choice then you cannot call it a system state. The system then has only one condition available - whatever the forcing dictates.