Modeling hierarchical control

hi all,
Together with Ton van Amelsfort, a science teacher at Technical University Eindhoven, I’m working on trying to model hierarchical control in Vensim software. This exercise teaches us many things about PCT, especially how many difficulties you encounter when trying to convert a mental model, a basic idea, into a functional model in which all the relationships are correctly defined and can be used for simulations.

What we’re basically trying to build is a model to demonstrate how conflict in MOL can be resolved through reorganisation.This should help us in understanding the nature of reorganisation in detail. In order to do this, we try to build a model of 4 levels where each control system (x in the table) connects to all the systems available at the level above and below.

Level K-1 K K+1
N x x x
N-1 x x x
N-2 x x x
0 x x x

While we are doing this, we are trying to incorporate our understanding of gain and memory in the model as well. So far the input part feels easy and correct: we can use an adder function to transform the many input signals from lower levels into one perceptual signal. But the output part seems more complicated. How do you go from an error signal to reference signals for lower levels? What kind of function is that? Is that the same output quantity that is distributed over lower level control systems, or are those different signals, determined by the output function?

My question to you is:
Has anyone succeeded in building a multiple-level model, preferably in vensim or software that is easy to share? How did you operationalise output function, gain and memory?

I’m looking forward to hearing your thoughts,

Hi Eva, this was one attempt:

And this:

We didn’t use memory, and we computed a simple summation of weighted signals to produce the reference signal for a lower level. But presumably or should be a reference function?

Here is my paper (from 1990!!) describing a spreadsheet model of a three level hierarchy of control systems with the systems at each level controlling different types of perceptions (from lowest to highest: intensity, sensation, relationship). And here is a downloadable, recent re-implementation of that spreadsheet in Excel. Hope this helps.

Best, Rick

Nor did I incorporate memory into my hierarchical control models. I don’t think we need to incorporate memory into these models until we are modeling the control of variables that are defined over time or when we are modeling the behavior seen in memory experiments, such as free recall tasks.

The function that combines several outputs from higher levels systems into a single reference to a lower level system is simple summation. The only thing you have to be concerned with is the sign of each output that enters the sum. The signs of these outputs must preserve negative feedback in the higher level system that is sending the output of the lower level system.

For example, assuming that the error in the higher level system is computed as e = r - p then negative feedback is preserved when the sign of the contribution of the higher level system’s output to the lower level system’s reference is the same as the sign of the contribution of the lower level system’s perceptual signal to the higher level system’s perceptual function. Of course, if the error in the higher level system is computed as e = p-r, the signs of the contributions of these two variables (to the reference and perceptual function, respectively) must be opposite.

Since your model apparently works, you must be doing that correctly.

Best, Rick

Thanks Rick!

You’re welcome.

By the way, since you seem to be keeping up on things PCT, do you have any information pertinent to my second question, about the status of Power Law research relevant to PCT, in the Two New Questions from an Old PCTer thread?

Thanks Warren and Rick, we’ll dive into this!

I think the block diagrams in B:CP have engendered some confusion about memory and reference values. I haven’t yet seen a way clear of it. Here’s the current state of my attempt to sort it out. What do you think?

memory.pdf (617 KB)

I wasn’t confused about the diagrams you mention until you mentioned it;-) I do think there is a problem with them and I think it is related to the point you bring up in your PDF about there is a “many-to-one relation of signals at the input function” (I don’t think the one-to-many relation at the output function is a problem because, in the model, the same value of reference signal is going to the many lower level systems that contribute the many perceptual signals going into the input function of the same system).

I’m going to try to draw what I think is a more general diagram of the memory function. I’m busy all weekend but I’ll try to have something to show early next week.

Best, Rick

Hi. Did you want to discuss something?

On what basis can we assume that error in a complex perception is reduced by an identical change in the reference values for all the inputs to that perception? .

Along the way between error output and reference input the change in rate of firing for one lower-level perception is likely to differ from that for another. Consider the changes in inputs for rotating a configuration.

Bill addressed this (double entendre not intended) by putting the local rate of firing in the ‘memory’ box in the diagram. As I said to Ted Cloak in Colorado, that doesn’t work because a static value stored in memory cannot be varied according to error output from above. A ‘normal’ (accustomed, ordinary, nominal, …) rate of firing may be invoked for remembering and imagining, but control must be able to override a stored value. Error perhaps is added to or subtracted from the default reference value (and yes, there is a bidirectional issue here).

I don’t think that’s a problem. The Figure in B:CP that I thought had problems was Fig. 15.3. It took me a while to realize that, once again, Bill had it right. I was pretty much convinced by this CSGNet post.

The most important part of that post (for me) was the last line: “Model it, Rick (or Bruce A.) You’ll see.” So I have taken to modeling it using my three level spreadsheet hierarchy. I haven’t completed all the modeling yet – I’ll show the results when I’ve finished it – but the epiphany I had was that the system in Figure 15.3 represents just one of many such systems, each simultaneously sending their “TO” signals to a HIGHER ORDER system and receiving corresponding “FROM” signals from it. And, perhaps most importantly, when the PERCEPTUAL and/or MEMORY SWITCHES in these systems are “thrown” (as shown for just one system in Figure 5.13) they are thrown in all systems simultaneously! This means that, in “imagination mode”, the HIGHER ORDER system gets the same perceptual inputs from from memory as it would get if all systems were operating in “Control Mode”. I’ve implemented this imagination system architecture into the spreadsheet hierarchy model and it works like a charm.

I think the fact that the perceptual and memory switches are thrown simultaneously is hard to pick up from Figure 15.3. After I’ve completed the spreadsheet model I’ll see if I can come up with a diagram of how it works that makes things a bit clearer. But I think it’s important to remember what Bill said about this memory model in his CSGNet post: "In Chapter 15 of BCP, I was constructing an hypothesis, not saying how things really are" (emphasis mine).This applies to EVERY ASPECT of the PCT model.

Just because a model works doesn’t mean that the behavior modeled works that way. You’ve got to TEST the model to see if its behavior matches that of the living systems being modeled.

The hypothesis supports an explanation of remembering and imagining, but under this hypothesis it is not possible to desire something that has not previously been experienced.

There is a further test, how do neurons and neurochemicals do that, and indeed can they.

Good point. I think Bill was aware of this and commented a bit on it in the CSGNet post when he said “That postulate [that all behavior consists of reproducing past perceptions] is more general than it needs to be, and it’s not specific enough because it doesn’t take levels of perception into account.” I can’t think of a way to test this but my guess is that the hypothesis that it is not possible to control for something that has not previously been experienced may be true for higher level perceptions but not for lower level ones (including intrinsic controlled perceptions like glucose level).

I think this is more a constraint than a test. Since the functions described in the model must be carried out by neurophysiological systems – neural, muscular and glandular – it’s important that these functions be reasonably consistent with what we know about how these systems work. We don’t have to know exactly how the neurophysiological systems carry out these functions; we just have to know that they can carry them out. That’s is the reason for the existence of chapter 3, Premises, in B:CP. It shows how what we know of how the nervous system works can be the basis for understanding how control functions could be implemented in humans.

Limiting discussion just to model terms, ignoring neurology, the location of the comparator in the hierarchy is a form of memory, meaning its location relative to its lower inputs and outputs and relative to all the higher systems to which its CV branches. This location is the ‘address’ of the comparator. This structural memory (location within the structure of the control hierarchy) cannot be represented by a box in a diagram of the hierarchy placed between error output and reference input.

The reference signal, with a variable reference value, is shown coming out of ‘memory’. The value of the reference variable results from the values of higher-level error variables.

Those higher systems do not all simultaneously control the given perceptual input (=the perceptual signal controlled through the given comparator), nor do they all output the same error signal at the same time. These error signals are variable, and the reference value of the reference signal entering the comparator is a variable, not a static memory.

I don’t understand your point. Are there predictive consequences for the model of not seeing the location of the comparator as a form of memory? Can’t the location of any box that represents a function in a control system – input, output and comparator – be considered a form of memory? If so, so what? If not, so what?


True. If they did there would be conflict. However, several higher level systems, each controlling a different perceptual variable, can each be contributing to the references of the lower level perceptual variables of which the perceptions they are controlling are a function. This is kind of complicated but I think you can get some idea of how it works by playing around with my spreadsheet model of a control hierarchy. The write-up on it at that site as well as my old 1990 paper describing the original model might help as well. Also, you might enjoy this PowerPoint presentation. If nothing else you should enjoy the title. :wink:

Yes, all of this is part of the spreadsheet model. And it is taken into account by my new implementation of the model that now correctly includes the “imagination connection” described in Fig… 15.3 of B:CP.

The diagram with memory and imagination switches is the scope of discussion.

A first poiint is that it is misleading to represent the memory of a perception by a box intervening between plural error outputs and single reference input. The proper label for that box is reference input function or RIF.

Yes, that is a consequence of what I said: memory is located not at every function because (as I quote neuroscientists saying) memory is located at every synapse.

I think that plural reference inputs result so seldom in conflict because (disjunctive list)

  • At a given time all but one are controlling with very low gain.
  • They control at similar reference levels.
  • A range of values is adequate input for controlling the higher-level perception to which this CV contributes (a.k.a. ‘tolerance’).
  • … ?

Because the box (and its location at the transformation from error outputs to reference input) cannot be identified with ‘memory of this perception’, the diagram of switches has to be re-thought. But the functions of the switches don’t require switches.

Observation is control of the orientation of sensory organs toward an aspect of the environment. This control loop is independent of loops controlling perceptions of those aspects of the environment, though both can be so engaged simultaneously and often are, and ‘automatic’ mode is control while these organs of perceptual input are directed to other phenomena.

Other ways have been advanced for modeling the return of reference value to perception input. Given that internally-generated perceptual signal, memory is to imagination as observation is to control. When we imagine controlling something, we move our eyes, turn our heads as though listening, gesture with our hands, etc. even though the imagined phenomena are not located in spaces to which those organs of perceptual input and control output are oriented.

If you are referring for Fig. 15.3, I don’t see plural error inputs to the memory box. I see one signal coming in as an address signal and one coming out as a reference signal. Oh, and a perceptual signal is coming in for storage but that is not part of the control loop (per the dotted lines).

I think what would make the Figure more accurate would be to have several (N) outputs from the memory box, each becoming reference signals going to different lower level systems (including the one already shown). Then you would also have to show that the perceptual signal is only one of N perceptual inputs going to the higher level system’s perceptual function (not currently shown).

Each one of the N “plural” reference signals always go to a different one of N lower level systems, which are the ones sending copies of the N different perceptions they control back up to become components of the higher level perception controlled by the system that sent out the plural references. In other words, the higher level system functions are a single control system. So there is no question of conflict arising from plural references since they all work as a single output acting to control the perception controlled by the higher level system.

My hierarchical spreadsheet model with the imagination connection in place is now functioning just fine and I can use it to show you how a hierarchical control model that can go into imagination mode actually works.

That last sentence makes a great point. I believe I have seen research that shows that to be true; do you have a reference to it? I think it such a finding does require rethinking how the imagination connection works.

[Emphasis added.]

Here and throughout, you are assuming that each lower-level system receives reference input from only one higher-level system.

This is simply not the case. In my spreadsheet model, each lower level system gets references from 1 or more higher-level system. Indeed, each of the 6 level 1 systems in that model gets a reference signal that is the sum of a different combination of the outputs of all 6 level 2 systems. That’s because each of the level 2 systems controls a perception that is a different combination of perceptual inputs from the level 1 systems.

What would create a conflict in this hierarchy is if two or more higher-level (say, level 2) systems were controlling perceptions that were the same combination of lower-level (level 1) perceptual signals. Remember, conflict results when two control systems try to get the same perception into different reference states.