PCT and Optimal Control Theory (OCT)

Hello, all --

Here is the latest in the conversation with Stephen Scott. First, his permission to share, then my request for it, then the last post I sent him.


Hi Bill,

Sorry for the delay. Work gets a little busy some days.

I'm glad to hear my opinions were not seen as negative as I believe
there is more commonality than differences.

I'm happy to have you share my e-mails with your group. Admittedly, I
feel like I have a bit of a disadvantage as you have a few more years
experience particularly on your theories, but will do my best!


On 27-Oct-11, at 11:25 AM, Bill Powers wrote:

Hello, Stephen --

Believe it or not, your reply greatly encourages me. Before I make a
real reply, do I have your permission to let the others in my group
see our exchanges, including your first one? You have reciprocal
permission from me. I'll keep it private if you prefer.

Best regards,

... And here's what I sent yesterday. Quotes from Stephen's post are indented.

Hello Stephen and cohort:

SS: Well, some feedback from papers are positive and some are negative. Yours appears to be in the latter camp and that certainly never makes me feel good.

Don't worry, my objective is not to make you feel bad but to look for common ground. I'm sure we are looking at the same territory, but are just using different maps. And perhaps different assumptions about causation in behavior.

One could find inspiration for these experiments from many sources including yours, Bernstein, Kelso and any others that work from a dynamical systems approach. As the experiments were predominantly inspired by the ideas of optimal feedback control, our limited citation for theory was to the work of Todorov as many other studies had to be cited. You can certainly bring up this problem with Nature if you wish but they are very sticky on the 30 citations.

No need to bother Nature since we're now talking.

I'm aware of Bernstein; he was writing excellent stuff at the same time I was developing PCT in the 1950s, but unfortunately in Russian so I never saw his work until quite recently. He (like von Holst) almost got the message about control theory, but too late in his life to do anything with it. Kelso deals mainly in metaphors and begs too many questions (how does a coordinative structure coordinate anything?) and his models are not to be taken seriously.

In my opinion as an experimentalist, theory is only useful for an experimentalist if it helps to design an experiment. You may have profound problems with the ideas of optimal feedback control, but it has been very influential for me (broadly described in Scott, Nature Reviews Neuroscience, 2004) and I have generated a large number of studies using this framework. Many other labs are starting to follow suit. You may not like the concept, but the explicit nature of the theory makes it great for testing hypotheses.

It's the multiplicity of labs adopting optimal control theory that has cowed me -- I can argue with one or two people, but crowds of people on bandwagons just don't or can't listen. I can't yell loud enough.

I concur fully with your idea that theory and experiment have to go together.

I cannot say why some theoretical ideas have greater impact than others. It may be timing, with some ideas immediately filling a void in a field of study. It is an interesting question.

In my case, it's a reversal of causation that causes the problem, and it's an enormous problem. It undermines most of what has been accepted in the more scientific branches of behavioral science. When control theory was first worked out in the 1930s, even before Weiner came on the scene led by Rosenblatt [Rosenbleuth: WTP] , people thought they saw parallels with human behavior (and Cannon's work on homeostasis) and started resisting the idea. I didn't start that fight, or even know about it until the 1950s. You can't understand real control systems if you think inputs to organisms cause their outputs, and many people immediately started looking for ways to understand control behavior that didn't require giving up the idea that environments (including experimenters like Skinner) control organisms. The Kalman filter came along in 1960, the same year I published, with Clark and MacFarland, the first paper on what became PCT. That opened the way to "modern control theory" and "optimal control theory" and "robust control," all of which tried to explain control behavior without taking control away from the environment and the experimenter.

Admittedly, the brain doesn't work like an optimal feedback controller, but that's fine with me. All theories are wrong at some level. As an experimentalist, I believe one should date theories, have some fun, but never marry them. Like some marriages it can get dull and boring (just don't tell my wife!!).

I promise. But what if a theory is fundamentally wrong, at the level of its premises? Doesn't that make every conclusion drawn from it, every interpretation guided by it, suspect? Sometimes that idea makes me shudder when I realize how vulnerable PCT is to disconfirmation.

If you don't like the ideas of optimal feedback control for biological control, you might want to pick up the conversation with Emo Todorov who has been influential for spreading these ideas to the field of biological motor control. From your comments below, I think you may have missed some of the key ideas of optimal feedback control as formulated by Todorov. It is certainly not open-loop control as feedback is front and centre. The framework does predict a substantial amount of knowledge about the limb and environment and in fact several studies have demonstrated this point over the years. I can point to these studies if you like. Again, I would discuss your concerns with Emo Todorov.

I'm afraid of anyone who is good at complex mathematics, which I am not. But I'll try to look. Fortunately, in the CSG (control systems group) there are some real mathematicians who can come to my rescue and have done so in the past, so maybe I can hold my own with a bit of help. Actually, if I could subvert you, you might be quite helpful.

Your anger over our Nature article has certainly made me look a bit at your work and perhaps I will take some time to read further. At a first glance, I think it would seem strange to think about controlling sensory signals for an EMG response that occurs in 60 ms generated from an external perturbation. It just seems easier to think about it from a control standpoint. This is only from my perspective but am happy for you to elaborate.

No problem, that's what would be expected from a hierarchical arrangement with the first few levels being the spinal control systems (formerly called reflexes). A mechanical disturbance alters muscle length signals (from spindles) as well as disturbing Golgi force-sensors in the tendons, and those signals only have to go to the spinal cord and back to result in opposing changes in muscle contraction. More precise control comes later from higher systems which work by varying the reference signals for the spinal systems (a snippet from the PCT Order of Service).

Your analogies of cruise control provide an interesting point that control is only as good as the sensory feedback and is effectively dictated by this sensory input. How one thinks about sensory and motor/perception and action is a philosophical argument. Generally, it seems like just inverting the equations to re-organize what is dependent versus not dependent.

Precisely. That is the barrier I have been bumping against for 60 years, now. It's not just that the quality of control depends on feedback -- the very concept of control, when you look carefully enough, leads to the conclusion that what organisms control is ONLY what they sense. The feedback signals are the sensory signals and they are all that the brain (or biochemistry) can actually control -- maintain constant or vary systematically despite disturbances. Organisms vary their outputs as required to bring sensory signals into a match with reference signals from higher systems. As long as their outputs can directly affect the variables being sensed and controlled, the system doesn't have to predict disturbances or even know what caused them, or have any idea why sending certain signals outward affects the world of perception. You may recognize that those capabilities are thought to be essential by those who have the Kalman filter and model-based control in their backgrounds.

In any control system of the PCT kind, there are two independent variables: a disturbance that affects the input independently of the system's own output effects at the same place, and a reference signal originating from other systems of higher order (or perhaps built in). All the signals in the closed negative feedback loop are dependent variables: the perceptual signal, the error signal, and the output, as well as variables in the part of the environment that externally close the loop.

Changing the reference signal forces the input variable to change correspondingly. Changing the disturbing variable(s) results in an output change that feeds back to oppose the effect of the disturbing variable on the controlled input. That last effect explains how scientists were fooled into mistaking control systems for stimulus-response systems.

Certainly interesting. The merits of one over the other may differ with one view better for certain types of problems (social interactions looks like a good example for perceptual based ideas), but may not be that important for the relatively low level motor issues I tend to keep myself entertained with. Admittedly, I will likely start to head to more complex issues in voluntary behaviours so another perspective may be fruitful.

In PCT, it's control systems all the way down. The lowest neuromotor control system is the tendon reflex, which causes a signal representing muscle tension to match a reference signal entering the spinal motor neuron; the inhibition from the sensory signal nearly matches the excitatory reference signal (on the agonist side), with the difference, the error signal, being amplified by the muscle and converted to an output force. See T. A. McMahon, "Muscles, Reflexes, and Locomotion" (Princeton Univ. Press 1984) for lots of good detail, or Powers (1973) for a control-system interpretation.

With regards to the field of voluntary motor control, it seems that the importance of feedback died in the 1980s due to the problem of delayed feedback and limb mechanics.

Yes, I noticed. Damn Lashley and his stupid hatchet job. He didn't know that real control systems have a frequency-response curve that makes the quality of control fall off as disturbances and changes in reference signals become more rapid, ultimately falling to the level of an open-loop system. So what if a pianist can emit 10 notes per second? How good is the control at that speed? Answer, from a friend who teaches piano to concert professionals, "lousy." A disturbance that comes and goes in 1/10 of a second simply alters the perceived arpeggio with no chance of preventing the mistake. However, if there are no disturbances, the envelope of the arpeggio or glissando or run can be nicely controlled (listen to Dinu Lipatti), rising and falling in speed and loudness as the run reaches its hair-raising climax. The mistakes that occur in a tenth of a second are not corrected, but they aren't perceived by either the audience or the performer (though the performer is usually more aware of them than the audience: Lipatti, after completing a beautiful fast passage as I would hear it, has been heard to mutter "Droit de macaron", macaroni fingers).

A key idea in optimal feedback control is the use of optimal state estimation. This latter component is influential because it resolves the problem of delayed feedback. Can you explain how your theories can handle delayed feedback?

Easily. See www.billPCT.org and download the demonstration programs (free). You'll have to find a library with the book that goes with them, but I trust you can manage that, or even spring for the book from Amazon (see link at bottom). Actually you can probably figure out most of the demos from the brief instructions included. See particularly Demo 3-1, LiveBlock, which is a running model of a canonical PCT control system that you can play with by adjusting parameters. It includes a perceptual transport lag with a default value of 133 milliseconds, the modal value obtained in Demo 4-1 which is a tracking experiment that provides data for a model to fit. You can see how increasing the lag reduces stability, and how increasing the time constant of the output restores it. If you have a MAC, the programs run fine under a Windows emulator.

I don't see these ideas presented at meetings such as Society for Neuroscience, or the Neural Control of Movement. The former meeting is certainly the main venue for studying biological motor control. Maybe its time to bring people with different ideas together.

You don't see them in mainstream journals much, either. They tend to be rejected by people who consider control theory something like alchemy, or else assume that everything worth saying about them has been said. Locke, the personality theorist involved in goal-directed behavior, said he didn't need to read my 1973 book because the title was clearly incorrect.

I'm only beginning to make some inroads into neuroscience, with very strong support from a neuroscientist at Duke University, and a few others in the department of neuroscience and psychology at the University of Colorado, near Lafayette where I live. In England, the University of Manchester is a hotbed of PCTers, and there are outposts in Australia, Europe, and the People's Republic of China (where they published a Mandarin version of my 1973 Behavior: The control of perception).

OK, I'll sit on this until I hear from you and if you give the OK I'll distribute it to my list.