[From Bill Powers (2007.11.08.0714 MST)]
I finally got my copy of "Control Theory: a guided tour" by J. R. Leigh (1992). I can't remember who recommended it -- was it Fred Nickols? I agree that it's very clearly written.
I'm writing because Chapter 12, State Estimation, discusses the Kalman Filter, and I want to know what Richard Kennaway (and anyone else) thinks of it. It reminds me a lot of the way we construct models and adjust them so their behavior fits that of a real person. This is apparently taken as the primary means of control. It works this way:
A control output u is sent into "the plant" (the real environment) and also into a model of the plant. The output of the real plant (or a vector of outputs) is compared with the output of of the model, and discrepancies are corrected by adjusting the parameters of the model. When the discrepancies have been minimized, the response of the model to the control output u is nearly the same as the observed respose of the real plant to the same output, so the output of the model can then be used as a pseudo-perception of the output of the plant. The output of the model is then compared with the desired state of the output of the plant (i.e., the reference signal that we use in PCT), and the error signal is u, the control output that enters the real plant as well as the model. Thinking of the model as a perceptual input function, then, we can see that the whole system works just like a PCT control system in the imagination mode. The main difference from real closed-loop control is that this system can't resist changes in the perception due to unmodelled variations in the environment, such as novel disturbances or changes in properties of the plant that are not monitored. The control system works in the imagination mode, taking the reference signal being sent to lower systems directly as one input, and producing an imagined output that is like the real plant's output. The actual output of the plant is monitored, but only for the purpose of adjusting the model -- not as a real-time feedback signal to the comparator.
The entire modeling step seems superfluous to me, since the result of the modeling, after all adjustments are complete, is a perceptual signal that is just like the perceptual signal obtained by observing the output of the plant. Why not just use the measured output of the plant, which is what we want to control, as the perceptual signal? The only advantage I can see of using the model is that if perception of the real plant's output is interrupted for a brief time, the model will keep running and providing an artificial feedback signal, so the control system can continue producing a reasonable control output for some short time. This was discussed some years ago in CSGnet exchanges with Oded Maler. To obtain this advantage, however, one must give up the ability to resist unpredictable disturbances in real time, and greatly reduce the bandwidth of control (because of the need for continuous correction of the model parameters and smoothing of random disturbances, which are ignored in the model).
It could be that this model-based control process might work satisfactorily for higher-level systems that are slow anyway, and that are somewhat protected against disturbances by the actions of lower-level systems. I would have to see some experimental evidence, however, before I would believe that any brain process works that way.
I'd like to say something about this in the new book, but am uncertain of my ground. Any help will be appreciated.
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