No, you just asserted that people were using “model” in your sense in some posts you cited; there was nothing clear in any of the examples that implied they meant it in your sense rather than mine. And you didn’t quote from any book on model based control, and even if you did, you would still need to show how it’s not equivalent to merely having mutual information.
With respect to the links I provided to earlier postings on OB/LW I shall only say that I have reviewed them and stand by the characterisation I made of them at the time (which went beyond mere assertion that they agree with me). To amplify my claim regarding books on model-based control theory, the following notes are drawn from the books I have to hand which include an easily identified statement of what the authors mean by a model. All of them are talking about a system that is specifically similar in structure to and not merely entangled with the thing modelled. At this point I think it is up to you to show that these things are equivalent. As I said at the end of my last comment, this would be a highly non-trivial task, a complete reconstruction of the content of books such as these. (It is too large to do in the columns of Less Wrong, but I look forward to reading it, whoever writes it.)
1. Brosilow & Joseph “Techniques of Model-Based Control”
Page 10, Figure 1.6, “Generic form of the model-based control strategy.” This is a block diagram in which one block is labelled “Process”, and another “Model”; the Model is a subsystem of the control system, designed to have the same input-output behaviour as the Process which the control system is to control. Ding!
2. Marlin, “Process Control”. Page 584, section 19.2, “The Model Predictive Control Structure”.
Here the author introduces the eponymous control method, in which a model of the process to be controlled is constructed and used to predict its future behaviour, in order to overcome the problem that (in the motivating example) the process contains substantial transport lags (a common situation in process control). The model is, as in the previous reference, a mathematical scheme designed to have the same input-output-relation as the real process, and is used by the controller to predict the future values of some of the variables. Ding!
3. Goodwin, Graebe, and Salgado, “Control System Design”.
Pages 29-30, section 2.5: (paraphrased slightly) “Let us also assume that the output is related to the input by a known functional relationship of the form y = f(u)+d, where f is a transformation that describes the input-output relations in the plant. We call a relationship of this type a model.” Ding!
Another block diagram as in Brosilow & Joseph. Ding!
5. Leigh, “Control Theory” (2nd. ed.)
Chapter 6, “Mathematical modelling”.
Sorry, no nuggets to quote, you’ll have to read it yourself. But it’s a whole chapter about models in the above sense. This, in fact, is a book I’d recommend as an introduction to control theory in general, which is why I mention it, despite it not lending itself to concise quotation. Ding!
With respect to the links I provided to earlier postings on OB/LW I shall only say that I have reviewed them and stand by the characterisation I made of them at the time (which went beyond mere assertion that they agree with me). To amplify my claim regarding books on model-based control theory, the following notes are drawn from the books I have to hand which include an easily identified statement of what the authors mean by a model. All of them are talking about a system that is specifically similar in structure to and not merely entangled with the thing modelled. At this point I think it is up to you to show that these things are equivalent. As I said at the end of my last comment, this would be a highly non-trivial task, a complete reconstruction of the content of books such as these. (It is too large to do in the columns of Less Wrong, but I look forward to reading it, whoever writes it.)
1. Brosilow & Joseph “Techniques of Model-Based Control”
Page 10, Figure 1.6, “Generic form of the model-based control strategy.” This is a block diagram in which one block is labelled “Process”, and another “Model”; the Model is a subsystem of the control system, designed to have the same input-output behaviour as the Process which the control system is to control. Ding!
2. Marlin, “Process Control”. Page 584, section 19.2, “The Model Predictive Control Structure”.
Here the author introduces the eponymous control method, in which a model of the process to be controlled is constructed and used to predict its future behaviour, in order to overcome the problem that (in the motivating example) the process contains substantial transport lags (a common situation in process control). The model is, as in the previous reference, a mathematical scheme designed to have the same input-output-relation as the real process, and is used by the controller to predict the future values of some of the variables. Ding!
3. Goodwin, Graebe, and Salgado, “Control System Design”.
Pages 29-30, section 2.5: (paraphrased slightly) “Let us also assume that the output is related to the input by a known functional relationship of the form y = f(u)+d, where f is a transformation that describes the input-output relations in the plant. We call a relationship of this type a model.” Ding!
4. Astrom and Wittenmark, “Adaptive Control”
Page 20, Chapter 1, “Model-Reference Adaptive Systems”
Another block diagram as in Brosilow & Joseph. Ding!
5. Leigh, “Control Theory” (2nd. ed.)
Chapter 6, “Mathematical modelling”.
Sorry, no nuggets to quote, you’ll have to read it yourself. But it’s a whole chapter about models in the above sense. This, in fact, is a book I’d recommend as an introduction to control theory in general, which is why I mention it, despite it not lending itself to concise quotation. Ding!
Ding! Ding! Ding! Ding! Ding!