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Dane Sabo 2024-08-30 16:21:59 -04:00
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.obsidian/workspace.json vendored
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3-99 Research/6. Researching Techniques/Highlighting Colors and What they Mean.md
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F9: Remove Highligh
## For reading papers:
<mark style="background: #BBFABBA6;">Green</mark>: This is a quotable item
<mark style="background: #FFB8EBA6;">Purple</mark>: Secondary source of something that's interesting
<mark style="background: #D2B3FFA6;">Purple</mark>: Secondary source of something that's interesting
<mark style="background: #FFB86CA6;">Orange</mark>: I don't know what this means
<mark style="background: #FF5582A6;">Red</mark>: I think this is wrong
@ -10,4 +11,6 @@
<mark style="background: #FFB86CA6;">Orange</mark>: I think this is weak.
<mark style="background: #FF5582A6;">Red</mark>: This shouldn't even be here
<mark style="background: #FFF3A3A6;">Yellow</mark>: Important words, don't overuse
<mark style="background: #ADCCFFA6;">Blue</mark>: This needs a citation.
<mark style="background: #ADCCFFA6;">Blue</mark>: This needs a citation.
<mark style="background: #CACFD9A6;">Gray</mark>: This needs more explanation
<mark style="background: #D2B3FFA6;">Purple</mark>:

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4. Qualifying Exam/2. Writing/QE Abstract.md
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@ -40,4 +40,25 @@ What we cannot do is easily validate our guarantees on a real controller. While
We suggest using new technologies to create unstructured perturbations. The diffusion generative model has shown great promise in creating novel and realistic samples from training data, and there is potential to apply this technology to robust control. A diffusion generative model we be trained as a lossy denoiser on Bode plots of various training plants. Then, the model can be used in concert with a noise-induced plant Bode plot to generate new plants with slightly different Bode plots. The key here is the loss of the original plant in the denoising: this creates the unstructured perturbation. From here, we can numerically create transfer functions of the generated plant to determine if it is an element of the allowable set.
**STATS: 367 words, 117 too many.**
**STATS: 367 words, 117 too many.**
## Edits
Real world control systems do not operate on nominal plants, but instead control a physical plant that has similar but slightly different dynamics. This discrepancy of dynamics is called a perturbation, and can affect controller performance. The amount of perturbation that a control system can tolerate without violating performance or safety requirements is a crucial property to understand for high assurance systems. The field of robust control and robustness analysis establishes bounds for the allowable amount of perturbation for a given controller and set of requirements. We can know the set of allowable plants that our controller can command, and we can make guarantees about plants within those sets using robust control.
What we cannot do is <mark style="background: #FFB86CA6;">easily</mark> validate our guarantees on a real controller. [^3]<mark style="background: #FF5582A6;">While we have been able to find the set of perturbed plants for decades,</mark> <mark style="background: #FFB86CA6;">being able to create and test a controller with elements from that set is by no means trivial.</mark> The most common way of accomplishing this task today is by using structured perturbations, where an engineer traces throughout the system where uncertainty comes from and then establishes probability density functions for each uncertainty, culminating in a probabilistic model that can be sampled to create elements of the set[^4]. <mark style="background: #CACFD9A6;">This is an expensive way to create perturbations.[^5] The other way is by using unstructured perturbations.</mark> For this method, some transfer function $\delta$ <mark style="background: #FF5582A6;">with a maximum gain</mark> <mark style="background: #FFB86CA6;">is used to augment the nominal plant model</mark[^6]>. <mark style="background: #CACFD9A6;">Creating $\delta$ however is an opaque challenge.</mark>
We suggest using new technologies to create unstructured perturbations. The diffusion generative model has shown great promise in creating novel and realistic samples from training data, <mark style="background: #FFB86CA6;">and there is potential to apply this technology to robust control.</mark> <mark style="background: #FFB86CA6;">A diffusion generative model we be trained as a lossy denoiser on Bode plots of various training plants. Then, the model can be used in concert with a noise-induced plant Bode plot to generate new plants with slightly different Bode plots. The key here is the loss of the original plant in the denoising: this creates the unstructured perturbation. From here, we can numerically create transfer functions of the generated plant to determine if it is an element of the allowable set.</mark>
[^3]: This is confusing. I bring up a 'real controller' but it doesn't really make sense what that is? Maybe talk specifically about how the set of controllable plants is fine for an abstract controller, but when one is actually built, you can't test that real controller with a set. It needs experiments with actual plants.
[^4]: This sentence MUST be written shorter. It does the job of being long and yes that's good symbolism, but it's too much. It loses the reader so they never get the point in the first place.
[^5]:Why?
[^6]: Passive voice
# Take 3
## Attempt
Real world control systems do not operate on nominal plants, but instead control a physical plant that has slightly different dynamics. This discrepancy is called a perturbation, and can affect controller performance. The field of robust control creates a way to establish set of allowable perturbations for a given plant, controller, and design requirements. As a result, we can make guarantees about the ability of a controller to meet performance or safety criterion when our model of the plant is not correct.
While a model of a controller can be proven to control a set of plants, a real controller can only be tested controlling one plant at a time. Validating this real controller requires extracted elements of the perturbed set, which can be deceptively difficult to create. Perturbed plants commonly are generated by using structured uncertainty, where an engineer attributes probability distributions to system parameters. These distributions are sampled, and then are used to create a perturbed plant. This is an expertise intense process.
We suggest using a new technology to more efficiently generate perturbed plants. The diffusion generative model has shown great promise in creating novel and realistic samples from training data. We suggest training a generative model to create Bode plots of transfer functions. This trained model will then be given a warm start with the nominal plant as an input, with which it will then be able to generate a limitless number of perturbed plants. This model can remove the laborious effort of creating perturbed plants.
**STATS: 250 words!**