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4. Qualifying Exam/2. Writing/QE Abstract.md
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@ -38,4 +38,6 @@ Real world control systems do not operate on nominal plants, but instead control
What we cannot do is easily validate our guarantees on a real controller. While we have been able to find the set of perturbed plants for decades, being able to create and test a controller with elements from that set is by no means trivial. 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. This is an expensive way to create perturbations. The other way is by using unstructured perturbations. For this method, some transfer function $\delta$ with a maximum gain is used to augment the nominal plant model. Creating $\delta$ however is an opaque challenge.
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.
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.**