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4 Qualifying Exam/2 Writing/1. QE Goals and Outcomes.md
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@ -93,5 +93,6 @@ Perturbing a nominal plant to establish robustness is not a new technique. Robus
Experimentally verifying robustness for implementations of controllers requires elements to be extracted from the set. There are two main ways this has been done: structured and unstructured perturbations. Structured perturbations are created manually: an engineer attributes probability distributions to certain system parameters to include a margin of error. These distributions are sampled to create the perturbation. Unstructured perturbations are trickier to generate, because the perturbation form is not defined. It can be difficult to find perturbations that are 'random' while remaining within the allowable set.
This research will utilize a diffusion model to make generation of unstructured perturbations easier. The generative diffusion model is great at creating new samples with a controlled amount of distortion compared to training data. We will use this feature of the diffusion model to generate unstructured perturbations. The diffusion model consists of two processes: a forward process that degrades inputs with noise, and a reverse process that the learned model attempts to denoise the input. This reverse process will be trained using time and frequency response data of a variety of dynamic systems, so that noise removal creates samples that look like dynamic systems. Finally, we will control the amount of perturbation by controlling how much we destruct the input of a nominal plant with noise. By introducing less noise we create smaller perturbations, while to create large pertubations we do the opposite.
This research will utilize a diffusion model to make generation of unstructured perturbations easier. The generative diffusion model is great at creating new samples with a controlled amount of distortion compared to training data. We will use this feature of the diffusion model to generate unstructured perturbations. The diffusion model consists of two processes: a forward process that degrades inputs with noise, and a reverse process that the learned model attempts to denoise the input. This reverse process will be trained using time and frequency response data of a variety of dynamic systems, so that noise removal creates samples that look like dynamic systems. Finally, we will control the amount of perturbation by controlling how much we destruct the input of a nominal plant with noise. By introducing less noise we create smaller perturbations, while to create large perturbations we do the opposite.
Verifying implementations of controllers has been an onerous task. Perturbations take a significant effort to generate