vault backup: 2024-08-29 17:10:15

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4. Qualifying Exam/2. Writing/QE Abstract.md

@@ -32,4 +32,14 @@ This method of perturbation generation can be very powerful for robust controlle
 ## First thoughts
 1. Introduce what a perturbation set is
 2. Generating unstructured perturbations is hard, but maybe we can use diffusion to do it
-3. 
+3. Who gives a fuck about validation and verification. Why do we need to do actual samples?
+## Attempt
+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 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 uncertainty.