vault backup: 2024-09-10 12:18:25

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4. Qualifying Exam/2. Writing/0. QE Abstract.md

@@ -84,13 +84,35 @@ We suggest using a recent technology to more efficiently generate perturbed plan
 [[QE Abstract For Dan]]
 
 # Take 5
+## Attempt
 The goal of this research is to use a generative diffusion model to create unstructured perturbations of a nominal plant. If this research is successful, this diffusion model will accomplish three main tasks:
+1. Generate Bode plots based on training data of example dynamic systems
+2. Perturb a nominal plant in an unstructured manner with a controllable amount of uncertainty
+3. Approximate a set of controllable plants by generating a large number of perturbed examples
+
+The diffusion generative model has shown great promise in creating novel and realistic samples from training data. This research will train a generative model to create Bode plots of transfer functions. This model will be given a nominal plant as an input and then generate a perturbed plant. Once created, this perturbed plant can be evaluated if it belongs to the set of controllable plants for a desired controller. This process will be repeated several times to generate enough plants to approximate the set of controllable plants.
+
+These generated plants can be used to verify robustness of controller implementations. A model of a controller can use robust control theory to establish the set of controllable plants, but an actual implementation of a controller can not be verified as robust in the same way. Instead, it must be verified experimentally using elements of the set. Extracting elements of the set is not a trivial task, but if this research is successful, a generative model can reduce the effort required to create perturbed plants.
+
+**STATS: 247 / 250 words**
+
+## Edits
+Dan's biggest comments were that it needed to be:
+1. <mark style="background: #FF5582A6;">Goal of the research ...</mark>
+2. <mark style="background: #FFF3A3A6;">outcomes</mark>
+3. <mark style="background: #ABF7F7A6;">approach</mark>
+4. <mark style="background: #FFB8EBA6;">impact</mark>
+
+<mark style="background: #FF5582A6;">The goal of this research is to use a generative diffusion model to create unstructured perturbations of a nominal plant.</mark> If this research is successful, this diffusion model will accomplish three main tasks:
+
+<mark style="background: #FFF3A3A6;">
+
 1. Generate Bode plots based on training data of example dynamic systems
 2. Perturb a nominal plant in an unstructured manner with a controllable difference between perturbed and nominal plants
 3. Approximate a set of controllable plants by generating a large number of perturbed examples
+</mark>
 
-The diffusion generative model has shown great promise in creating novel and realistic samples from training data. This research will train a generative model to create Bode plots of transfer functions. This trained model will then be given a warm start of nominal plant as an input, and then generate a limitless number of unique perturbed plants for controller validation. Once created, these perturbed plants can be evaluated if the belong in the set of controllable plants. We create several perturbed plants
+<mark style="background: #ABF7F7A6;">The diffusion generative model has shown great promise in creating novel and realistic samples from training data. This research will train a generative model to create Bode plots of transfer functions. This model will be given a nominal plant as an input and then generate a perturbed plant. Once created, this perturbed plant can be evaluated if it belongs to the set of controllable plants for a given controller. This process will be repeated several times to generate enough plants to approximate the set of controllable plants.[^10]</mark>
 
-For a given controller, an engineer can use robust control theory to find the set of allowable perturbations. This theory gives confidence that a model of a controller is robust, but verifying robustness on an implementation of a controller requires perturbed plants to be extracted from the set. 
+<mark style="background: #FFB8EBA6;">These extracted elements can be used to verify robustness of controller implementations.</mark> A model of a controller can use robust control theory to establish the set of controllable plants, but an actual implementation of a controller can not be verified as robust in the same way. Instead, it must be verified experimentally using elements of the set. <mark style="background: #FFB8EBA6;">Extracting elements of the set is not a trivial task, but if this research is successful, a generative model can reduce the effort required to create perturbed plants.</mark>
-
+[^10]: How?
-This model can reduce the effort required of creating perturbed plants.

4. Qualifying Exam/2. Writing/1. QE Goals and Outcomes.md

@@ -7,4 +7,10 @@
 2. What are the outcomes?
 	1. Train a diffusion generative model to generate Bode plots of dynamic systems.
 	2. Use that generative model to generate perturbations of a given input plant
-	3. Modulate the amount of perturbation by modulating the amount of noise used in the diffusion model	
+	3. Modulate the amount of perturbation by modulating the amount of noise used in the diffusion model	
+
+The goal of this research is to use a generative diffusion model to create unstructured perturbations of a nominal plant. If this research is successful, this diffusion model will accomplish three main tasks:
+1. Generate Bode plots based on training data of example dynamic systems
+2. Perturb a nominal plant in an unstructured manner with a controllable difference between perturbed and nominal plants
+3. Approximate a set of controllable plants by generating a large number of perturbed examples
+	1. (USE LOCATIONS OF POLES AND ZEROS TO MEASURE DISTANCE)

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

@@ -1,9 +1,12 @@
 **Diffusion Generative Models For Unstructured Uncertainty Perturbations**
 
-Real world control systems operate on physical plants that can have different dynamics than a nominal model. This discrepancy is called a perturbation, and can affect controller performance. The field of robust control creates a way to establish a set of allowable perturbations for a given plant, controller, and design requirements. We can make guarantees that a controller meets performance or safety criterion when the real plant does not perfectly match the nominal model.
+The goal of this research is to use a generative diffusion model to create unstructured perturbations of a nominal plant. If this research is successful, this diffusion model will accomplish three main tasks:
+1. Generate Bode plots based on training data of example dynamic systems
+2. Perturb a nominal plant in an unstructured manner with a controllable amount of uncertainty
+3. Approximate a set of controllable plants by generating a large number of perturbed examples
 
-A model controller can be proven to control a set of plants, but a real controller can only control one plant at a time. Validating robustness for a real controller requires extracted elements of the perturbed set, which can be deceptively difficult to create. Perturbed plants are commonly generated by using a structured uncertainty, where an engineer creates distributed ranges for system parameters. These distributions are then sampled and used to create a perturbed plant. This is an knowledge intensive and time consuming process.
+The diffusion generative model has shown great promise in creating novel and realistic samples from training data. This research will train a generative model to create Bode plots of transfer functions. This model will be given a nominal plant as an input and then generate a perturbed plant. Once created, this perturbed plant can be evaluated if it belongs to the set of controllable plants for a desired controller. This process will be repeated several times to generate enough plants to approximate the set of controllable plants.
 
-We suggest using generative artificial intelligence to efficiently create perturbed plants. The diffusion generative model has shown great promise in creating novel and realistic samples from training data. This model can be used to remove the laborious effort of creating perturbed plants. 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 unique perturbed plants for controller validation. 
+These generated plants can be used to verify robustness of controller implementations. A model of a controller can use robust control theory to establish the set of controllable plants, but an actual implementation of a controller can not be verified as robust in the same way. Instead, it must be verified experimentally using elements of the set. Extracting elements of the set is not a trivial task, but if this research is successful, a generative model can reduce the effort required to create perturbed plants.
 
-**STATS: 249 / 250 words**
+**STATS: 247 / 250 words**