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4 Qualifying Exam/4 Presentation/Outline.md

@@ -14,7 +14,81 @@ Ideas taken from https://services.anu.edu.au/files/development_opportunity/Resea
 - As a result, we need to reverify robustness on built controllers
 	- This exists for structured perturbations. We 
 # Gap In The Literature
+### **Slide 1: Robust Control Foundations**
+
+**Assertion:** Robust control ensures stability despite system discrepancies.  
+**Evidence:**
+
+- Controllers are based on physical models that differ from real systems.
+- Robust control analyzes resilience to system perturbations.
+- Evolved from single-input single-output to multi-input multi-output systems.  
+    _(Cite Doyle, Green, Brunton)_
+
+---
+
+### **Slide 2: Structured vs. Unstructured Perturbations**
+
+**Assertion:** Robust control addresses structured and unstructured perturbations differently.  
+**Evidence:**
+
+- **Structured:** Based on physical tolerances (e.g., spring rates).
+- **Unstructured:** Accounts for unmodeled dynamics and broader uncertainties.  
+    _(Diagram comparing structured and unstructured perturbations)_  
+    _(Cite Doyle, Green)_
+
+---
+
+### **Slide 3: Disk-Based Unstructured Uncertainty**
+
+**Assertion:** Disk-based perturbation quantifies unstructured uncertainties.  
+**Evidence:**
+
+- Key equation: $\tilde{P} = (1 + \Delta W_2) P$
+    - $P$: Nominal plant.
+    - $\Delta$: Perturbation transfer function.
+    - $W_2$: Uncertainty envelope.
+- Conditions for $W_2$ and $\Delta$:
+    - $\left| \frac{\tilde{P}(j\omega)}{P(j\omega)} - 1 \right| \leq \beta |W_2(j\omega)|$
+    - $||\Delta||_\infty \leq \beta$.
+
+_(Include a visual of how $\Delta$ affects $P$)_
+
+---
+
+### **Slide 4: Current Limitations in Robust Control**
+
+**Assertion:** Current methods lack discrete examples of unstructured perturbations.  
+**Evidence:**
+
+- $\Delta$ is undefined for experimental robustness verification.
+- Structured uncertainties are used experimentally but neglect unmodeled dynamics.  
+    _(Cite Farzan, Hamilton)_
+
+---
+
+### **Slide 5: Diffusion Models as a Solution**
+
+**Assertion:** Diffusion models can generate unstructured perturbations.  
+**Evidence:**
+
+- Forward process transforms data to Gaussian distribution.
+- Reverse process generates approximations of target data.
+- Applications in protein folding, training data generation.  
+    _(Diagram of forward/reverse processes in diffusion models)_  
+    _(Cite Sohl-Dickstein, Abramson)_
+
+---
+
+### **Slide 6: Parallels Between Diffusion Models and This Project**
+
+**Assertion:** Diffusion models address sparse perturbation generation in engineering.  
+**Evidence:**
+
+- Diffusion models create diverse training data from sparse sets.
+- Proposed approach: Generate unstructured perturbations from structured sets.  
+    _(Illustration of sparse-to-diverse transformation concept)_
 # Goals and Outcomes
+
 # Research Methodology
 # Metrics of Success
 # Risks and Contingencies