Danes-Vault/4 Qualifying Exam/4 Presentation/Outline.md

Ideas taken from https://services.anu.edu.au/files/development_opportunity/ResearchProposalTips_0.pdf

Title / Topic

Research Problem (Justification)

• Why does robust control exist
  • air conditioning example - but what if the plant is different? What is buddy leaves a window open
  • We can examine whether or not our controller (the ac unit) can handle the perturbed plant
  • We can know how open the window is before we have problems
  • We can guarantee this for this controller design and designed laws
• So if we do this can be sure when we build the unit that this is how it will perform?
  • Well if it's controlled with a microcontroller or other code based solution, no.
  • The abstraction between the design and the finished controller destroys the guarantee
  • Things can happen in implementation that make the controller built not true to design
• 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)

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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)

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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)

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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)

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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)

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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