From 134bbd52ff0b36c43aba3de3e472f0b5df36fbfa Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Thu, 31 Oct 2024 11:27:23 -0400 Subject: [PATCH] vault backup: 2024-10-31 11:27:23 --- .../2 Writing/2. QE State of the Art.md | 21 ++++++++++++++++ .../2 Writing/3. QE Research Approach.md | 24 ++++++++++++++++++- 2 files changed, 44 insertions(+), 1 deletion(-) diff --git a/4 Qualifying Exam/2 Writing/2. QE State of the Art.md b/4 Qualifying Exam/2 Writing/2. QE State of the Art.md index 20ac27aa..12e758e2 100644 --- a/4 Qualifying Exam/2 Writing/2. QE State of the Art.md +++ b/4 Qualifying Exam/2 Writing/2. QE State of the Art.md @@ -45,3 +45,24 @@ This is useful for us. If we can find an uncertainty transfer function $W_2$ tha $\Delta$ is almost always considered a free variable transfer function. Since $||\Delta||_\infty < 1 \text{ } \forall \omega$, $\Delta$ will not decrease the minimum robustness margin. This is fine for developing a controller, but when it comes to actually verifying robustness of a controller implementation, $\Delta$ cannot be a variable. To create a plant to simulate a perturbed plant, $\Delta$ must have an expression. **Limitation**: *There is no current method for creating random examples of $\Delta$.* Because of this, it is not currently possible to test implementations of controllers against unstructured perturbations. + +# Take 2 +I got ChatGPT to help me with some stuff following the first version: Here was an idea of an outline to use: +## ChatGPT Analysis +### **Robust Control Theory and Perturbation Challenges** +**1.1 Robust Control Principles**: Briefly introduce robust control, emphasizing its focus on stability and performance despite uncertainties. Clarify that robust control aims to ensure reliability under a range of conditions. +**1.2 Types of Uncertainty in Control Systems**: Explain structured vs. unstructured uncertainties and why unstructured uncertainties, though useful for capturing unmodeled dynamics, are challenging to generate. +**1.3 Limitations of Current Perturbation Methods**: Discuss the current methods for structured perturbation generation and the lack of effective techniques for generating random, unstructured perturbations, especially for validating controller implementations. +### **Generative Models and Their Potential in Engineering** +**2.1 Evolution of Generative Modeling**: Provide a brief history of generative models, covering GANs, VAEs, and diffusion models, highlighting their application in creating realistic samples. +**2.2 Limitations of Existing Models for Control**: Explain why traditional generative models are impractical for control applications, especially where controllable, unstructured perturbations are required. +### **Diffusion Models: Mechanism and Promise** +**3.1 Overview of Diffusion Models**: Detail how diffusion models work, focusing on the forward process (adding noise) and reverse process (learning to remove noise), allowing for controlled perturbation creation. +**3.2 Suitability of Diffusion Models for Unstructured Perturbations**: Highlight that diffusion models’ ability to generate realistic outputs with tunable noise levels makes them ideal for generating unstructured perturbations. +**3.3 Positioning Diffusion Models for Robust Control Applications**: Summarize how this approach leverages diffusion models to meet a specific need in robust control: creating a set of realistic, unstructured perturbations for robust validation. +### Transition to Research Approach +End the **State of the Art** by introducing diffusion models as a potential solution to bridge the gap between theoretical robustness and practical implementation verification. Emphasize the research’s aim to develop and test this idea for generating unstructured perturbations, with promising applications in controller validation and system resilience. + +I'm going to write in LaTeX for this part from now on. Will put notes here. + + diff --git a/4 Qualifying Exam/2 Writing/3. QE Research Approach.md b/4 Qualifying Exam/2 Writing/3. QE Research Approach.md index 64728d00..5e254b0f 100644 --- a/4 Qualifying Exam/2 Writing/3. QE Research Approach.md +++ b/4 Qualifying Exam/2 Writing/3. QE Research Approach.md @@ -62,4 +62,26 @@ Something to justify, why diffusion model as opposed to other generative AI The purpose of this proposal is to suggest that using a generative network to create unstructured perturbations can be a viable way to advance the state of the art. But to do this, the current state of diffusion models and their place must be introduced. The generative diffusion model is a recent breakthrough in generative models [@sohl-dicksteinDeepUnsupervisedLearning2015]. Diffusion generative models are the state of the art for image and video generation, and have demonstrated promise for audio generation and noise removal [@kongDiffWaveVersatileDiffusion2020] [@SoraCreatingVideo]. A diffusion generative model, AlphaFold 3, won the Nobel Prize in Chemistry [@AlphaFold3Predicts2024] Diffusion models do this through a forward noise-inducing process, and a learned backwards noise-removing process. -The forward diffusion process works by introducing small amounts of noise into \ No newline at end of file +The forward diffusion process works by introducing small amounts of noise into + +## ChatGPT Analysis +Similar to the [[2. QE State of the Art]] I had some help creating an outline: +**Objective: Applying Diffusion Models for Unstructured Perturbations** + +### **3.1 Research Goals and Hypothesis** +Restate the main goal: to create a diffusion model that can generate unstructured perturbations, assisting in robustness verification. Clearly outline the hypothesis that diffusion models can reliably and efficiently generate realistic perturbations within the desired uncertainty bounds. + +### **Methodology** + +**4.1 Model Training with Structured Perturbations**: Explain the training process, using a structured set of perturbed plants. Detail how parameters for the uncertainty function W2W_2W2​ will be chosen based on robustness requirements, and why training on structured perturbations is effective. +**4.2 Diffusion Model Forward Process for Noise Introduction**: Describe the forward process, introducing Gaussian noise in small increments to structured perturbations. Discuss how the amount of noise relates to the uncertainty level. +**4.3 Diffusion Model Reverse Process for Perturbation Generation**: Explain the reverse process, where a neural network denoises the plant sample to produce novel, unstructured perturbations. + - **4.4 Experimental Design for Verifying Perturbation Validity**: Outline how you’ll validate that the generated plants belong to the allowable set, ensuring they meet robust stability/performance criteria by checking Nyquist stability. +### **Expected Outcomes and Verification of Results** + + **5.1 Outcome 1**: A set of valid unstructured perturbations that satisfy robustness requirements. + **5.2 Outcome 2**: Quantitative assessment of the model’s ability to approximate the uncertainty bounds in W2W_2W2​. + **5.3 Outcome 3**: Reduced effort in generating perturbations for robustness verification in controller implementation. +### **Implications and Potential Applications** + + - Discuss broader implications for robust control, such as reducing the cost and complexity of verification processes for infrastructure systems. Explain how success could advance diffusion models’ applications beyond robust control, perhaps influencing fields requiring resilient system validation. \ No newline at end of file