Thesis/CLAUDE.md

CLAUDE.md

This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.

Project Overview

This is a PhD thesis proposal for developing a methodology to build High-Assurance Hybrid Autonomous Control Systems (HAHACS) for critical infrastructure. The proposal is titled "From Cold Start to Critical: Formal Synthesis of Autonomous Hybrid Controllers."

Intellectual Merit: The contribution is architectural unification rather than algorithmic novelty. The methodology provides a systematic decomposition mapping verification techniques to control mode types, composing existing formal methods into a complete framework where none existed.

Key Insight: The methodology formalizes EXISTING discrete abstractions from operating procedures (especially nuclear) rather than imposing arbitrary ones. Operating procedures already define go/no-go conditions as discrete predicates - this work provides the formalization and verification framework.

Document Structure

The proposal uses a modular LaTeX structure with numbered section directories:

• main.tex - Root document that inputs all sections
• 1-goals-and-outcomes/ - Research statement and goals
• 2-state-of-the-art/ - Literature review
• 3-research-approach/ - Core methodology (CURRENTLY ACTIVE WORK)
• 4-metrics-of-success/ - Success criteria
• 5-risks-and-contingencies/ - Risk analysis
• 6-broader-impacts/ - Broader impacts
• 8-schedule/ - Timeline

Each section directory contains:

• v1.tex (or v2.tex for actively revised sections) - Main content
• outline.md (optional) - Planning notes and structure

IMPORTANT: Section 3 (research-approach) is currently being revised. main.tex inputs v2.tex for this section, which contains extensive inline comments and questions prefixed with % and % Q:.

Building the Document

# Full build with bibliography
pdflatex main.tex
bibtex main
pdflatex main.tex
pdflatex main.tex

# Quick build (no bibliography updates)
pdflatex main.tex

# Use latexmk for automated builds
latexmk -pdf main.tex

# Clean auxiliary files
latexmk -c

The output is main.pdf.

Key Technical Concepts

Mathematical Notation

• Continuous state space: X ⊆ ℝⁿ
• Discrete modes: Q = {q₁, q₂, ...}
• Per-mode continuous regions: X_entry,i, X_exit,i, X_safe,i
• Discrete predicates: pᵢ: X → {true, false} (Boolean functions over continuous state)

Three Control Mode Types

Each mode type has distinct control objectives and verification methods:

1. Transitory modes: Transition between discrete states

   • Objective: reach(X_entry) → reach(X_exit) while maintaining x(t) ∈ X_safe
   • Verification: Reachability analysis
   • Formal: Reach(X_entry, f(x,u), T) ⊆ X_exit ∪ X_safe

2. Stabilizing modes: Maintain steady state

   • Objective: remain(X_target) where X_target ⊂ X_safe
   • Verification: Barrier certificates
   • Formal: ∇B(x)·f(x,u) ≤ 0 on boundary ∂X_safe

3. Expulsory modes: Safe shutdown under failures

   • Objective: reach(X_current) → reach(X_safe_shutdown) under parametric uncertainty
   • Verification: Parametric robust reachability
   • Formal: Reach(X_current, f(x,u,θ), T) ⊆ X_safe_shutdown for all θ ∈ Θ_failure

Scope Boundaries

• Verify continuous controllers, not synthesize them (analogous to model checking)
• Assume controllers can be designed using standard control theory
• Contribution is verification that candidate controllers compose correctly with discrete layer

Active Development Context

Current Focus (as of 2026-01-26)

Editing the research approach section (3-research-approach/v2.tex) with a Wednesday (2026-01-28) draft deadline.

Open Technical Questions

Questions are embedded in v2.tex comments. Key unresolved issues:

Easier to address:

• Hysteresis and sensor noise handling (standard control theory)
• Mealy machine formalization (presentation issue)
• Failure detection scope boundaries (precision in claims)

More challenging:

• Timing constraint verification (timed automata integration)
• Parametric uncertainty bounds methodology
• Numerical precision in discrete abstraction (task 36 in taskwarrior)
• Controller design gap (scope vulnerability)

Taskwarrior Integration

The user tracks tasks in taskwarrior. The Thesis project has ~45 tasks including:

• 9 writing tasks for research approach sections (due 2026-01-28)
• Multiple reading tasks on hybrid systems, reachability, formal methods
• Outstanding question (task 36): "How do we handle numerical barriers when creating discrete automata?"

Use task list project:Thesis to see current tasks.

Bibliography

References are in references.bib using IEEE transaction format. The bibliography includes:

• Hybrid systems theory and verification
• Formal methods (reactive synthesis, temporal logic)
• Control theory (reachability, barrier certificates)
• Nuclear regulatory documents (NUREG, 10 CFR)
• Industrial control systems

Custom LaTeX Class

dane_proposal_format.cls provides:

• NSF-compliant formatting (Times New Roman, 1" margins)
• Custom \task{title}{description} command for numbered tasks
• TikZ libraries for diagrams
• Table and figure formatting
• Default metadata (title, author, advisor)

Writing Style Notes

• Inline comments in .tex files starting with % are working notes
• Comments with % Q: indicate open questions requiring research/decisions
• Sections marked with \iffalse ... \fi are draft text, not compiled
• Text after \iffalse blocks are outlines/notes for future writing