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 # ERLM Proposal Writing Review - Executive Summary
 **Date**: December 2, 2025 **Reviewer**: Claude Code
 **Framework**: Gopen's Sense of Structure
 ---
 ## Overview
 This proposal demonstrates strong technical content, clear
 methodology, and comprehensive coverage of all required
 elements. The research approach is well-conceived, and the
 progression from problem statement through solution is
 logical. The writing is generally clear and professional.
 **Key Strengths:**
 - Excellent technical depth and specificity
 - Strong motivation established through human factors
 statistics
 - Clear three-thrust research structure
 - Comprehensive risk analysis with concrete contingencies
 - Good use of specific examples (TMI accident, HARDENS
 project)
 **Priority Areas for Revision:**
 - Sentence-level: Strengthen stress positions to emphasize
 key claims
 - Paragraph-level: Sharpen point-issue structure in some
 sections
 - Section-level: Tighten organization in State of the Art
 section
 - Big picture: Strengthen "so what" connections throughout
 ---
 ## Priority Issues (Top 10)
 ### 1. **SOTA Section Length and Organization**
 [SECTION-LEVEL] **Location**: State of the Art section (358
 lines) **Issue**: The SOTA section is the longest in the
 proposal and covers multiple distinct topics (current
 procedures, human factors, HARDENS). While comprehensive, it
 risks overwhelming readers and obscuring your key
 contributions. **Impact**: HIGH - Reviewers may lose track
 of your argument in the density **Recommendation**:
 Consider restructuring with clearer signposting. Each
 subsection should explicitly connect back to what gap
 you're filling. The current "\textbf{LIMITATION:}" callouts
 are excellent—ensure every major subsection has one.
 ### 2. **Weak Stress Positions Throughout** [SENTENCE-LEVEL]
 **Location**: All sections, especially Goals and State of
 the Art **Issue**: Many sentences place old/known
 information in stress position (sentence-final), missing
 opportunities to emphasize new claims **Impact**:
 MEDIUM-HIGH - Reduces rhetorical impact of key claims **See
 Pattern**: "Stress Position Weakness" below for examples and
 fixes
 ### 3. **Missing "So What" Connections** [BIG PICTURE]
 **Location**: Transitions between major sections **Issue**:
 The proposal moves from problem → approach → metrics without
 always explicitly stating "this matters because..." at
 transition points **Impact**: MEDIUM-HIGH - Reviewers may
 not fully grasp significance **Recommendation**: Add
 explicit "if successful, this enables..." statements at the
 end of Goals section and beginning of Metrics section
 ### 4. **Passive Voice Obscuring Agency** [SENTENCE-LEVEL]
 **Location**: Research Approach, especially subsection
 introductions **Issue**: Passive constructions like "will be
 employed" and "will be used" hide who does what and reduce
 directness **Impact**: MEDIUM - Reduces clarity and makes
 writing feel less confident **See Pattern**: "Passive Voice"
 below
 ### 5. **Point-Issue Structure in Paragraphs**
 [PARAGRAPH-LEVEL] **Location**: State of the Art, Risk
 sections **Issue**: Some paragraphs present information
 without first establishing why readers should care (the
 "issue") **Impact**: MEDIUM - Readers may wonder "why are
 you telling me this?" **See Pattern**: "Point-Issue
 Structure" below
 ### 6. **Topic String Breaks** [PARAGRAPH-LEVEL]
 **Location**: Research Approach, subsection transitions
 **Issue**: Topic position doesn't always establish clear
 continuity from previous sentence, forcing readers to
 reconstruct connections **Impact**: MEDIUM - Increases
 cognitive load **See Pattern**: "Topic Position &
 Continuity" below
 ### 7. **Nominalization Hiding Action** [SENTENCE-LEVEL]
 **Location**: Throughout, especially Research Approach
 **Issue**: Action buried in nouns (e.g., "implementation"
 instead of "implement", "verification" instead of "verify")
 **Impact**: MEDIUM - Makes writing feel static rather than
 dynamic **Recommendation**: Convert nominalizations to
 active verbs where possible
 ### 8. **Long Complex Sentences** [SENTENCE-LEVEL]
 **Location**: State of the Art (lines 45-51), Risks (lines
 72-79) **Issue**: Some sentences exceed 40-50 words with
 multiple subordinate clauses, challenging comprehension
 **Impact**: MEDIUM - Reviewers may have to re-read
 **Recommendation**: Break into 2-3 shorter sentences with
 clear logical flow
 ### 9. **Subsection Balance in Risks Section**
 [SECTION-LEVEL] **Location**: Risks and Contingencies
 section **Issue**: Four subsections of vastly different
 lengths (computational tractability gets more space than
 discrete-continuous interface, despite latter being more
 fundamental) **Impact**: LOW-MEDIUM - May suggest misaligned
 priorities **Recommendation**: Consider whether space
 allocation reflects actual risk magnitude
 ### 10. **Broader Impacts Underutilized** [BIG PICTURE]
 **Location**: Broader Impacts section (75 lines vs 358 for
 SOTA) **Issue**: This section is relatively brief given that
 economic impact is a major motivation for SMRs **Impact**:
 LOW-MEDIUM - Missing opportunity to strengthen value
 proposition **Recommendation**: Consider expanding economic
 analysis or adding brief discussion of workforce/educational
 impacts
 ---
 ## Key Patterns Identified
 ### Pattern 1: Stress Position Weakness
 **Principle** (Gopen): The stress position (end of sentence)
 should contain the most important new information. Readers
 expect climax at sentence-end and are disappointed when they
 find old information or weak phrases there.
 **Example 1** (Goals and Outcomes, lines 13-17): ```
 Current: "Currently, nuclear plant operations rely on
 extensively trained human operators who follow detailed
 written procedures and strict regulatory requirements to
 manage reactor control." ```
 - **Issue**: Sentence ends with "manage reactor control"—a
 restatement of the opening. The key claim is buried
 mid-sentence: "extensively trained...detailed
 procedures...strict requirements"
 - **Fixed**: "Currently, nuclear plant operations require
 extensively trained human operators following detailed
 written procedures under strict regulatory requirements."
 **Example 2** (State of the Art, lines 53-54): ``` Current:
 "Procedures lack formal verification of correctness and
 completeness." ```
 - **Issue**: Ends weakly with "completeness" which is minor
 compared to the bigger issue
 - **Fixed**: "Procedures lack formal verification, leaving
 correctness and completeness unproven."
 **Example 3** (Research Approach, lines 41-42): ``` Current:
 "The following sections discuss how these thrusts will be
 accomplished." ```
 - **Issue**: Pure metadiscourse in stress position, provides
 no new information
 - **Fixed**: Delete this sentence—the enumeration provides
 sufficient transition, or combine with previous sentence:
 "...through three main thrusts, each detailed below."
 **Similar instances**:
 - Goals lines 29-32: "...we will combine formal methods..."
 - State of the Art lines 81-85: "...no application of hybrid
 control theory exists..."
 - Research Approach lines 115-116: "...enable progression to
 the next step..."
 - Metrics lines 29-31: "...makes this metric directly
 relevant..."
 - Risks lines 12-13: "...identification of remaining
 barriers to deployment"
 **How to fix**: Identify the most important new claim in
 each sentence and move it to the end. Often this means
 converting from "X does Y to achieve Z" to "X achieves Z by
 doing Y."
 ---
 ### Pattern 2: Passive Voice Obscuring Agency
 **Principle** (Gopen): Passive voice obscures who does what
 and reduces directness. In proposal writing, active voice
 demonstrates confidence and control. Use passive only when
 the agent is truly unimportant or unknown.
 **Example 1** (Research Approach, line 118): ``` Current:
 "We will employ state-of-the-art reactive synthesis
 tools..." ```
 - **Issue**: "Employ" is weak; you're not hiring the tools,
 you're using them
 - **Better**: "We will use Strix, a state-of-the-art
 reactive synthesis tool..."
 - **Best**: "Strix will translate our temporal logic
 specifications into deterministic automata..." (Shows what
 the tool *does*, not just that you'll use it)
 **Example 2** (Research Approach, line 207): ``` Current:
 "Control barrier functions will be employed when..." ```
 - **Issue**: Passive—who employs them? And "employed" sounds
 formal/stuffy
 - **Fixed**: "We will use control barrier functions to
 verify..." or better "Control barrier functions verify..."
 **Example 3** (Metrics, line 67): ``` Current: "This
 milestone delivers an internal technical report..." ```
 - **Issue**: Milestones don't deliver, people do
 - **Fixed**: "We will deliver an internal technical report
 documenting..."
 **Similar instances**:
 - Research Approach lines 161, 175, 206, 220: "will be
 employed", "will be developed", "will be used"
 - Metrics lines 69, 73, 79, 84: "...delivers a [document]"
 - Risks lines 57, 109, 163: various passives
 **How to fix**:
 1. Identify the real agent (usually "we")
 2. Make agent the subject: "We will X" or "X will Y"
 3. Choose strong active verbs: use/apply/develop/verify (not
 employ/utilize)
 ---
 ### Pattern 3: Point-Issue Structure Weakness
 **Principle** (Gopen): Paragraphs should begin by
 establishing (1) the point/claim being made and (2) why it
 matters (the issue). Discussion then supports that point.
 Readers need context before details.
 **Example 1** (State of the Art, lines 88-107): ``` Current
 paragraph begins: "The persistent role of human error in
 nuclear safety incidents, despite decades of
 improvements..." ```
 - **Analysis**: This paragraph immediately dives into the
 "persistent role" without first establishing why we're
 discussing human factors at all. Reader thinks: "Wait,
 weren't we just talking about procedures?"
 - **Fixed**: Add issue statement first: "Human factors
 provide the most compelling motivation for formal automated
 control. Despite decades of improvements in training and
 procedures, human error persists in 70-80% of nuclear
 incidents—suggesting that operator-based control faces
 fundamental, not remediable, limitations."
 **Example 2** (Risks, first paragraph): ``` Current: "This
 research relies on several critical assumptions that, if
 invalidated, would require scope adjustment..." ```
 - **Analysis**: Good—this establishes both point (critical
 assumptions exist) and issue (invalidity requires
 adjustment) immediately. The paragraph then delivers on this
 promise. This is a good model!
 **Example 3** (Research Approach, lines 166-169): ```
 Current: "While discrete system components will be
 synthesized with correctness guarantees, they represent only
 half of the complete system." ```
 - **Analysis**: Good issue statement (discrete alone
 insufficient), but could be sharper about the point. What
 will this section show?
 - **Fixed**: "While discrete system components will be
 synthesized with correctness guarantees, they represent only
 half of the complete system. This section describes how we
 will develop continuous control modes, verify their
 correctness, and address the unique verification challenges
 at the discrete-continuous interface."
 **Similar instances**:
 - State of the Art lines 13-34: long paragraph with delayed
 point
 - Goals lines 103-119: impact paragraph could be tighter
 - Approach lines 178-208: three-mode classification needs
 clearer framing
 **How to fix**:
 1. First sentence should state the paragraph's point
 2. Second sentence (or same sentence) should state why this
 matters
 3. Remaining sentences provide supporting detail
 ---
 ### Pattern 4: Topic Position & Continuity
 **Principle** (Gopen): The topic position (beginning of
 sentence) should contain old/familiar information that links
 to what came before. This creates flow and coherence. Abrupt
 topic shifts disorient readers.
 **Example 1** (Goals, lines 18-23): ``` Sentence 1: "...this
 reliance on human operators prevents the introduction of
 autonomous control capabilities..."
 Sentence 2: "Emerging technologies like small modular
 reactors face significantly higher per-megawatt staffing
 costs..." ```
 - **Issue**: Topic shifts abruptly from "reliance on
 operators" to "emerging technologies". Connection exists
 (both about staffing challenges) but isn't explicit
 - **Fixed**: "...prevents autonomous control capabilities.
 This limitation creates particular challenges for emerging
 technologies like small modular reactors, which face
 significantly higher per-megawatt staffing costs..."
 **Example 2** (State of the Art, lines 234-243): ```
 Sentence about what HARDENS addressed: "...discrete digital
 control logic..."
 Next sentence: "However, the project did not address
 continuous dynamics..." ```
 - **Analysis**: Good use of "however, the project" in topic
 position—maintains focus on HARDENS while pivoting to
 limitation. This is a good model!
 **Example 3** (Research Approach, lines 56-58): ``` Sentence
 1: "...we may be able to translate them into logical
 formulae..."
 Sentence 2: "Linear Temporal Logic (LTL) provides four
 fundamental operators..." ```
 - **Issue**: Abrupt topic shift from "translating
 procedures" to "LTL provides". Missing: why LTL? Why now?
 - **Fixed**: "...translate them into logical formulae. To
 formalize these procedures, we will use Linear Temporal
 Logic (LTL), which provides four fundamental operators..."
 **Similar instances**:
 - Goals lines 23-27: "emerging technologies" → "what is
 needed"
 - State of the Art lines 72-74: control modes → division
 between automated/human
 - Approach lines 183-185: stabilizing mode example →
 transitory mode definition
 **How to fix**:
 1. Identify the topic of the previous sentence
 2. Begin next sentence with something related to that topic
 3. Use transitional phrases when shifting topics: "This
 [previous thing] leads to [new thing]"
 ---
 ### Pattern 5: Long Complex Sentences
 **Principle**: Sentences with multiple subordinate clauses
 (especially over 35-40 words) tax reader working memory.
 Breaking into multiple sentences often improves clarity
 without losing sophistication.
 **Example 1** (State of the Art, lines 48-51): ``` Current
 (51 words): "Procedures undergo technical evaluation,
 simulator validation testing, and biennial review as part of
 operator requalification under 10 CFR 55.59, but despite
 these rigorous development processes, procedures
 fundamentally lack formal verification of key safety
 properties." ```
 - **Issue**: Long sentence with list, subordinate clause,
 and contrast—hard to parse
 - **Fixed (2 sentences)**: "Procedures undergo technical
 evaluation, simulator validation testing, and biennial
 review as part of operator requalification under 10 CFR
 55.59. Despite these rigorous development processes,
 procedures fundamentally lack formal verification of key
 safety properties."
 **Example 2** (Risks, lines 72-78): ``` Current (57 words):
 "Temporal logic operates on boolean predicates, while
 continuous control requires reasoning about differential
 equations and reachable sets, and guard conditions that
 require complex nonlinear predicates may resist boolean
 abstraction, making synthesis intractable." ```
 - **Issue**: Run-on with multiple clauses strung together
 with commas
 - **Fixed (3 sentences)**: "Temporal logic operates on
 boolean predicates, while continuous control requires
 reasoning about differential equations and reachable sets.
 Guard conditions requiring complex nonlinear predicates may
 resist boolean abstraction. This mismatch could make
 synthesis intractable."
 **Similar instances**:
 - State of the Art lines 44-51: procedure development
 description
 - Research Approach lines 40-45: hybrid system description
 - Risks lines 17-24: computational tractability discussion
 - Broader Impacts lines 13-23: economic analysis
 **How to fix**:
 1. Identify natural breakpoints (usually where you have
 "and" or "but")
 2. Create new sentences at these breaks
 3. Ensure each new sentence has clear topic position
 4. May need to repeat/reference previous sentence's subject
 for clarity
 ---
 ## Section-Level Issues
 ### Goals and Outcomes Section **Strengths**: Excellent
 structure with clear goal → problem → approach → outcomes →
 impact progression. The four-paragraph opening is very
 strong.
 **Issues**:
 - Lines 29-53 (Approach paragraph): This is dense and tries
 to cover too much. Consider breaking into two paragraphs:
 one on the approach concept, one on the hypothesis and
 rationale.
 - Outcomes enumeration: Very clear, but could strengthen the
 transition from strategy to outcome in each item. Currently
 reads as "we'll do X. [new sentence] This enables Y."
 Consider: "We'll do X, enabling Y."
 ### State of the Art Section **Strengths**: Comprehensive,
 well-researched, excellent use of the HARDENS case study as
 both positive example and gap identifier.
 **Issues**:
 - **Length**: At 358 lines, this risks losing readers. Most
 concerning: readers may forget your framing by the time they
 reach your contribution.
 - **Organization**: Four major subsections (procedures,
 human factors, HARDENS, research imperative) would benefit
 from a roadmap sentence at the beginning: "To understand the
 need for hybrid control synthesis, we first examine..."
 - **Balance**: HARDENS subsection is 89 lines—nearly 25% of
 SOTA. While impressive, consider whether this should be a
 separate section or whether some detail could move to an
 appendix.
 - **Transition to Approach**: The "Research Imperative"
 subsection is excellent but feels like it belongs at the
 start of Research Approach rather than end of SOTA.
 ### Research Approach Section **Strengths**: Clear
 three-thrust structure, good use of equations and examples,
 strong technical detail.
 **Issues**:
 - **Subsection transitions**: The transitions between the
 three main subsections (Procedures→Temporal,
 Temporal→Discrete, Discrete→Continuous) could be smoother.
 Each starts somewhat abruptly.
 - **SmAHTR introduction**: The SmAHTR demonstration case is
 introduced suddenly at line 253. Consider introducing it
 earlier (perhaps in Goals section or at start of Approach)
 so readers know it's coming.
 - **Three-mode classification**: Lines 178-208 present the
 stabilizing/transitory/expulsory framework, which is
 innovative. This deserves more prominence—consider
 highlighting it as a key contribution.
 ### Metrics of Success Section **Strengths**: TRL framework
 is well-justified, progression through levels is clear.
 **Issues**:
 - **Defensive tone**: Lines 11-30 spend considerable space
 justifying why TRL is appropriate. This is good but could be
 more concise. Consider: one paragraph on why TRLs (lines
 10-19) rather than two.
 - **Grading criteria**: The TRL definitions (3, 4, 5) are
 excellent. Very concrete and measurable.
 ### Risks and Contingencies Section **Strengths**:
 Comprehensive, each risk has indicators and contingencies,
 well-organized.
 **Issues**:
 - **Subsection balance**: Four subsections range from 41
 lines (computational) to 65 lines (discrete-continuous).
 Ensure space reflects actual risk level.
 - **Mitigation vs. contingency**: Some subsections blur
 "mitigation" (preventing problems) and "contingency"
 (response if they occur). Consider clarifying this
 structure.
 ### Broader Impacts Section **Strengths**: Clear economic
 motivation, good connection to SMRs and datacenter
 application.
 **Issues**:
 - **Brevity**: At 75 lines, this is the shortest technical
 section. Given that economic viability is a key motivation,
 consider expanding.
 - **Missed opportunities**: Could briefly mention
 workforce/educational impacts (training future engineers in
 formal methods), equity (providing reliable clean energy to
 underserved areas), broader applicability beyond nuclear.
 ### Budget Section **Brief review**: Budget is
 comprehensive, well-justified, appropriate. Minor note:
 Consider whether the high-performance workstation (Year 1)
 might need upgrades in Year 2-3 as synthesis scales up.
 ### Schedule Section **Brief review**: Schedule is ambitious
 but realistic. Six trimesters for dissertation research is
 reasonable. Publication strategy is smart (nuclear community
 first, then broader control theory community). Minor note:
 Line 73 has a space issue ("t ranslation").
 ---
 ## Big Picture Observations
 ### Narrative and Argument Structure
 **Strengths**:
 - Clear problem-solution arc: operators make errors →
 procedures lack formal guarantees → hybrid control synthesis
 provides guarantees
 - Good use of motivating examples (TMI, human error
 statistics, HARDENS)
 - Technical progression is logical: discrete synthesis →
 continuous verification → integrated system
 **Opportunities**:
 1. **Strengthen "so what" transitions**: The proposal
 sometimes presents information without explicitly stating
 significance. Add more "This matters because..." statements.
 2. **Emphasize novelty earlier**: The three-mode
 classification and discrete-continuous interface
 verification are novel contributions. Signal this earlier
 and more explicitly.
 3. **Create more callbacks**: When describing Research
 Approach, refer back to specific limitations identified in
 State of the Art. Currently these connections are implicit.
 ### Rhetorical Effectiveness
 **Credibility established through**:
 - Comprehensive literature review
 - Specific technical detail
 - Access to industry hardware (Emerson partnership)
 - Prior conference recognition (best student paper)
 **Value proposition**:
 - Clear economic impact (O&M cost reduction)
 - Safety improvement (mathematical guarantees vs. human
 operators)
 - Broader applicability (methodology generalizes)
 **Could strengthen**:
 - More explicit statements of what's novel vs. what's
 established practice
 - Stronger emphasis on the unique combination of discrete
 synthesis + continuous verification (others do one or the
 other, not both)
 ### Content Gaps and Consistency
 **Terminology**:
 - Generally consistent
 - Good introduction of technical terms (hybrid automata,
 temporal logic, reachability analysis)
 - Minor: "correct by construction" vs. "provably
 correct"—used interchangeably, which is fine, but could note
 they're synonymous
 **Scope consistency**:
 - Excellent—stays focused on startup procedures for SmAHTR
 - Appropriately acknowledges limitations (TRL 5, not
 deployment-ready)
 - Risk section addresses what happens if scope must narrow
 **Potential gaps**:
 1. **Cybersecurity**: Not mentioned. For autonomous nuclear
 control, shouldn't there be at least a paragraph on security
 verification?
 2. **Regulatory path**: You mention "regulatory
 requirements" but don't detail what NRC approval process
 would look like. Even a paragraph would strengthen
 credibility.
 3. **Comparison with alternatives**: What about machine
 learning approaches to autonomous control? Worth a paragraph
 explaining why formal methods are superior for
 safety-critical systems.
 ---
 ## Gopen Framework Quick Reference
 **Stress Position**: End of sentence should contain most
 important new information. Readers expect climax there.
 **Topic Position**: Beginning of sentence should contain
 familiar information that links to previous sentence.
 Creates flow.
 **Point-Issue Structure**: Paragraphs should open by stating
 (1) the point/claim and (2) why it matters, before providing
 supporting detail.
 **Topic String**: The chain of topics across sentences in a
 paragraph. Strong topic strings create coherence; broken
 ones confuse readers.
 **Old→New Information Flow**: Information should flow from
 familiar (old) to unfamiliar (new) within sentences and
 paragraphs.
 ---
 ## Next Steps
 1. **Start with Priority Issues 1-3**: These have the
 highest impact
 2. **Apply Patterns**: Use the pattern examples to fix
 similar instances throughout
 3. **Consult Detailed Document**: For comprehensive
 checkbox-by-checkbox revisions
 4. **Section-by-section revision**: Work through one section
 at a time, applying patterns
 5. **Final pass for consistency**: Ensure changes maintain
 consistent terminology and tone
 This proposal has strong technical content and a solid
 structure. The revisions suggested here will strengthen
 clarity, emphasize key contributions, and make the argument
 even more compelling for reviewers. Good luck with your
 revisions!
--- a/Writing/THESIS_PROPOSAL/GOv1.pdf
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--- a/Writing/THESIS_PROPOSAL/Sabo-Supplemental-Sections.pdf
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--- a/Writing/THESIS_PROPOSAL/SaboBudgetAndJustification.pdf
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--- a/Writing/THESIS_PROPOSAL/Sabo_Whitepaper.pdf
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--- a/Writing/THESIS_PROPOSAL/references_old.bib
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@ -1,547 +0,0 @@
 % Foundational Papers
@article{alur1995algorithmic,
  title={The algorithmic analysis of hybrid systems},
  author={Alur, Rajeev and Courcoubetis, Costas and Halbwachs, Nicolas and Henzinger, Thomas A and Ho, Pei-Hsin and Nicollin, Xavier and Olivero, Alfredo and Sifakis, Joseph and Yovine, Sergio},
  journal={Theoretical Computer Science},
  volume={138},
  number={1},
  pages={3--34},
  year={1995},
  publisher={Elsevier}
 }
@inproceedings{alur1993hybrid,
  title={Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems},
  author={Alur, Rajeev and Courcoubetis, Costas and Henzinger, Thomas A and Ho, Pei-Hsin},
  booktitle={Hybrid Systems},
  pages={209--229},
  year={1993},
  publisher={Springer}
 }
@article{mitchell2005time,
  title={A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games},
  author={Mitchell, Ian M and Bayen, Alexandre M and Tomlin, Claire J},
  journal={IEEE Transactions on Automatic Control},
  volume={50},
  number={7},
  pages={947--957},
  year={2005},
  publisher={IEEE}
 }
@article{platzer2008differential,
  title={Differential dynamic logic for hybrid systems},
  author={Platzer, Andr{\'e}},
  journal={Journal of Automated Reasoning},
  volume={41},
  number={2},
  pages={143--189},
  year={2008},
  publisher={Springer}
 }
@article{platzer2017complete,
  title={A complete uniform substitution calculus for differential dynamic logic},
  author={Platzer, Andr{\'e}},
  journal={Journal of Automated Reasoning},
  volume={59},
  number={2},
  pages={219--265},
  year={2017},
  publisher={Springer}
 }
@inproceedings{donze2010robust,
  title={Robust satisfaction of temporal logic over real-valued signals},
  author={Donz{\'e}, Alexandre and Maler, Oded},
  booktitle={International Conference on Formal Modeling and Analysis of Timed Systems},
  pages={92--106},
  year={2010},
  publisher={Springer}
 }
 % Control Theory and Stability
@article{geromel2006stability,
  title={Stability and stabilization of continuous-time switched linear systems},
  author={Geromel, Jos{\'e} C and Colaneri, Patrizio},
  journal={SIAM Journal on Control and Optimization},
  volume={45},
  number={5},
  pages={1915--1930},
  year={2006},
  publisher={SIAM}
 }
@book{liberzon2003switching,
  title={Switching in systems and control},
  author={Liberzon, Daniel},
  year={2003},
  publisher={Birkh{\"a}user Boston}
 }
@article{branicky1998multiple,
  title={Multiple Lyapunov functions and other analysis tools for switched and hybrid systems},
  author={Branicky, Michael S},
  journal={IEEE Transactions on Automatic Control},
  volume={43},
  number={4},
  pages={475--482},
  year={1998},
  publisher={IEEE}
 }
 % Recent Advances (2020-2025)
@article{yang2024learning,
  title={Learning Local Control Barrier Functions for Hybrid Systems},
  author={Yang, Shuo and Chen, Yiwei and Yin, Xiang and Mangharam, Rahul},
  journal={arXiv preprint arXiv:2401.14907},
  year={2024}
 }
@inproceedings{su2024switching,
  title={Switching Controller Synthesis for Hybrid Systems Against STL Formulas},
  author={Su, Mingyu and Vizel, Yakir and Vardi, Moshe Y},
  booktitle={International Symposium on Formal Methods},
  pages={231--248},
  year={2024},
  publisher={Springer}
 }
@article{yao2024model,
  title={Model predictive control of stochastic hybrid systems with signal temporal logic constraints},
  author={Yao, Li and Wang, Yiming and Chen, Xiang},
  journal={Automatica},
  volume={159},
  pages={111037},
  year={2024},
  publisher={Elsevier}
 }
@article{yu2024online,
  title={Online control synthesis for uncertain systems under signal temporal logic specifications},
  author={Yu, Pian and Gao, Yulong and Jiang, Frank J and Johansson, Karl H and Dimarogonas, Dimos V},
  journal={The International Journal of Robotics Research},
  volume={43},
  number={3},
  pages={284--307},
  year={2024},
  publisher={SAGE}
 }
 % Tools and Frameworks
@inproceedings{meyer2018strix,
  title={Strix: Explicit reactive synthesis strikes back!},
  author={Meyer, Philipp J and Luttenberger, Michael},
  booktitle={International Conference on Computer Aided Verification},
  pages={578--586},
  year={2018},
  publisher={Springer}
 }
@techreport{giannakopoulou2022fret,
  title={Capturing and Analyzing Requirements with FRET},
  author={Giannakopoulou, Dimitra and Mavridou, Anastasia and Rhein, Julian and Pressburger, Thomas and Schumann, Johann and Shi, Nija},
  institution={NASA Ames Research Center},
  year={2022},
  number={NASA/TM-20220007610}
 }
@inproceedings{fulton2015keymaera,
  title={KeYmaera X: An axiomatic tactical theorem prover for hybrid systems},
  author={Fulton, Nathan and Mitsch, Stefan and Quesel, Jan-David and V{\"o}lp, Marcus and Platzer, Andr{\'e}},
  booktitle={International Conference on Automated Deduction},
  pages={527--538},
  year={2015},
  publisher={Springer}
 }
@inproceedings{frehse2011spaceex,
  title={SpaceEx: Scalable verification of hybrid systems},
  author={Frehse, Goran and Le Guernic, Colas and Donz{\'e}, Alexandre and Cotton, Scott and Ray, Rajarshi and Lebeltel, Olivier and Ripado, Rodolfo and Girard, Antoine and Dang, Thao and Maler, Oded},
  booktitle={International Conference on Computer Aided Verification},
  pages={379--395},
  year={2011},
  publisher={Springer}
 }
@inproceedings{chen2013flow,
  title={Flow*: An analyzer for non-linear hybrid systems},
  author={Chen, Xin and {\'A}brah{\'a}m, Erika and Sankaranarayanan, Sriram},
  booktitle={International Conference on Computer Aided Verification},
  pages={258--263},
  year={2013},
  publisher={Springer}
 }
@inproceedings{larsen1997uppaal,
  title={UPPAAL in a nutshell},
  author={Larsen, Kim G and Pettersson, Paul and Yi, Wang},
  journal={International Journal on Software Tools for Technology Transfer},
  volume={1},
  number={1-2},
  pages={134--152},
  year={1997},
  publisher={Springer}
 }
 % Reachability and Verification
@INPROCEEDINGS{bansal2017hamilton,
  author={Bansal, Somil and Chen, Mo and Herbert, Sylvia and Tomlin, Claire J.},
  booktitle={2017 IEEE 56th Annual Conference on Decision and Control (CDC)}, 
  title={Hamilton-Jacobi reachability: A brief overview and recent advances}, 
  year={2017},
  volume={},
  pages={2242-2253},
  keywords={Games;Safety;Tools;Trajectory;Tutorials;Level set;Aircraft},
  doi={10.1109/CDC.2017.8263977}
 }
@article{althoff2021set,
  title={Set propagation techniques for reachability analysis},
  author={Althoff, Matthias and Frehse, Goran and Girard, Antoine},
  journal={Annual Review of Control, Robotics, and Autonomous Systems},
  volume={4},
  pages={369--395},
  year={2021},
  publisher={Annual Reviews}
 }
@inproceedings{tabuada2004compositional,
  title={Compositional abstractions of hybrid control systems},
  author={Tabuada, Paulo and Pappas, George J and Lima, Pedro},
  journal={Discrete Event Dynamic Systems},
  volume={14},
  number={2},
  pages={203--238},
  year={2004},
  publisher={Springer}
 }
 % Applications
@article{varaiya1993smart,
  title={Smart cars on smart roads: Problems of control},
  author={Varaiya, Pravin},
  journal={IEEE Transactions on Automatic Control},
  volume={38},
  number={2},
  pages={195--207},
  year={1993},
  publisher={IEEE}
 }
@article{verlinden2024hybrid,
  title={Hybrid reliability modeling of nuclear safety systems: A case study on the reactor protection system of a research reactor},
  author={Verlinden, S and Deridder, F and Wagemans, P},
  journal={Nuclear Engineering and Design},
  volume={417},
  pages={112868},
  year={2024},
  publisher={Elsevier}
 }
 % Competitions and Benchmarks
@inproceedings{hscc2024proceedings,
  title={Proceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control},
  booktitle={HSCC '24},
  year={2024},
  publisher={ACM},
  address={New York, NY, USA}
 }
@inproceedings{jacobs2017syntcomp,
  title={The 4th reactive synthesis competition (SYNTCOMP 2017): Benchmarks, participants \& results},
  author={Jacobs, Swen and Bloem, Roderick and Brenguier, Romain and others},
  booktitle={6th Workshop on Synthesis},
  year={2017},
  series={EPTCS},
  volume={260}
 }
 % Supporting Papers
@article{wabersich2018linear,
  title={Linear model predictive safety certification for learning-based control},
  author={Wabersich, Kim P and Zeilinger, Melanie N},
  journal={Automatica},
  volume={97},
  pages={48--59},
  year={2018},
  publisher={Elsevier}
 }
@inproceedings{prajna2004safety,
  title={Safety verification of hybrid systems using barrier certificates},
  author={Prajna, Stephen and Jadbabaie, Ali},
  booktitle={International Workshop on Hybrid Systems: Computation and Control},
  pages={477--492},
  year={2004},
  publisher={Springer}
 }
@article{ames2017control,
  title={Control barrier function based quadratic programs for safety critical systems},
  author={Ames, Aaron D and Xu, Xiangru and Grizzle, Jessy W and Tabuada, Paulo},
  journal={IEEE Transactions on Automatic Control},
  volume={62},
  number={8},
  pages={3861--3876},
  year={2017},
  publisher={IEEE}
 }
@article{srinivasan2018control,
  title={Control of mobile robots using barrier functions under temporal logic specifications},
  author={Srinivasan, Mohit and Coogan, Samuel},
  journal={IEEE Transactions on Robotics},
  volume={37},
  number={2},
  pages={363--374},
  year={2021},
  publisher={IEEE}
 }
 %broader impacts
@techreport{eia_lcoe_2022,
  author       = {{U.S. Energy Information Administration}},
  title        = {Levelized Costs of New Generation Resources in the Annual Energy Outlook 2022},
  institution  = {U.S. Energy Information Administration},
  year         = {2022},
  month        = {March},
  type         = {Report},
  url          = {https://www.eia.gov/outlooks/aeo/pdf/electricity_generation.pdf},
  note         = {See Table 1b, page 9}
 }
@misc{eesi_datacenter_2024,
  author       = {{Environmental and Energy Study Institute}},
  title        = {Data Center Energy Needs Are Upending Power Grids and Threatening the Climate},
  howpublished = {Web article},
  year         = {2024},
  url          = {https://www.eesi.org/articles/view/data-center-energy-needs-are-upending-power-grids-and-threatening-the-climate},
  note         = {Accessed: 2025-09-29}
 }
@techreport{DOE-HDBK-1028-2009,
  title        = {Human Performance Handbook},
  author       = {{U.S. Department of Energy}},
  institution  = {U.S. Department of Energy},
  year         = {2009},
  number       = {DOE-HDBK-1028-2009},
  type         = {Handbook}
 }
@misc{WNA2020,
  title        = {Safety of Nuclear Power Reactors},
  author       = {{World Nuclear Association}},
  year         = {2020},
  howpublished = {\url{https://www.world-nuclear.org/information-library/safety-and-security/safety-of-plants/safety-of-nuclear-power-reactors.aspx}}
 }
@article{Wang2025,
  title   = {Analysis of Human Error in Nuclear Power Plant Operations: A Systematic Review of Events from 2007--2020},
  author  = {Wang, Y. and others},
  journal = {Journal of Nuclear Safety},
  year    = {2025},
  note    = {Analysis of 190 events at Chinese nuclear power plants}
 }
@misc{10CFR55,
  title        = {Operators' Licenses},
  author       = {{U.S. Nuclear Regulatory Commission}},
  howpublished = {10 CFR Part 55},
  note         = {Code of Federal Regulations}
 }
@techreport{Kemeny1979,
  title       = {Report of the President's Commission on the Accident at Three Mile Island},
  author      = {Kemeny, John G. and others},
  institution = {President's Commission on the Accident at Three Mile Island},
  year        = {1979},
  month       = {October}
 }
@misc{10CFR50,
  title        = {Domestic Licensing of Production and Utilization Facilities},
  author       = {{U.S. Nuclear Regulatory Commission}},
  howpublished = {10 CFR Part 50},
  note         = {Code of Federal Regulations}
 }
@techreport{NUREG-0899,
  title       = {Guidelines for the Preparation of Emergency Operating Procedures},
  author      = {{U.S. Nuclear Regulatory Commission}},
  institution = {U.S. Nuclear Regulatory Commission},
  year        = {1982},
  number      = {NUREG-0899}
 }
@techreport{IAEA-TECDOC-1580,
  title       = {Good Practices for Cost Effective Maintenance of Nuclear Power Plants},
  author      = {{International Atomic Energy Agency}},
  institution = {International Atomic Energy Agency},
  year        = {2007},
  number      = {TECDOC-1580}
 }
@techreport{NUREG-2114,
  title       = {Cognitive Basis for Human Reliability Analysis},
  author      = {{U.S. Nuclear Regulatory Commission}},
  institution = {U.S. Nuclear Regulatory Commission},
  year        = {2016},
  number      = {NUREG-2114}
 }
@article{Zerovnik2023,
  title   = {Knowledge Transfer Challenges in Nuclear Operations},
  author  = {\v{Z}erovnik, Gašper and others},
  journal = {Nuclear Engineering and Design},
  year    = {2023},
  note    = {Analysis of knowledge transfer from experienced operators}
 }
@article{Jo2021,
  title   = {Automation Paradox in Nuclear Power Plant Control: Effects on Operator Situation Awareness},
  author  = {Jo, Y. and others},
  journal = {Nuclear Engineering and Technology},
  year    = {2021},
  note    = {Empirical study of automation effects on operator performance}
 }
@techreport{IAEA2008,
  title       = {Modern Instrumentation and Control for Nuclear Power Plants: A Guidebook},
  author      = {{International Atomic Energy Agency}},
  institution = {International Atomic Energy Agency},
  year        = {2008},
  number      = {Technical Reports Series No. 387}
 }
@article{Lee2019,
  title   = {Autonomous Control of Nuclear Reactors Using Long Short-Term Memory Networks},
  author  = {Lee, D. and others},
  journal = {Nuclear Engineering and Technology},
  year    = {2019},
  note    = {Demonstration of LSTM-based autonomous control in LOC and SGTR scenarios}
 }
@inproceedings{IEEE2019,
  title     = {Formal Verification Challenges for Nuclear I\&C Systems},
  author    = {{IEEE Working Group}},
  booktitle = {IEEE Conference on Nuclear Power Instrumentation, Control and Human-Machine Interface Technologies},
  year      = {2019},
  note      = {Discussion of state space explosion in formal verification}
 }
@misc{IAEA-severe-accidents,
  title        = {Human Error as Root Cause in Severe Nuclear Accidents},
  author       = {{International Atomic Energy Agency}},
  howpublished = {IAEA Safety Report},
  note         = {Analysis of TMI, Chernobyl, and Fukushima accidents}
 }
@article{Dumas1999,
  title   = {Worker Error and Safety in Nuclear Facilities},
  author  = {Dumas, Lloyd},
  journal = {Journal of Nuclear Safety},
  year    = {1999},
  note    = {Study of incidents at 10 nuclear centers}
 }
@techreport{IAEA-INSAG-1,
  title       = {Summary Report on the Post-Accident Review Meeting on the Chernobyl Accident},
  author      = {{International Nuclear Safety Advisory Group}},
  institution = {International Atomic Energy Agency},
  year        = {1986},
  number      = {INSAG-1}
 }
@techreport{IAEA-INSAG-7,
  title       = {The Chernobyl Accident: Updating of INSAG-1},
  author      = {{International Nuclear Safety Advisory Group}},
  institution = {International Atomic Energy Agency},
  year        = {1992},
  number      = {INSAG-7}
 }
@techreport{NUREG-CR-1278,
  title       = {Handbook of Human Reliability Analysis with Emphasis on Nuclear Power Plant Applications (THERP)},
  author      = {Swain, A. D. and Guttmann, H. E.},
  institution = {U.S. Nuclear Regulatory Commission},
  year        = {1983},
  number      = {NUREG/CR-1278}
 }
@techreport{NUREG-CR-6883,
  title       = {The SPAR-H Human Reliability Analysis Method},
  author      = {Gertman, D. and others},
  institution = {U.S. Nuclear Regulatory Commission},
  year        = {2005},
  number      = {NUREG/CR-6883}
 }
@techreport{NUREG-2127,
  title       = {International HRA Empirical Study: Phase 1 Report},
  author      = {{U.S. Nuclear Regulatory Commission}},
  institution = {U.S. Nuclear Regulatory Commission},
  year        = {2013},
  number      = {NUREG-2127}
 }
@article{Rasmussen1983,
  title   = {Skills, Rules, and Knowledge; Signals, Signs, and Symbols, and Other Distinctions in Human Performance Models},
  author  = {Rasmussen, J.},
  journal = {IEEE Transactions on Systems, Man, and Cybernetics},
  year    = {1983},
  volume  = {SMC-13},
  number  = {3},
  pages   = {257--266}
 }
@article{Miller1956,
  title   = {The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information},
  author  = {Miller, George A.},
  journal = {Psychological Review},
  year    = {1956},
  volume  = {63},
  number  = {2},
  pages   = {81--97}
 }
@techreport{NUREG-2256,
  title       = {Integrated Human Event Analysis System for Emergency Crew Actions (IDHEAS-ECA)},
  author      = {{U.S. Nuclear Regulatory Commission}},
  institution = {U.S. Nuclear Regulatory Commission},
  year        = {2022},
  number      = {NUREG-2256}
 }
@book{Reason1990,
  title     = {Human Error},
  author    = {Reason, James},
  publisher = {Cambridge University Press},
  year      = {1990}
 }
@article{Lee2018,
  title   = {Deep Reinforcement Learning for Autonomous Nuclear Reactor Control},
  author  = {Lee, D. and others},
  journal = {Nuclear Engineering and Design},
  year    = {2018},
  note    = {Demonstration of autonomous control superior to human-plus-automation}
 }
@techreport{Kiniry2022,
  title       = {High Assurance Rigorous Digital Engineering for Nuclear Safety (HARDENS) Final Technical Report},
  author      = {Kiniry, Joseph and Bakst, Alexander and Podhradsky, Michal and Hansen, Simon and Bivin, Andrew},
  institution = {Galois, Inc. / U.S. Nuclear Regulatory Commission},
  year        = {2022},
  number      = {ML22326A307},
  note        = {NRC Contract 31310021C0014}
 }
--- a/Writing/THESIS_PROPOSAL/sabo-quad-chart.pdf
+++ b/Writing/THESIS_PROPOSAL/sabo-quad-chart.pdf
--- a/Writing/THESIS_PROPOSAL/sabo_broader_impacts.pdf
+++ b/Writing/THESIS_PROPOSAL/sabo_broader_impacts.pdf
--- a/Writing/THESIS_PROPOSAL/sabo_research_approach.pdf
+++ b/Writing/THESIS_PROPOSAL/sabo_research_approach.pdf
--- a/Writing/THESIS_PROPOSAL/sabodaneSOTA-v1.pdf
+++ b/Writing/THESIS_PROPOSAL/sabodaneSOTA-v1.pdf
--- a/Writing/THESIS_PROPOSAL/whitepaper/v1.tex
+++ b/Writing/THESIS_PROPOSAL/whitepaper/v1.tex
@ -1,421 +0,0 @@
 % PROJECT SUMMARY
 \section*{Project Summary}
 \subsection*{Overview}
 This research will develop a methodology for creating autonomous hybrid control
 systems with mathematical guarantees of safe and correct behavior. Nuclear power
 plants require the highest levels of control system reliability, where failures
 can result in significant economic losses or radiological release. Currently,
 nuclear operations rely on extensively trained human operators who follow
 detailed written procedures to manage reactor control. However, reliance on
 human operators prevents introduction of autonomous control capabilities and
 creates fundamental economic challenges for next-generation reactor designs.
 Without introducing automation, emerging technologies like small modular
 reactors face significantly higher per-megawatt staffing costs than conventional
 plants, threatening their economic viability.
 To address this need, we will combine formal methods from computer science 
 with control theory to build hybrid control systems that are correct by 
 construction. Hybrid systems use discrete logic to switch between continuous 
 control modes, similar to how operators change control strategies. Existing 
 formal methods can generate provably correct switching logic from written 
 requirements, but they cannot handle the continuous dynamics that occur during 
 transitions between modes. Meanwhile, traditional control theory can verify 
 continuous behavior but lacks tools for proving correctness of discrete 
 switching decisions. By synthesizing discrete mode transitions directly from 
 written operating procedures and verifying continuous behavior between 
 transitions, we can create hybrid control systems with end-to-end correctness 
 guarantees.
 \subsection*{Intellectual Merit}
 The intellectual merit lies in unifying discrete synthesis and continuous 
 verification to enable end-to-end correctness guarantees for hybrid systems. 
 This research will advance knowledge by developing a systematic, 
 tool-supported methodology for translating written procedures into temporal 
 logic, synthesizing provably correct discrete switching logic, and developing 
 verified continuous controllers. The approach addresses a fundamental gap in 
 hybrid system design by bridging formal methods from computer science and 
 control theory.
 \subsection*{Broader Impacts}
 This research directly addresses the multi-billion dollar operations and 
 maintenance cost challenge facing nuclear power deployment. By synthesizing 
 provably correct hybrid controllers, we can automate routine operational 
 sequences that currently require constant human oversight, enabling a shift 
 from direct operator control to supervisory monitoring. Beyond nuclear 
 applications, this research will establish a generalizable framework for 
 autonomous control of safety-critical systems including chemical process 
 control, aerospace systems, and autonomous transportation.
 \newpage
 % RESEARCH DESCRIPTION
 \section*{Research Description}
 \section{Objectives}
 % GOAL PARAGRAPH
 The goal of this research is to develop a methodology for creating autonomous
 control systems with event-driven control laws that have guarantees of safe and
 correct behavior.
 % INTRODUCTORY PARAGRAPH Hook
 Nuclear power relies on extensively trained operators who follow detailed
 written procedures to manage reactor control. Based on these procedures and
 operators' interpretation of plant conditions, operators make critical decisions
 about when to switch between control objectives. 
 % Gap
 While human operators have maintained the nuclear industry's exceptional safety
 record, reliance on human operators has created an economic challenge for
 next-generation nuclear power plants. Small modular reactors face significantly
 higher per-megawatt staffing costs than conventional plants, threatening their
 economic viability. Autonomous control systems are needed that can safely manage
 complex operational sequences with the same assurance as human-operated systems,
 but without constant supervision.
 % APPROACH PARAGRAPH Solution
 To address this need, we will combine formal methods from computer science with
 control theory to build hybrid control systems that are correct by construction. 
 % Rationale
 Hybrid systems use discrete logic to switch between continuous control modes,
 similar to how operators change control strategies. Existing formal methods
 generate provably correct switching logic but cannot handle continuous dynamics
 during transitions, while traditional control theory verifies continuous
 behavior but lacks tools for proving discrete switching correctness. 
 % Hypothesis and Technical Approach
 We will bridge this gap through a three-stage methodology. First, we will
 translate written operating procedures into temporal logic specifications using
 NASA's Formal Requirements Elicitation Tool (FRET), which structures
 requirements into scope, condition, component, timing, and response elements.
 This structured approach enables realizability checking to identify conflicts
 and ambiguities in procedures before implementation. Second, we will synthesize
 discrete mode switching logic from these specifications using reactive synthesis
 tools such as Strix, which generates deterministic automata that are provably
 correct by construction. Third, we will develop and verify continuous
 controllers for each discrete mode using standard control theory and
 reachability analysis. We will classify continuous modes based on their
 transition objectives, and then employ assume-guarantee contracts and barrier
 certificates to prove that mode transitions occur safely and as defined by the
 deterministic automata. This compositional approach enables local verification
 of continuous modes without requiring global trajectory analysis across the
 entire hybrid system. We will demonstrate this methodology by developing an
 autonomous startup controller for a Small Modular Advanced High Temperature
 Reactor (SmAHTR) and implementing it on an Emerson Ovation control system using
 the ARCADE hardware-in-the-loop platform. 
 % Pay-off
 This approach will demonstrate autonomous control can be used for complex
 nuclear power operations while maintaining safety guarantees.
 \vspace{11pt}
 % OUTCOMES PARAGRAPHS
 If this research is successful, we will be able to do the following:
 \begin{enumerate}
  % OUTCOME 1 Title
  \item \textit{Synthesize written procedures into verified control logic.} 
    % Strategy
    We will develop a methodology for converting written operating procedures
    into formal specifications. These specifications will be synthesized into
    discrete control logic using reactive synthesis tools. This process uses
    structured intermediate representations to bridge natural language and
    mathematical logic. 
    % Outcome
    Control engineers will be able to generate mode-switching controllers from
    regulatory procedures with little formal methods expertise, reducing
    barriers to high-assurance control systems.
    % OUTCOME 2 Title
  \item \textit{Verify continuous control behavior across mode transitions. }
    % Strategy
    We will develop methods using reachability analysis to ensure continuous control modes 
    satisfy discrete transition requirements. 
    % Outcome
    Engineers will be able to design continuous controllers using standard
    practices while ensuring system correctness and proving mode transitions
    occur safely at the right times.
    % OUTCOME 3  Title
  \item \textit{Demonstrate autonomous reactor startup control with safety
    guarantees. }
    % Strategy
    We will implement this methodology on a small modular reactor simulation
    using industry-standard control hardware. This trial will include multiple
    coordinated control modes from cold shutdown through criticality to power
    operation on a SmAHTR reactor simulation in a hardware-in-the-loop
    experiment. 
    % Outcome
    Control engineers will be able to implement high-assurance autonomous
    controls on industrial platforms they already use, enabling users to
    achieve autonomy without retraining costs or developing new equipment.
 \end{enumerate}
 \section{State of the Art and Limits of Current Practice}
 Automation of some nuclear power operations is already performed today. Highly
 automated systems handle reactor protection and emergency core cooling, while
 human operators retain strategic decision-making. Autonomous systems are trusted
 to handle emergency situations that are considered terminal operations, but
 otherwise introduce too much risk to reactor operations. Contrary to this notion
 is the fact that 70--80\% of all nuclear power plant events are attributed to
 human error rather than equipment failures. The persistence of this ratio despite
 four decades of improvements to procedures and control rooms suggests
 fundamental cognitive limitations rather than remediable deficiencies.
 The Nuclear Regulatory Commission has recognized that introducing automation
 into the control room is the only way forward. Recent efforts to apply formal
 methods to nuclear control have shown both promise and remaining gaps. The High
 Assurance Rigorous Digital Engineering for Nuclear Safety (HARDENS) project
 represents the most advanced application to date. HARDENS produced a complete
 Reactor Trip System with full traceability from NRC requirements through formal
 specifications to verified binaries of a controller implementation. The project
 employed formal methods along the control design stack. This comprehensive
 approach demonstrated that formal methods may be technically feasible and
 economically viable for nuclear protection systems.
 But despite these accomplishments, HARDENS has a fundamental limitation directly
 relevant to our work. The project addressed only discrete digital control logic
 without modeling or verifying continuous reactor dynamics. Real reactor safety
 depends on interaction between continuous processes and discrete control
 decisions. HARDENS verified the discrete controller in isolation but not the
 closed-loop hybrid system behavior. 
 \section{Research Approach}
 This research will overcome the identified limitations by combining formal 
 methods from computer science with control theory to build hybrid control 
 systems that are correct by construction. We accomplish this through three 
 main thrusts:
 \begin{enumerate} 
  \item We will translate natural language procedures and
  requirements into temporal logic specifications using the Formal Requirements
  Elicitation Tool (FRET). 
  \item We will synthesize these temporal logic
  specifications into the discrete component of the hybrid controller using
  reactive synthesis. 
  \item We will build continuous control modes that satisfy discrete controller
  transition requirements.
 \end{enumerate}
 Commercial nuclear power operations remain manually controlled despite
 significant advances in control systems. The key insight is that procedures
 performed by human operators are highly prescriptive and well-documented. To
 formalize these procedures, we will use temporal logic, which captures system
 behaviors through temporal relations. Linear Temporal Logic provides four
 fundamental operators: next ($X$), eventually ($F$), globally ($G$), and until
 ($U$). These operators enable precise specification of time-dependent
 requirements. The most efficient path to accomplish this translation is through
 NASA's Formal Requirements Elicitation Tool (FRET). FRET employs FRETish, a
 specialized requirements language that restricts requirements to easily
 understood components while eliminating ambiguity. FRET enforces structure by
 requiring all requirements to contain six components: Scope, Condition,
 Component, Shall, Timing, and Response.
 FRET provides functionality to check realizability of a system. Realizability 
 analysis determines whether written requirements are complete by examining the 
 six structural components. Complete requirements neither conflict with one 
 another nor leave any behavior undefined. Systems that are not realizable 
 contain behavioral inconsistencies that represent the physical equivalent of 
 software bugs. Using FRET during autonomous controller development allows us 
 to identify and resolve these errors systematically. FRET exports requirements 
 in temporal logic format compatible with reactive synthesis tools, enabling 
 the second thrust of our approach.
 Reactive synthesis is an active research field focused on generating discrete 
 controllers from temporal logic specifications. The term reactive indicates 
 that the system responds to environmental inputs to produce control outputs. 
 These synthesized systems are finite in size, where each node represents a 
 unique discrete state. The connections between nodes, called state 
 transitions, specify the conditions under which the discrete controller moves 
 from state to state. This complete mapping constitutes a discrete automaton.
 We will employ reactive synthesis tools which translate linear temporal logic
 specifications into deterministic automata automatically while maximizing
 generated automata quality. Once constructed, the automaton can be
 straightforwardly implemented using standard programming control flow
 constructs. The discrete automata representation yields an important theoretical 
 guarantee. Because the discrete automaton is synthesized entirely through 
 automated tools from design requirements and operating procedures, we can 
 prove that the automaton---and therefore our hybrid switching behavior---is 
 correct by construction. 
 This correctness guarantee is paramount. Mode switching represents the primary
 responsibility of human operators in control rooms today. Human operators
 possess the advantage of real-time judgment. When mistakes occur, they can
 correct them dynamically. Autonomous control lacks this adaptive advantage. By
 synthesizing controllers from logical specifications with guaranteed
 correctness, we eliminate the possibility of switching errors.
 While discrete system components will be synthesized with correctness 
 guarantees, they represent only half of the complete system. The continuous 
 modes will be developed after discrete automaton construction, leveraging the 
 automaton structure and transitions to design multiple smaller, specialized 
 continuous controllers. 
 The discrete automaton transitions mark decision points for switching between 
 continuous control modes and define their strategic objectives. We will 
 classify three types of high-level continuous controller objectives: 
 Stabilizing modes maintain the hybrid system within its current discrete mode, 
 corresponding to steady-state normal operating modes like full-power 
 load-following control. Transitory modes have the primary goal of 
 transitioning the hybrid system from one discrete state to another, such as 
 controlled warm-up procedures. Expulsory modes are specialized transitory 
 modes with additional safety constraints that ensure the system is directed to 
 a safe stabilizing mode during failure conditions, such as reactor SCRAM.
 Building continuous modes after constructing discrete automata enables local 
 controller design focused on satisfying discrete transitions. The primary 
 challenge in hybrid system verification is ensuring global stability across 
 transitions. Current techniques struggle with this problem because dynamic 
 discontinuities complicate verification. This work alleviates these problems 
 by designing continuous controllers specifically with transitions in mind. By 
 decomposing continuous modes according to their required behavior at 
 transition points, we avoid solving trajectories through the entire hybrid 
 system.
 To ensure continuous modes satisfy their requirements, we will employ three 
 complementary techniques. Reachability analysis computes the reachable set of 
 states for a given input set. We will use reachability when continuous 
 state ranges at discrete transition boundaries are defined and verify that 
 continuous modes only can reach such defined ranges. Otherwise, assume-guarantee contracts will be 
 employed when continuous state boundaries are not explicitly defined. For any 
 given mode, the input range for reachability analysis is defined by the output 
 ranges of discrete modes that transition to it. This compositional approach 
 ensures each continuous controller is prepared for its possible input range. 
 Finally, barrier certificates will prove that mode transitions are satisfied. Control 
 barrier functions provide a method to certify safety by establishing 
 differential inequality conditions that guarantee forward invariance of safe 
 sets.
 Combining these three techniques will enable us to prove that continuous 
 components satisfy discrete requirements and thus complete system behavior. To 
 demonstrate this methodology, we will develop an autonomous startup controller 
 for a Small Modular Advanced High Temperature Reactor (SmAHTR). SmAHTR 
 represents an ideal test case with well-documented startup procedures that 
 must transition through multiple distinct operational modes: initial cold 
 conditions, controlled heating to operating temperature, approach to 
 criticality, low-power physics testing, and power ascension to full operating 
 capacity. We have access to an already developed high-fidelity SmAHTR model in Simulink that 
 captures the thermal-hydraulic and neutron kinetics behavior. 
 The synthesized hybrid controller will be implemented on an Emerson Ovation
 control system platform, which is representative of industry-standard control
 hardware. This control system will be used in a hardware-in-the-loop simulation,
 where the Advanced Reactor Cyber Analysis and Development Environment
 (ARCADE) suite will serve as the integration layer. This
 hardware-in-the-loop configuration enables validation of the controller
 implementation on actual industrial control equipment.
 \section{Metrics of Success}
 This research will be measured by advancement through Technology Readiness
 Levels, progressing from fundamental concepts to validated prototype
 demonstration. The work begins at TRL 2--3 and aims to reach TRL 5, where system
 components operate successfully in a relevant laboratory environment. TRLs
 provide the ideal success metric because they explicitly measure the gap between
 academic proof-of-concept and practical deployment. This gap is precisely what
 our work aims to bridge. TRLs capture both theoretical rigor and practical
 feasibility simultaneously. The nuclear industry already uses TRLs for
 technology assessment, making this metric directly relevant to potential
 adopters.
 Moving from current state (TRL 2--3) to target (TRL 5) requires progressing
 through component isolation, system integration, and hardware validation. By
 reaching TRL 5, we will have demonstrated a complete autonomous hybrid
 controller operating on industrial control hardware through hardware-in-the-loop
 testing. Achieving TRL 5 establishes both theoretical validity and practical
 feasibility, proving that the methodology produces verified controllers
 implementable with current technology and providing a clear pathway for nuclear
 industry adoption and broader application to safety-critical autonomous systems.
 \section{Broader Impacts}
 Nuclear power presents both a compelling application domain and an urgent 
 economic challenge. Recent interest in powering artificial intelligence 
 infrastructure has renewed focus on small modular reactors for hyperscale 
 datacenters. According to the U.S. Energy Information Administration, advanced 
 nuclear power entering service in 2027 is projected to cost \$88.24 per 
 megawatt-hour. With datacenter electricity demand projected to reach 1,050 
 terawatt-hours annually by 2030, operations and maintenance costs represent 
 approximately 23--30\% of total levelized cost, translating to \$21--28 
 billion annually for projected datacenter demand.
 This research directly addresses the multi-billion dollar O\&M cost challenge.
 Current nuclear operations require full control room staffing for each reactor.
 These staffing requirements drive high O\&M costs, particularly for smaller
 reactor designs where the same overhead must be spread across lower power
 output. The economic burden threatens the viability of next-generation nuclear
 technologies. But, by synthesizing provably correct hybrid controllers, we can
 automate routine operational sequences that currently require constant human
 oversight. This enables a change from direct operator control to
 supervisory monitoring where operators oversee multiple autonomous reactors
 rather than manually controlling individual units. The transition fundamentally
 changes the economics of nuclear operations.
 The correct-by-construction methodology is critical for this transition. 
 Traditional automation approaches cannot provide sufficient safety guarantees 
 for nuclear applications where regulatory requirements and public safety 
 concerns demand the highest levels of assurance. By formally verifying both 
 discrete mode-switching logic and continuous control behavior, this research 
 will produce controllers with mathematical proofs of correctness. These 
 guarantees enable automation to safely handle routine operations that 
 currently require human operators to follow written procedures.
 Beyond nuclear applications, this research will establish a generalizable
 framework for autonomous control of safety-critical systems. The methodology of
 translating operational procedures into formal specifications, synthesizing
 discrete switching logic, and verifying continuous mode behavior applies to any
 hybrid system with documented operational requirements. Potential applications
 include chemical process control, aerospace systems, and autonomous
 transportation. These domains share similar economic and safety considerations
 that favor increased autonomy with provable correctness guarantees. By
 demonstrating this approach in nuclear power this research will establish both
 technical feasibility and regulatory pathways for broader adoption across
 critical infrastructure.
 \newpage
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