From cbc24672193492b4603a2235abf910f39455e422 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Tue, 10 Mar 2026 17:17:50 -0400 Subject: [PATCH] fixed edit mode --- 3-research-approach/approach.tex | 4 +- main.aux | 168 ++++-------------- main.blg | 16 +- main.fdb_latexmk | 29 ++-- main.fls | 10 +- main.log | 287 ++++++------------------------- main.pdf | Bin 199129 -> 184723 bytes main.tex | 2 +- main.toc | 46 ++--- 9 files changed, 136 insertions(+), 426 deletions(-) diff --git a/3-research-approach/approach.tex b/3-research-approach/approach.tex index ea290ea..1a056f0 100644 --- a/3-research-approach/approach.tex +++ b/3-research-approach/approach.tex @@ -427,11 +427,11 @@ reachable within time horizon $T$: \text{Reach}(\mathcal{X}_{entry}, f_i, [0,T]) \cap \mathcal{X}_{exit} \neq \emptyset \] -\textcolor{blue}{Because the discrete controller defines clear boundaries in continuous state +Because the discrete controller defines clear boundaries in continuous state space, the verification problem for each transitory mode is well-posed. We know the possible initial conditions, we know the target conditions, and we know the safety envelope. The verification task is to confirm that the candidate -continuous controller achieves the objective from all possible starting points.} +continuous controller achieves the objective from all possible starting points. Several tools exist for computing reachable sets of hybrid systems, including CORA, Flow*, SpaceEx, and JuliaReach. 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{subsection}{\numberline {2.2}Human Factors in Nuclear Accidents}{4}{}% -\contentsline {subsection}{\numberline {2.3}Formal Methods}{5}{}% -\contentsline {subsubsection}{\numberline {2.3.1}HARDENS}{5}{}% -\contentsline {subsubsection}{\numberline {2.3.2}Sequent Calculus and Differential Dynamic Logic}{6}{}% -\contentsline {section}{\numberline {3}Research Approach}{8}{}% -\contentsline {subsection}{\numberline {3.1}System Requirements, Specifications, and Discrete Controllers}{9}{}% -\contentsline {subsection}{\numberline {3.2}Continuous Control Modes}{13}{}% -\contentsline {subsubsection}{\numberline {3.2.1}Transitory Modes}{14}{}% -\contentsline {subsubsection}{\numberline {3.2.2}Stabilizing Modes}{15}{}% -\contentsline {subsubsection}{\numberline {3.2.3}Expulsory Modes}{16}{}% -\contentsline {subsection}{\numberline {3.3}Industrial Implementation}{17}{}% -\contentsline {section}{\numberline {4}Metrics for Success}{18}{}% -\contentsline {paragraph}{TRL 3 \textit {Critical Function and Proof of Concept}}{18}{}% -\contentsline {paragraph}{TRL 4 \textit {Laboratory Testing of Integrated Components}}{18}{}% -\contentsline {paragraph}{TRL 5 \textit {Laboratory Testing in Relevant Environment}}{19}{}% -\contentsline {section}{\numberline {5}Risks and Contingencies}{20}{}% -\contentsline {subsection}{\numberline {5.1}Computational Tractability of Synthesis}{20}{}% -\contentsline {subsection}{\numberline {5.2}Discrete-Continuous Interface Formalization}{20}{}% -\contentsline {subsection}{\numberline {5.3}Procedure Formalization Completeness}{22}{}% -\contentsline {section}{\numberline {6}Broader Impacts}{24}{}% -\contentsline {section}{\numberline {7}Schedule, Milestones, and Deliverables}{26}{}% -\contentsline {subsection}{\numberline {7.1}Milestones and Deliverables}{26}{}% -\contentsline {section}{References}{27}{}% +\contentsline {subsection}{\numberline {2.2}Human Factors in Nuclear Accidents}{3}{}% +\contentsline {subsection}{\numberline {2.3}Formal Methods}{4}{}% +\contentsline {subsubsection}{\numberline {2.3.1}HARDENS}{4}{}% +\contentsline {subsubsection}{\numberline {2.3.2}Sequent Calculus and Differential Dynamic Logic}{5}{}% +\contentsline {section}{\numberline {3}Research Approach}{7}{}% +\contentsline {subsection}{\numberline {3.1}System Requirements, Specifications, and Discrete Controllers}{8}{}% +\contentsline {subsection}{\numberline {3.2}Continuous Control Modes}{11}{}% +\contentsline {subsubsection}{\numberline {3.2.1}Transitory Modes}{12}{}% +\contentsline {subsubsection}{\numberline {3.2.2}Stabilizing Modes}{12}{}% +\contentsline {subsubsection}{\numberline {3.2.3}Expulsory Modes}{13}{}% +\contentsline {subsection}{\numberline {3.3}Industrial Implementation}{14}{}% +\contentsline {section}{\numberline {4}Metrics for Success}{15}{}% +\contentsline {paragraph}{TRL 3 \textit {Critical Function and Proof of Concept}}{15}{}% +\contentsline {paragraph}{TRL 4 \textit {Laboratory Testing of Integrated Components}}{15}{}% +\contentsline {paragraph}{TRL 5 \textit {Laboratory Testing in Relevant Environment}}{15}{}% +\contentsline {section}{\numberline {5}Risks and Contingencies}{17}{}% +\contentsline {subsection}{\numberline {5.1}Computational Tractability of Synthesis}{17}{}% +\contentsline {subsection}{\numberline {5.2}Discrete-Continuous Interface Formalization}{17}{}% +\contentsline {subsection}{\numberline {5.3}Procedure Formalization Completeness}{18}{}% +\contentsline {section}{\numberline {6}Broader Impacts}{20}{}% +\contentsline {section}{\numberline {7}Schedule, Milestones, and Deliverables}{22}{}% +\contentsline {subsection}{\numberline {7.1}Milestones and Deliverables}{22}{}% +\contentsline {section}{References}{23}{}%