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M  .task/backlog.data

M  .task/pending.data

M  .task/undo.data

M  Writing/ERLM/dane_proposal_format.cls

M  Writing/ERLM/main.aux

M  Writing/ERLM/main.fdb_latexmk

M  Writing/ERLM/main.fls

M  Writing/ERLM/main.log
This commit is contained in:
Dane Sabo 2025-09-14 22:04:41 -04:00
parent 7009f1a3d6
commit 1c1f398df7
11 changed files with 104 additions and 97 deletions
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1
.task/backlog.data
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@ -33,3 +33,4 @@
{"description":"Read Branicky Lyapunov paper","entry":"20250911T183429Z","modified":"20250911T201816Z","project":"Thesis","status":"pending","uuid":"f4d32147-ec74-4f68-b8d5-146c0b6f35df","tags":["reading"]} {"description":"Read Branicky Lyapunov paper","entry":"20250911T183429Z","modified":"20250911T201816Z","project":"Thesis","status":"pending","uuid":"f4d32147-ec74-4f68-b8d5-146c0b6f35df","tags":["reading"]}
{"description":"Write zettel about lipschitz continuity","entry":"20250911T211029Z","modified":"20250911T211029Z","status":"pending","uuid":"b7f68988-8c06-4d18-bf77-91d7e39fd55f","tags":["zk"]} {"description":"Write zettel about lipschitz continuity","entry":"20250911T211029Z","modified":"20250911T211029Z","status":"pending","uuid":"b7f68988-8c06-4d18-bf77-91d7e39fd55f","tags":["zk"]}
{"description":"Read Branicky Lyapunov paper","end":"20250911T214953Z","entry":"20250911T183429Z","modified":"20250911T214953Z","project":"Thesis","status":"completed","uuid":"f4d32147-ec74-4f68-b8d5-146c0b6f35df","tags":["reading"]} {"description":"Read Branicky Lyapunov paper","end":"20250911T214953Z","entry":"20250911T183429Z","modified":"20250911T214953Z","project":"Thesis","status":"completed","uuid":"f4d32147-ec74-4f68-b8d5-146c0b6f35df","tags":["reading"]}
{"description":"Write first draft of state of the art","due":"20250912T040000Z","entry":"20250909T203258Z","modified":"20250915T003655Z","project":"ERLM","start":"20250915T003655Z","status":"pending","uuid":"4bec1530-18bc-43cb-9f0b-61e35dbf1730","tags":["writing"],"depends":["8e7a8e19-9197-4008-b7d9-521ffcf7ba91","96c76e6b-5c33-4f54-a156-5c59e718f01a","f4d32147-ec74-4f68-b8d5-146c0b6f35df"]}

2
.task/pending.data
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@ -2,7 +2,7 @@
[description:"Write zettels about webofscience database" entry:"1757443242" modified:"1757443242" project:"zk" status:"pending" uuid:"9cb17c85-f1e6-4280-86da-a5af8f229b15"] [description:"Write zettels about webofscience database" entry:"1757443242" modified:"1757443242" project:"zk" status:"pending" uuid:"9cb17c85-f1e6-4280-86da-a5af8f229b15"]
[description:"Look over obsidian tasks and see if anything is worth moving over" entry:"1757443262" modified:"1757443262" status:"pending" tags:"taskwarrior" tags_taskwarrior:"x" uuid:"c1a5390d-5b84-4f9c-8acb-ffb970682660"] [description:"Look over obsidian tasks and see if anything is worth moving over" entry:"1757443262" modified:"1757443262" status:"pending" tags:"taskwarrior" tags_taskwarrior:"x" uuid:"c1a5390d-5b84-4f9c-8acb-ffb970682660"]
[description:"Look around for summer internships with national labs" entry:"1757449731" modified:"1757449731" status:"pending" uuid:"d3f3dc53-4feb-4b7e-8de5-86ebf3c535d5"] [description:"Look around for summer internships with national labs" entry:"1757449731" modified:"1757449731" status:"pending" uuid:"d3f3dc53-4feb-4b7e-8de5-86ebf3c535d5"]
[dep_8e7a8e19-9197-4008-b7d9-521ffcf7ba91:"x" dep_96c76e6b-5c33-4f54-a156-5c59e718f01a:"x" dep_f4d32147-ec74-4f68-b8d5-146c0b6f35df:"x" depends:"8e7a8e19-9197-4008-b7d9-521ffcf7ba91,96c76e6b-5c33-4f54-a156-5c59e718f01a,f4d32147-ec74-4f68-b8d5-146c0b6f35df" description:"Write first draft of state of the art" due:"1757649600" entry:"1757449978" modified:"1757885608" project:"ERLM" status:"pending" tags:"writing" tags_writing:"x" uuid:"4bec1530-18bc-43cb-9f0b-61e35dbf1730"] [dep_8e7a8e19-9197-4008-b7d9-521ffcf7ba91:"x" dep_96c76e6b-5c33-4f54-a156-5c59e718f01a:"x" dep_f4d32147-ec74-4f68-b8d5-146c0b6f35df:"x" depends:"8e7a8e19-9197-4008-b7d9-521ffcf7ba91,96c76e6b-5c33-4f54-a156-5c59e718f01a,f4d32147-ec74-4f68-b8d5-146c0b6f35df" description:"Write first draft of state of the art" due:"1757649600" entry:"1757449978" modified:"1757896615" project:"ERLM" start:"1757896615" status:"pending" tags:"writing" tags_writing:"x" uuid:"4bec1530-18bc-43cb-9f0b-61e35dbf1730"]
[description:"get FSAE COM and track data to Matt barry for statics problem. He also wants a cad model?" due:"1758254400" entry:"1757515988" modified:"1757515988" status:"pending" uuid:"48f997bf-b686-4c0b-bee5-ac8e5f874ad9"] [description:"get FSAE COM and track data to Matt barry for statics problem. He also wants a cad model?" due:"1758254400" entry:"1757515988" modified:"1757515988" status:"pending" uuid:"48f997bf-b686-4c0b-bee5-ac8e5f874ad9"]
[description:"Read Opportunities, Challenges, and Research Needs for Remote Microreactor Operations" entry:"1757516723" modified:"1757516723" project:"Thesis" status:"pending" tags:"reading" tags_reading:"x" uuid:"96c76e6b-5c33-4f54-a156-5c59e718f01a"] [description:"Read Opportunities, Challenges, and Research Needs for Remote Microreactor Operations" entry:"1757516723" modified:"1757516723" project:"Thesis" status:"pending" tags:"reading" tags_reading:"x" uuid:"96c76e6b-5c33-4f54-a156-5c59e718f01a"]
[description:"Write zettel about lipschitz continuity" entry:"1757625029" modified:"1757625029" status:"pending" tags:"zk" tags_zk:"x" uuid:"b7f68988-8c06-4d18-bf77-91d7e39fd55f"] [description:"Write zettel about lipschitz continuity" entry:"1757625029" modified:"1757625029" status:"pending" tags:"zk" tags_zk:"x" uuid:"b7f68988-8c06-4d18-bf77-91d7e39fd55f"]

4
.task/undo.data
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@ -116,3 +116,7 @@ time 1757627393
old [description:"Read Branicky Lyapunov paper" entry:"1757615669" modified:"1757621896" project:"Thesis" status:"pending" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"] old [description:"Read Branicky Lyapunov paper" entry:"1757615669" modified:"1757621896" project:"Thesis" status:"pending" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"]
new [description:"Read Branicky Lyapunov paper" end:"1757627393" entry:"1757615669" modified:"1757627393" project:"Thesis" status:"completed" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"] new [description:"Read Branicky Lyapunov paper" end:"1757627393" entry:"1757615669" modified:"1757627393" project:"Thesis" status:"completed" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"]
--- ---
time 1757896615
old [dep_8e7a8e19-9197-4008-b7d9-521ffcf7ba91:"x" dep_96c76e6b-5c33-4f54-a156-5c59e718f01a:"x" dep_f4d32147-ec74-4f68-b8d5-146c0b6f35df:"x" depends:"8e7a8e19-9197-4008-b7d9-521ffcf7ba91,96c76e6b-5c33-4f54-a156-5c59e718f01a,f4d32147-ec74-4f68-b8d5-146c0b6f35df" description:"Write first draft of state of the art" due:"1757649600" entry:"1757449978" modified:"1757885608" project:"ERLM" status:"pending" tags:"writing" tags_writing:"x" uuid:"4bec1530-18bc-43cb-9f0b-61e35dbf1730"]
new [dep_8e7a8e19-9197-4008-b7d9-521ffcf7ba91:"x" dep_96c76e6b-5c33-4f54-a156-5c59e718f01a:"x" dep_f4d32147-ec74-4f68-b8d5-146c0b6f35df:"x" depends:"8e7a8e19-9197-4008-b7d9-521ffcf7ba91,96c76e6b-5c33-4f54-a156-5c59e718f01a,f4d32147-ec74-4f68-b8d5-146c0b6f35df" description:"Write first draft of state of the art" due:"1757649600" entry:"1757449978" modified:"1757896615" project:"ERLM" start:"1757896615" status:"pending" tags:"writing" tags_writing:"x" uuid:"4bec1530-18bc-43cb-9f0b-61e35dbf1730"]
---

2
Writing/ERLM/dane_proposal_format.cls
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@ -2,7 +2,7 @@
\ProvidesClass{prayer_circle}[2025/09/02 Custom class for academic documents] \ProvidesClass{prayer_circle}[2025/09/02 Custom class for academic documents]
% Pass options and load base class % Pass options and load base class
\PassOptionsToClass{10pt,titlepage}{article} \PassOptionsToClass{11pt,titlepage}{article}
\LoadClass{article} \LoadClass{article}
% Core packages % Core packages

8
Writing/ERLM/main.aux
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@ -2,10 +2,10 @@
\bibstyle{unsrt} \bibstyle{unsrt}
\providecommand \oddpage@label [2]{} \providecommand \oddpage@label [2]{}
\@writefile{toc}{\contentsline {section}{\numberline {1}Goals and Outcomes}{1}{}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {1}Goals and Outcomes}{1}{}\protected@file@percent }
\bibdata{references}
\@writefile{toc}{\contentsline {section}{\numberline {2}State of the art and limits of current practice}{3}{}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {2}State of the art and limits of current practice}{3}{}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Control Theory and Hybrid Systems}{3}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Control Theory and Hybrid Systems}{3}{}\protected@file@percent }
\newlabel{eq:hybrid-sys}{{2}{3}{Control Theory and Hybrid Systems}{}{}} \newlabel{eq:hybrid-sys}{{2}{3}{Control Theory and Hybrid Systems}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Formal Methods and Reactive Synthesis}{3}{}\protected@file@percent } \bibdata{references}
\@writefile{toc}{\contentsline {section}{References}{3}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Formal Methods and Reactive Synthesis}{4}{}\protected@file@percent }
\gdef \@abspage@last{4} \@writefile{toc}{\contentsline {section}{References}{4}{}\protected@file@percent }
\gdef \@abspage@last{5}

34
Writing/ERLM/main.fdb_latexmk
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@ -1,14 +1,14 @@
# Fdb version 4 # Fdb version 4
["bibtex main"] 1757866412.20829 "main.aux" "main.bbl" "main" 1757880660.67738 0 ["bibtex main"] 1757899416.09338 "main.aux" "main.bbl" "main" 1757900978.83336 0
"./references.bib" 1757866237.16684 0 d41d8cd98f00b204e9800998ecf8427e "" "./references.bib" 1757896122.21556 0 d41d8cd98f00b204e9800998ecf8427e ""
"/usr/share/texlive/texmf-dist/bibtex/bst/base/unsrt.bst" 1292289607 18030 1376b4b231b50c66211e47e42eda2875 "" "/usr/share/texlive/texmf-dist/bibtex/bst/base/unsrt.bst" 1292289607 18030 1376b4b231b50c66211e47e42eda2875 ""
"main.aux" 1757880660.60211 759 c340ead263222262cc9d66ce4adc65f5 "pdflatex" "main.aux" 1757900978.60047 759 3051c697f76ee5e29dc620b2ef1fb2b5 "pdflatex"
(generated) (generated)
"main.bbl" "main.bbl"
"main.blg" "main.blg"
(rewritten before read) (rewritten before read)
["pdflatex"] 1757880660.23063 "main.tex" "main.pdf" "main" 1757880660.67755 2 ["pdflatex"] 1757900977.5298 "main.tex" "main.pdf" "main" 1757900978.8337 0
"/etc/texmf/web2c/texmf.cnf" 1726065852.27662 475 c0e671620eb5563b2130f56340a5fde8 "" "/etc/texmf/web2c/texmf.cnf" 1722610814.59577 475 c0e671620eb5563b2130f56340a5fde8 ""
"/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc" 1165713224 4850 80dc9bab7f31fb78a000ccfed0e27cab "" "/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc" 1165713224 4850 80dc9bab7f31fb78a000ccfed0e27cab ""
"/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/adobe/helvetic/phvb7t.tfm" 1136768653 2240 eb56c13537f4d8a0bd3fafc25572b1bd "" "/usr/share/texlive/texmf-dist/fonts/tfm/adobe/helvetic/phvb7t.tfm" 1136768653 2240 eb56c13537f4d8a0bd3fafc25572b1bd ""
@ -20,15 +20,15 @@
"/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1246382020 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1246382020 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1246382020 916 f87d7c45f9c908e672703b83b72241a3 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1246382020 916 f87d7c45f9c908e672703b83b72241a3 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.tfm" 1246382020 924 9904cf1d39e9767e7a3622f2a125a565 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm" 1246382020 928 2dc8d444221b7a635bb58038579b861a "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm" 1246382020 928 2dc8d444221b7a635bb58038579b861a ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1246382020 908 2921f8a10601f252058503cc6570e581 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1246382020 908 2921f8a10601f252058503cc6570e581 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm" 1246382020 940 75ac932a52f80982a9f8ea75d03a34cf ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1246382020 940 228d6584342e91276bf566bcf9716b83 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1246382020 940 228d6584342e91276bf566bcf9716b83 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmex10.tfm" 1136768653 992 662f679a0b3d2d53c1b94050fdaa3f50 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmex10.tfm" 1136768653 992 662f679a0b3d2d53c1b94050fdaa3f50 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi10.tfm" 1136768653 1528 abec98dbc43e172678c11b3b9031252a ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi12.tfm" 1136768653 1524 4414a8315f39513458b80dfc63bff03a "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi12.tfm" 1136768653 1524 4414a8315f39513458b80dfc63bff03a ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi6.tfm" 1136768653 1512 f21f83efb36853c0b70002322c1ab3ad "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi6.tfm" 1136768653 1512 f21f83efb36853c0b70002322c1ab3ad ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi8.tfm" 1136768653 1520 eccf95517727cb11801f4f1aee3a21b4 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi8.tfm" 1136768653 1520 eccf95517727cb11801f4f1aee3a21b4 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr10.tfm" 1136768653 1296 45809c5a464d5f32c8f98ba97c1bb47f ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr12.tfm" 1136768653 1288 655e228510b4c2a1abe905c368440826 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr12.tfm" 1136768653 1288 655e228510b4c2a1abe905c368440826 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr6.tfm" 1136768653 1300 b62933e007d01cfd073f79b963c01526 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr6.tfm" 1136768653 1300 b62933e007d01cfd073f79b963c01526 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr8.tfm" 1136768653 1292 21c1c5bfeaebccffdb478fd231a0997d "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr8.tfm" 1136768653 1292 21c1c5bfeaebccffdb478fd231a0997d ""
@ -36,7 +36,7 @@
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm" 1136768653 1116 933a60c408fc0a863a92debe84b2d294 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm" 1136768653 1116 933a60c408fc0a863a92debe84b2d294 ""
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm" 1136768653 1120 8b7d695260f3cff42e636090a8002094 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm" 1136768653 1120 8b7d695260f3cff42e636090a8002094 ""
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1248133631 36299 5f9df58c2139e7edcf37c8fca4bd384d "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1248133631 36299 5f9df58c2139e7edcf37c8fca4bd384d ""
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb" 1248133631 36281 c355509802a035cadc5f15869451dcee "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi8.pfb" 1248133631 35469 70d41d2b9ea31d5d813066df7c99281c ""
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1248133631 35752 024fb6c41858982481f6968b5fc26508 "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1248133631 35752 024fb6c41858982481f6968b5fc26508 ""
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1248133631 32569 5e5ddc8df908dea60932f3c484a54c0d "" "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1248133631 32569 5e5ddc8df908dea60932f3c484a54c0d ""
"/usr/share/texlive/texmf-dist/fonts/type1/urw/helvetic/uhvb8a.pfb" 1136849748 35941 f27169cc74234d5bd5e4cca5abafaabb "" "/usr/share/texlive/texmf-dist/fonts/type1/urw/helvetic/uhvb8a.pfb" 1136849748 35941 f27169cc74234d5bd5e4cca5abafaabb ""
@ -150,7 +150,7 @@
"/usr/share/texlive/texmf-dist/tex/latex/base/article.cls" 1705352648 20144 147463a6a579f4597269ef9565205cfe "" "/usr/share/texlive/texmf-dist/tex/latex/base/article.cls" 1705352648 20144 147463a6a579f4597269ef9565205cfe ""
"/usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty" 1705352648 5319 2b738d02ce36ada6dcdd9534940db0ee "" "/usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty" 1705352648 5319 2b738d02ce36ada6dcdd9534940db0ee ""
"/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty" 1705352648 5048 425739d70251273bf93e3d51f3c40048 "" "/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty" 1705352648 5048 425739d70251273bf93e3d51f3c40048 ""
"/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo" 1705352648 8448 dbc0dbf4156c0bb9ba01a1c685d3bad0 "" "/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo" 1705352648 8464 59874a3b0776c73e2a138b025d8473dd ""
"/usr/share/texlive/texmf-dist/tex/latex/booktabs/booktabs.sty" 1579038678 6078 f1cb470c9199e7110a27851508ed7a5c "" "/usr/share/texlive/texmf-dist/tex/latex/booktabs/booktabs.sty" 1579038678 6078 f1cb470c9199e7110a27851508ed7a5c ""
"/usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty" 1425427964 26218 19edeff8cdc2bcb704e8051dc55eb5a7 "" "/usr/share/texlive/texmf-dist/tex/latex/cite/cite.sty" 1425427964 26218 19edeff8cdc2bcb704e8051dc55eb5a7 ""
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@ -31,10 +31,10 @@ In this description there are two functions: \(f(\cdot)\) and
inputs: the continuous states \(x\), the discrete state \(q\), and an optional inputs: the continuous states \(x\), the discrete state \(q\), and an optional
control input \(u\). \(f_i(\cdot)\) here is a nonlinear function, where \(q\) control input \(u\). \(f_i(\cdot)\) here is a nonlinear function, where \(q\)
changes the mode of the continuous dynamics, but is otherwise dependent on the changes the mode of the continuous dynamics, but is otherwise dependent on the
current continuous states and control input. \(\nu_i(\codt)\) can be much more current continuous states and control input. \(\nu_i(\cdot)\) can be much more
generally created. The only restriction on \(\nu_i(\codt)\) is that it must generally created. The only restriction on \(\nu_i(\cdot)\) is that it must
not create an infinite number of jumps in a finite amount of time. not create an infinite number of jumps in a finite amount of time.
\(\nu_i(\codt)\) can depend a control input \(u\), or can be \(\nu_i(\cdot)\) can depend a control input \(u\), or can be
\textit{autonomous}, where the discrete mode is defined by the system states \textit{autonomous}, where the discrete mode is defined by the system states
\(x\) and \(q\). While an autonomous system may not have a control input, that \(x\) and \(q\). While an autonomous system may not have a control input, that
does not mean the system is not controlled, as the continuous dynamics does not mean the system is not controlled, as the continuous dynamics
@ -73,3 +73,47 @@ reachability because either the computation time makes the analysis infeasible,
or the compounding approximation errors makes the analysis meaningless. or the compounding approximation errors makes the analysis meaningless.
\subsection{Formal Methods and Reactive Synthesis} \subsection{Formal Methods and Reactive Synthesis}
Hybrid systems often are realized as cyber-physical systems. Cyber-physical
systems have a computational component responsible for control of a physical
process based on live sensors and actuators. Verification of these systems has
drawn two different communities together. We have previously discussed the
engineering perspective coming from the physical control theory background, but
in this section we discuss work coming from the cyber oriented persuasion.
Many cyber systems lend themselves to a finite number of possible states. For
these systems, a map of the possible states and the transition between them can
be drawn and analyzed. This is called a \textit{finite state machine}. Finite
state machines can be easily verified, as all possible states can be
exhaustively checked to meet requirements in a process called model checking.
Model checking has been used extensively in high-assurance digital systems and
to ensure software correctness for critical systems.
In order to check correctness, requirements for these automata must be defined.
Typically this is done using a formal language such as temporal logic. Temporal
logic allows system behaviors to be defined with temporal relations and includes
four operators: next (X), eventually (F), globally (G), and until (U). With
these operators, controller specifications can be created. In a nuclear context,
one might use temporal logic to define safety behaviors of a reactor core
control system. Let's consider an example:
Suppose we are trying to write safety requirements about SCRAM behavior. In
plain English, one might say "If a high temperature alarm is triggered, the
control rods will immediately be inserted and unable to be withdrawn unless
reset by an operator." In a linear temporal logic specification, this would be
written as follows:
\begin{equation}
\mathcal{G}(HighTemp \rightarrow \mathcal{X}(RodsInserted \land (\neg
RodsWithdrawn \text{ } \mathcal{U} \text{ } OperatorReset)))
\end{equation}
A significant body of work has been done around the translation of English
requirements into temporal logic specifications. The Formal Requirements
Elicitation Tool (FRET) developed by the NASA Ames Research Center to help
bridge the gap between natural language and mathematical specification. Using
FRET, one is able to take a bulk number of near-English requirements in a
language called FRETish, and translate them automatically into linear temporal
logic specifications. From this point, it can be examined whether or not
the set of requirements define a realizable system, or if there exists conflicts
between different specifications.