# ECE 821: Optimal Control and Variational Methods | UW–Madison [View on UW Courses](https://uwcourses.com/courses/ECE_821) ## Dataset ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ### repository twangodev/uwcourses ### schema version 6 ### importer version 7 ### projection id 94468b7d4154126ca413937bb4738a6d21e0c2277f6fa397a6078ad80a32384f ### observed at 2026-09-07T15:55:43.033547+00:00 ### built at 2026-09-10T23:19:01.870283+00:00 ### courses 8951 ### current instructors 5754 ### limited false ### terms * 1272 * 1264 * 1262 * 1254 * 1252 * 1244 * 1242 * 1234 * 1232 * 1224 * 1222 * 1212 * 1204 * 1202 * 1194 * 1192 * 1184 * 1182 * 1174 * 1172 * 1164 * 1162 * 1154 * 1152 * 1144 * 1142 * 1134 * 1132 * 1124 * 1122 * 1114 * 1112 * 1104 * 1102 * 1094 * 1092 * 1084 * 1082 * 1074 * 1072 ### term 1272 ### departments | subject | count | | --------- | ----- | | AAE | 90 | | ABT | 20 | | ACCTIS | 36 | | ACTSCI | 14 | | AFAERO | 10 | | AFRICAN | 87 | | AFROAMER | 71 | | AGROECOL | 21 | | AMERIND | 53 | | ANAT\&PHY | 7 | | ANATOMY | 2 | | ANESTHES | 8 | | ANSCI | 57 | | ANTHRO | 95 | | ART | 125 | | ARTED | 10 | | ARTHIST | 121 | | ASIALANG | 129 | | ASIAN | 109 | | ASIANAM | 28 | | ASTRON | 38 | | ATMOCN | 69 | | BIOCHEM | 51 | | BIOCORE | 10 | | BIOLOGY | 14 | | BIOMDSCI | 18 | | BME | 66 | | BMI | 41 | | BMOLCHEM | 10 | | BOTANY | 69 | | BSE | 44 | | C\&ESOC | 73 | | CBE | 48 | | CHEM | 101 | | CHICLA | 52 | | CIVENGR | 133 | | CLASSICS | 47 | | CNP | 10 | | CNSRSCI | 50 | | COMARTS | 137 | | COMPBIO | 15 | | COMPLIT | 11 | | COMPSCI | 138 | | COUNPSY | 78 | | CRB | 19 | | CS\&D | 71 | | CSCS | 40 | | CURRIC | 193 | | DANCE | 93 | | DERM | 8 | | DS | 88 | | DYSCI | 35 | | ECE | 155 | | ECON | 145 | | EDPOL | 114 | | EDPSYCH | 97 | | ELPA | 70 | | EMA | 53 | | EMERMED | 17 | | ENGL | 206 | | ENTOM | 40 | | ENVIRST | 148 | | EP | 15 | | EPD | 67 | | ESL | 16 | | F\&WECOL | 60 | | FAMMED | 22 | | FINANCE | 50 | | FOLKLORE | 40 | | FOODSCI | 43 | | FRENCH | 63 | | GEN\&WS | 145 | | GENBUS | 72 | | GENECSLR | 17 | | GENETICS | 60 | | GEOG | 113 | | GEOSCI | 83 | | GERMAN | 82 | | GLE | 48 | | GNS | 38 | | GREEK | 27 | | HDFS | 41 | | HEBR-BIB | 13 | | HEBR-MOD | 10 | | HISTORY | 233 | | HISTSCI | 56 | | HONCOL | 13 | | ILS | 43 | | INFOSYS | 9 | | INTEGART | 7 | | INTEGSCI | 22 | | INTER-AG | 18 | | INTER-HE | 11 | | INTER-LS | 22 | | INTEREGR | 16 | | INTLBUS | 21 | | INTLST | 50 | | ISYE | 83 | | ITALIAN | 53 | | JEWISH | 56 | | JOURN | 88 | | KINES | 128 | | LACIS | 26 | | LANDARC | 61 | | LATIN | 24 | | LAW | 120 | | LEGALST | 48 | | LINGUIS | 35 | | LIS | 89 | | LITTRANS | 78 | | LSC | 52 | | M\&ENVTOX | 7 | | MARKETNG | 62 | | MATH | 153 | | MDGENET | 8 | | ME | 130 | | MEDHIST | 43 | | MEDICINE | 60 | | MEDIEVAL | 32 | | MEDPHYS | 39 | | MEDSC-M | 29 | | MEDSC-V | 41 | | MHR | 68 | | MICROBIO | 45 | | MILSCI | 16 | | MM\&I | 22 | | MOLBIOL | 6 | | MS\&E | 59 | | MUSIC | 165 | | MUSPERF | 126 | | NAVSCI | 20 | | NE | 44 | | NEURODPT | 11 | | NEUROL | 7 | | NEURSURG | 4 | | NTP | 11 | | NURSING | 111 | | NUTRSCI | 65 | | OBS\&GYN | 18 | | OCCTHER | 39 | | ONCOLOGY | 14 | | OPHTHALM | 5 | | OTM | 43 | | PATH | 34 | | PATH-BIO | 29 | | PEDIAT | 26 | | PHARMACY | 31 | | PHILOS | 77 | | PHMCOL-M | 11 | | PHMPRAC | 45 | | PHMSCI | 60 | | PHYASST | 37 | | PHYSICS | 88 | | PHYSIOL | 3 | | PHYTHER | 37 | | PLANTSCI | 52 | | PLPATH | 35 | | POLISCI | 192 | | POPHLTH | 58 | | PORTUG | 33 | | PSYCH | 101 | | PSYCHIAT | 22 | | PUBAFFR | 54 | | PUBLHLTH | 23 | | RADIOL | 11 | | REALEST | 41 | | RELIGST | 90 | | RHABMED | 9 | | RMI | 24 | | RP\&SE | 102 | | S\&APHM | 17 | | SCANDST | 73 | | SLAVIC | 89 | | SOC | 149 | | SOCWORK | 87 | | SOILSCI | 46 | | SPANISH | 83 | | SRMED | 21 | | STAT | 94 | | STDYABRD | 52 | | STS | 8 | | SURGERY | 25 | | SURGSCI | 33 | | THEATRE | 91 | | URBRPL | 60 | | UROLOGY | 5 | | ZOOLOGY | 89 | ## course ### run id 20260907T155543-ce3781c4 ### semester 1272 ### observed at 2026-09-07 15:55:43.033547+00:00 ### record version id a3ed327c319a479297f95775f60b9c6d71659525c462c1fb9104266ddf2137c3 ### course id ECE 821 ### course uid course\_0b5ddbb0be4809d2ebe83f84 ### catalog version id abc9f93a06bad1dc6ba99675fe9b48bf1224fe8268780c54860081de4151ed71 ### course number 821 ### subjects * ECE ### title OPTIMAL CONTROL AND VARIATIONAL METHODS ### description Variational principles in optimization and optimal control, constrained control and reachability analysis, stability of optimal control, data-driven methods for optimal control. Knowledge of linear systems \[such asE C E 717] strongly encouraged. ### requirements text Graduate/professional standing ### credit offering ids None recorded. ### llm job id enrich-8b774950c2b6adfdc46d1b82 ### llm output id ec25fef159f7e1d296aa4e972961fd34c8219578151117cba61ef034b1167ad8 ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary Covers variational principles, constrained control, reachability, stability, and data-driven methods in optimal control. ### llm topics * Variational principles in optimization * Constrained control and reachability analysis * Stability of optimal control * Data-driven methods for optimal control ### llm skills * Applying variational principles to optimization problems * Performing constrained control and reachability analysis * Analyzing stability in optimal control systems * Implementing data-driven methods for optimal control ### llm assumed background * Linear systems theory and linear algebra fundamentals * Linear systems analysis ### llm search phrases * optimal control variational methods * ECE 821 optimal control * data-driven optimal control * reachability analysis control ### llm requirements status valid ### llm student summary status valid ### llm experience status insufficient\_evidence ### catalog variants None recorded. ### student summary #### context hash 6feeb8df98a7134553fba335644965768849a26b76ec255e869f05ff5b622978 #### course id ECE 821 #### current instructors None recorded. #### difficulty workload None recorded. #### errors None recorded. #### historical context None recorded. #### message No course-specific reviews available #### offered false #### profile hash 5cb4dabf887cdbcd8c00d5a1312e10828b95c63f30bc3ea76aea199565390d02 #### quick take Recent recorded grades — Spring 2013: 3.50 GPA, 50.0% A/AB (n=8 letter grades); Spring 2024: 3.69 GPA, 94.4% A/AB (n=18 letter grades); Spring 2026: 3.68 GPA, 92.9% A/AB (n=14 letter grades). ```json { "citations": [ { "course_id": "ECE 821", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "3fdc797c-3be5-3f62-9b18-02dd32f6bb5b", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1134", "type": "grade" }, { "course_id": "ECE 821", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "3fdc797c-3be5-3f62-9b18-02dd32f6bb5b", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1244", "type": "grade" }, { "course_id": "ECE 821", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "3fdc797c-3be5-3f62-9b18-02dd32f6bb5b", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1264", "type": "grade" } ] } ``` #### student experience None recorded. #### task hash 74fb0997943e888960bbc9e47db8c4fd12e4292d55c20509d8d89db6a9910f68 #### teaching history None recorded. #### term id 1272 #### term name 2026 Fall #### version 2 ### requirements #### nodes ```json [ { "children": [], "condition": "Graduate/professional standing", "course": null, "evidence": "Graduate/professional standing", "id": "n0", "kind": "condition" } ] ``` #### notes None recorded. #### root n0 #### status parsed ### instructors None recorded. ### offerings None recorded. ### sections None recorded. ### grade instructors ```json [ { "instructor_uid": "instructor_38bc1e3798ef85a6222c29c4", "source": "madgrades", "source_instructor_id": "315620", "identity_basis": "source_id", "identity_status": "source_identified", "name": "J. 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DANIEL COBB" ], "a": 4, "ab": 1, "b": 2, "bc": 1, "c": 0, "d": 0, "f": 0, "satisfactory": 1, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 9, "source_aliases": [ "ECE 821" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "ECE 821", "course_uid": "course_0b5ddbb0be4809d2ebe83f84", "term_id": "1134", "term_name": "Spring 2013", "instructors": [ "J. DANIEL COBB" ], "a": 4, "ab": 0, "b": 4, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 8, "source_aliases": [ "ECE 821" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "ECE 821", "course_uid": "course_0b5ddbb0be4809d2ebe83f84", "term_id": "1232", "term_name": "Fall 2022", "instructors": [ "Paul Milenkovic" ], "a": 0, "ab": 0, "b": 0, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 0, "source_aliases": [ "ECE 821" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "ECE 821", "course_uid": "course_0b5ddbb0be4809d2ebe83f84", "term_id": "1244", "term_name": "Spring 2024", "instructors": [ "Jeremy Coulson" ], "a": 8, "ab": 9, "b": 1, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 18, "source_aliases": [ "ECE 821" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "ECE 821", "course_uid": "course_0b5ddbb0be4809d2ebe83f84", "term_id": "1264", "term_name": "Spring 2026", "instructors": [ "Jeremy Coulson" ], "a": 6, "ab": 7, "b": 1, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 14, "source_aliases": [ "ECE 821" ] } ] ``` ### statistics #### gpa 3.625 #### graded 48 #### counts * 22 * 17 * 8 * 1 * 0 * 0 * 0 ### grade conflicts None recorded. ### evidence #### history * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_0b5ddbb0be4809d2ebe83f84-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_0b5ddbb0be4809d2ebe83f84-0.json) #### traces * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_0b5ddbb0be4809d2ebe83f84-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_0b5ddbb0be4809d2ebe83f84-0.json) #### results * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_0b5ddbb0be4809d2ebe83f84-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_0b5ddbb0be4809d2ebe83f84-0.json) ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ## context ### all #### term #### gpa 3.625 #### count 48 #### university ##### size 3199 ##### gpa Percentile 41 ##### count Percentile 24 ##### median Count 87 ##### histogram | range | count | current | | ------- | ----- | ------- | | 0.0–0.4 | 0 | false | | 0.4–0.8 | 0 | false | | 0.8–1.2 | 0 | false | | 1.2–1.6 | 0 | false | | 1.6–2.0 | 0 | false | | 2.0–2.4 | 0 | false | | 2.4–2.8 | 19 | false | | 2.8–3.2 | 299 | false | | 3.2–3.6 | 916 | false | | 3.6–4.0 | 1965 | true | #### departments ```json [ { "subject": "ECE", "comparison": { "size": 89, "gpaPercentile": 55, "countPercentile": 22, "medianCount": 94, "histogram": [ { "range": "0.0–0.4", "count": 0, "current": false }, { "range": "0.4–0.8", "count": 0, "current": false }, { "range": "0.8–1.2", "count": 0, "current": false }, { "range": "1.2–1.6", "count": 0, "current": false }, { "range": "1.6–2.0", "count": 0, "current": false }, { "range": "2.0–2.4", "count": 0, "current": false }, { "range": "2.4–2.8", "count": 2, "current": false }, { "range": "2.8–3.2", "count": 8, "current": false }, { "range": "3.2–3.6", "count": 36, "current": false }, { "range": "3.6–4.0", "count": 43, "current": true } ] } } ] ``` ### terms #### 1074 ##### term 1074 ##### gpa 3.5 ##### count 8 ##### departments | subject | comparison | | ------- | ---------- | | ECE | | #### 1134 ##### term 1134 ##### gpa 3.5 ##### count 8 ##### departments | subject | comparison | | ------- | ---------- | | ECE | | #### 1244 ##### term 1244 ##### gpa 3.6944444444444446 ##### count 18 ##### departments | subject | comparison | | ------- | ---------- | | ECE | | #### 1264 ##### term 1264 ##### gpa 3.6785714285714284 ##### count 14 ##### departments | subject | comparison | | ------- | ---------- | | ECE | | ### benchmarks #### all ##### school ###### size 3199 ###### gpa 3.6363810191629713 ###### top Share 80.53066858843856 ###### count 87 ##### ECE ###### size 89 ###### gpa 3.5424490731549536 ###### top Share 75.06154372508729 ###### count 94 #### terms ##### 1074 ###### school ###### size 695 ###### gpa 3.3616924722887376 ###### top Share 63.22509110105764 ###### count 69 ###### ECE ###### size 20 ###### gpa 3.110370466319829 ###### top Share 50.72606982804236 ###### count 46 ##### 1134 ###### school ###### size 852 ###### gpa 3.4138934207568203 ###### top Share 66.35946578182744 ###### count 66 ###### ECE ###### size 26 ###### gpa 3.3422063178165016 ###### top Share 62.38776016208119 ###### count 69 ##### 1232 ###### school ###### size 1216 ###### gpa 3.575457431972425 ###### top Share 77.33712216234007 ###### count 66 ###### ECE ###### size 44 ###### gpa 3.4583903966894223 ###### top Share 70.01102622146537 ###### count 70 ##### 1244 ###### school ###### size 1241 ###### gpa 3.5975573126929192 ###### top Share 78.29036874847135 ###### count 65 ###### ECE ###### size 38 ###### gpa 3.554019248602149 ###### top Share 75.22296238620345 ###### count 83.5 ##### 1264 ###### school ###### size 1283 ###### gpa 3.6229729166451925 ###### top Share 80.13669149396227 ###### count 66 ###### ECE ###### size 45 ###### gpa 3.5814138447018746 ###### top Share 77.53027985486403 ###### count 73 ## instructor Trends ```json [ { "uid": "instructor_821a000fde9fc8e085416f24", "name": "JEREMY COULSON", "count": 32, "terms": [ { "term": "1244", "count": 18, "sections": 1, "gpa": 3.6944444444444446 }, { "term": "1264", "count": 14, "sections": 1, "gpa": 3.6785714285714284 } ] }, { "uid": "instructor_38bc1e3798ef85a6222c29c4", "name": "J. DANIEL COBB", "count": 16, "terms": [ { "term": "1074", "count": 8, "sections": 1, "gpa": 3.5 }, { "term": "1134", "count": 8, "sections": 1, "gpa": 3.5 } ] } ] ``` ## following None recorded.