{"id":"https://openalex.org/W2137740230","doi":"https://doi.org/10.1109/cdc.2010.5717665","title":"Discrete Hamilton-Jacobi theory and discrete optimal control","display_name":"Discrete Hamilton-Jacobi theory and discrete optimal control","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2137740230","doi":"https://doi.org/10.1109/cdc.2010.5717665","mag":"2137740230"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2010.5717665","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717665","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082931316","display_name":"Tomoki Ohsawa","orcid":"https://orcid.org/0000-0001-9406-132X"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tomoki Ohsawa","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, La Jolla, CA, USA","Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, 92093-0112, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, 92093-0112, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105787826","display_name":"Anthony M. Bloch","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anthony M. Bloch","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, MI, USA","Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, 48109-1043, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, 48109-1043, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047012686","display_name":"Melvin Leok","orcid":"https://orcid.org/0000-0002-8326-0830"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Melvin Leok","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, La Jolla, CA, USA","Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, 92093-0112, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, 92093-0112, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082931316"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":3.2886,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.92166629,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"5438","last_page":"5443"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.8364500999450684},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.6751131415367126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6365984678268433},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6355571746826172},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.5368329286575317},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5239589214324951},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.515217125415802},{"id":"https://openalex.org/keywords/discrete-poisson-equation","display_name":"Discrete Poisson equation","score":0.5094323754310608},{"id":"https://openalex.org/keywords/discrete-system","display_name":"Discrete system","score":0.49919772148132324},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4788210988044739},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4332270622253418},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.362583190202713},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.25524699687957764},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1686045527458191},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06879141926765442}],"concepts":[{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.8364500999450684},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.6751131415367126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6365984678268433},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6355571746826172},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.5368329286575317},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5239589214324951},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.515217125415802},{"id":"https://openalex.org/C3062749","wikidata":"https://www.wikidata.org/wiki/Q5282040","display_name":"Discrete Poisson equation","level":4,"score":0.5094323754310608},{"id":"https://openalex.org/C96314035","wikidata":"https://www.wikidata.org/wiki/Q5282062","display_name":"Discrete system","level":2,"score":0.49919772148132324},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4788210988044739},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4332270622253418},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.362583190202713},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25524699687957764},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1686045527458191},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06879141926765442},{"id":"https://openalex.org/C70615421","wikidata":"https://www.wikidata.org/wiki/Q339444","display_name":"Laplace's equation","level":3,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2010.5717665","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717665","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.170.4720","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.170.4720","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ucsd.edu/%7Emleok/pdf/OhBlLe2010_dhj.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.2320","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.2320","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ucsd.edu/%7Emleok/pdf/OhBlLe2010_dhj.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G188481304","display_name":"CAREER: Computational Geometric Mechanics: Foundations, Computation, and Applications","funder_award_id":"1010687","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2787541785","display_name":null,"funder_award_id":"DMS-0726263","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4547775278","display_name":null,"funder_award_id":"DMS-1010687","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4617287987","display_name":"Dynamics and Control of Nonholonomic and Quantum Systems","funder_award_id":"0907949","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6801668122","display_name":"Computational Geometric Mechanics and its Applications to Geometric Control Theory","funder_award_id":"0726263","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7818882944","display_name":null,"funder_award_id":"DMS-0907949","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W52863450","https://openalex.org/W1482909360","https://openalex.org/W1486629500","https://openalex.org/W1500910471","https://openalex.org/W1524590822","https://openalex.org/W1540059687","https://openalex.org/W1569339351","https://openalex.org/W1988645344","https://openalex.org/W1994246733","https://openalex.org/W2003161517","https://openalex.org/W2016372951","https://openalex.org/W2023242456","https://openalex.org/W2086963403","https://openalex.org/W2110504905","https://openalex.org/W2112197455","https://openalex.org/W2126479355","https://openalex.org/W2144582735","https://openalex.org/W2146354864","https://openalex.org/W2170039048","https://openalex.org/W2331739408","https://openalex.org/W2618385486","https://openalex.org/W3038698521","https://openalex.org/W3097976696","https://openalex.org/W3135593729","https://openalex.org/W3207782042","https://openalex.org/W4285719527","https://openalex.org/W6603426297","https://openalex.org/W6630125883","https://openalex.org/W6632438093","https://openalex.org/W6634018283","https://openalex.org/W6738488870","https://openalex.org/W6780363903","https://openalex.org/W6980371487"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W1563296412","https://openalex.org/W2127238600","https://openalex.org/W2096105566","https://openalex.org/W2114791549","https://openalex.org/W16457797","https://openalex.org/W2792258377","https://openalex.org/W1530596433"],"abstract_inverted_index":{"We":[0,47,91],"develop":[1],"a":[2,37,110],"discrete":[3,12,17,21,28,38,49,71,80,97,105],"analogue":[4,39],"of":[5,11,40,51,59],"Hamilton-Jacobi":[6,18,45,56,62],"theory":[7,95],"in":[8,23,79],"the":[9,44,55,60,70,86,94,104],"framework":[10],"Hamiltonian":[13,31,99],"mechanics.":[14],"The":[15,25],"resulting":[16],"equation":[19,57,107],"is":[20],"only":[22],"time.":[24],"correspondence":[26],"between":[27],"and":[29,58,75,101],"continuous":[30],"mechanics":[32],"naturally":[33],"gives":[34],"rise":[35],"to":[36,43,54,69,96],"Jacobi's":[41,52],"solution":[42,53],"equation.":[46],"prove":[48],"analogues":[50],"geometric":[61],"theorem.":[63],"These":[64],"results":[65,78],"are":[66],"readily":[67],"applied":[68],"optimal":[72,81],"control":[73,82],"setting,":[74],"some":[76],"well-known":[77],"theory,":[83],"such":[84],"as":[85,109],"Bellman":[87],"equation,":[88],"follow":[89],"immediately.":[90],"also":[92],"apply":[93],"linear":[98],"systems,":[100],"show":[102],"that":[103],"Riccati":[106],"follows":[108],"special":[111],"case.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
