{"id":"https://openalex.org/W2123744712","doi":"https://doi.org/10.1109/acc.2009.5160681","title":"Approximate solution of hyper-sensitive optimal control problems using finite-time Lyapunov analysis","display_name":"Approximate solution of hyper-sensitive optimal control problems using finite-time Lyapunov analysis","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2123744712","doi":"https://doi.org/10.1109/acc.2009.5160681","mag":"2123744712"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2009.5160681","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5160681","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","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/A5067753000","display_name":"E. Aykutlu\u011f","orcid":null},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]},{"id":"https://openalex.org/I4210140791","display_name":"Irvine University","ror":"https://ror.org/04ysmca02","country_code":"US","type":"education","lineage":["https://openalex.org/I4210140791"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erkut Aykutlug","raw_affiliation_strings":["Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA","Mechanical and Aerospace Engineering, University of California, Irvine, 92697, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA","institution_ids":["https://openalex.org/I4210140791","https://openalex.org/I204250578"]},{"raw_affiliation_string":"Mechanical and Aerospace Engineering, University of California, Irvine, 92697, USA","institution_ids":["https://openalex.org/I4210140791","https://openalex.org/I204250578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002372347","display_name":"Kenneth D. Mease","orcid":"https://orcid.org/0000-0002-5625-8233"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]},{"id":"https://openalex.org/I4210140791","display_name":"Irvine University","ror":"https://ror.org/04ysmca02","country_code":"US","type":"education","lineage":["https://openalex.org/I4210140791"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kenneth D. Mease","raw_affiliation_strings":["Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA","Mechanical and Aerospace Engineering, University of California, Irvine, 92697, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA","institution_ids":["https://openalex.org/I4210140791","https://openalex.org/I204250578"]},{"raw_affiliation_string":"Mechanical and Aerospace Engineering, University of California, Irvine, 92697, USA","institution_ids":["https://openalex.org/I4210140791","https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.17832916,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1034","last_page":"1039"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.9993000030517578,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6367239952087402},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5829214453697205},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5410453677177429},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5321865081787109},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.49860525131225586},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.47986453771591187},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4713156819343567},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.452487975358963},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.443729430437088},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4305436313152313},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4107382893562317},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37354549765586853},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3692355751991272},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.33516085147857666},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2047133445739746},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09587925672531128},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07546034455299377},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07056581974029541}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6367239952087402},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5829214453697205},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5410453677177429},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5321865081787109},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.49860525131225586},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.47986453771591187},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4713156819343567},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.452487975358963},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.443729430437088},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4305436313152313},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4107382893562317},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37354549765586853},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3692355751991272},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33516085147857666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2047133445739746},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09587925672531128},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07546034455299377},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07056581974029541},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2009.5160681","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5160681","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1019.2733","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1019.2733","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.nt.ntnu.no/users/skoge/prost/proceedings/acc09/data/papers/1318.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1512099607","https://openalex.org/W1568666422","https://openalex.org/W1576765607","https://openalex.org/W1967965813","https://openalex.org/W1989491420","https://openalex.org/W2010330390","https://openalex.org/W2012507994","https://openalex.org/W2065264928","https://openalex.org/W2069824076","https://openalex.org/W2084755618","https://openalex.org/W2100897968","https://openalex.org/W2109714134","https://openalex.org/W2113397886","https://openalex.org/W2152481940","https://openalex.org/W2153095350","https://openalex.org/W2162218551","https://openalex.org/W2164987313","https://openalex.org/W4238206007","https://openalex.org/W4403868128"],"related_works":["https://openalex.org/W2284157877","https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W1789972284","https://openalex.org/W2374426356","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W3194517843","https://openalex.org/W1979419366"],"abstract_inverted_index":{"Solving":[0],"optimal":[1,59],"control":[2],"problems":[3],"by":[4],"an":[5],"indirect":[6],"method":[7,16,80,134],"is":[8,90,123,128],"often":[9],"abandoned":[10],"in":[11,48],"favor":[12],"of":[13,76],"a":[14,42,63,77,111],"direct":[15],"due":[17],"to":[18,22,114,130],"hyper-sensitivity":[19,39],"with":[20],"respect":[21],"unknown":[23,94],"boundary":[24,95],"conditions":[25,96],"for":[26,45,119],"the":[27,33,38,46,49,58,69,74,93,99,116,120,132],"Hamiltonian":[28,50],"boundary-value":[29],"problem":[30],"that":[31,54,67,98],"represents":[32],"first-order":[34],"necessary":[35],"conditions.":[36],"Yet":[37],"may":[40],"imply":[41],"manifold":[43],"structure":[44,53],"flow":[47],"phase":[51],"space,":[52],"provides":[55],"insight":[56],"regarding":[57],"solutions":[60],"and":[61,86,135],"suggests":[62],"solution":[64,78,100],"approximation":[65,79,133],"strategy":[66],"avoids":[68],"hyper-sensitivity.":[70],"This":[71],"paper":[72],"concerns":[73],"development":[75],"based":[81],"on":[82,91,104],"finite-time":[83,118],"Lyapunov":[84,121],"exponents":[85],"vectors.":[87],"The":[88],"focus":[89],"determining":[92],"such":[97],"end":[101],"points":[102],"lie":[103],"certain":[105],"invariant":[106],"manifolds.":[107],"Using":[108],"kinematic":[109],"eigenvalues,":[110],"systematic":[112],"approach":[113],"determine":[115],"appropriate":[117],"analysis":[122],"presented.":[124],"A":[125],"simple":[126],"example":[127],"used":[129],"illustrate":[131],"its":[136],"implementation.":[137]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}