{"id":"https://openalex.org/W7101897000","doi":"https://doi.org/10.48550/arxiv.2510.21944","title":"Fixed Horizon Linear Quadratic Covariance Steering in Continuous Time with Hilbert-Schmidt Terminal Cost","display_name":"Fixed Horizon Linear Quadratic Covariance Steering in Continuous Time with Hilbert-Schmidt Terminal Cost","publication_year":2025,"publication_date":"2025-10-24","ids":{"openalex":"https://openalex.org/W7101897000","doi":"https://doi.org/10.48550/arxiv.2510.21944"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2510.21944","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.21944","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2510.21944","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Sial, Tushar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sial, Tushar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Halder, Abhishek","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Halder, Abhishek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.25870001316070557,"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"}},"topics":[{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.25870001316070557,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.1615999937057495,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.13910000026226044,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5593000054359436},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5421000123023987},{"id":"https://openalex.org/keywords/terminal","display_name":"Terminal (telecommunication)","score":0.5383999943733215},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.450300008058548},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4424000084400177},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.43700000643730164},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.42809998989105225},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.42500001192092896},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4163999855518341}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6834999918937683},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5593000054359436},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5421000123023987},{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.5383999943733215},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.450300008058548},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44519999623298645},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4424000084400177},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.43700000643730164},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.42809998989105225},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.42500001192092896},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4163999855518341},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4108000099658966},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.3452000021934509},{"id":"https://openalex.org/C47096860","wikidata":"https://www.wikidata.org/wiki/Q575542","display_name":"Terminal value","level":4,"score":0.3400999903678894},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C28761237","wikidata":"https://www.wikidata.org/wiki/Q7805321","display_name":"Time horizon","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C159176650","wikidata":"https://www.wikidata.org/wiki/Q43261","display_name":"Horizon","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2565000057220459},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2510.21944","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.21944","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2510.21944","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.21944","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"formulate":[1],"and":[2,29,63,70,105],"solve":[3,52],"the":[4,27,30,37,76,82,87,93],"fixed":[5],"horizon":[6],"linear":[7,77],"quadratic":[8],"covariance":[9],"steering":[10],"problem":[11],"in":[12,20],"continuous":[13],"time":[14],"with":[15,101,107],"a":[16,43,59,102,108],"terminal":[17,32],"cost":[18],"measured":[19],"Hilbert-Schmidt":[21],"(i.e.,":[22],"Frobenius)":[23],"norm":[24],"error":[25],"between":[26],"desired":[28],"controlled":[31],"covariances.":[33],"For":[34],"this":[35,53],"problem,":[36],"necessary":[38],"conditions":[39],"of":[40,55,75,86],"optimality":[41],"become":[42],"coupled":[44],"matrix":[45,85],"ODE":[46],"two-point":[47],"boundary":[48],"value":[49],"problem.":[50],"To":[51,91],"system":[54],"equations,":[56],"we":[57,95],"design":[58],"matricial":[60],"recursive":[61],"algorithm":[62,69],"prove":[64],"its":[65,71],"convergence.":[66],"The":[67],"proposed":[68],"analysis":[72],"make":[73],"use":[74],"fractional":[78],"transforms":[79],"parameterized":[80],"by":[81],"state":[83,111],"transition":[84],"associated":[88],"Hamiltonian":[89],"matrix.":[90],"illustrate":[92],"results,":[94],"provide":[96],"two":[97,103],"numerical":[98],"examples:":[99],"one":[100],"dimensional":[104,110],"another":[106],"six":[109],"space.":[112]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-29T00:00:00"}
