{"id":"https://openalex.org/W7147530285","doi":"https://doi.org/10.1007/978-3-032-15791-1_3","title":"Asymptotic Convergence of\u00a0Phase Trajectories in\u00a0Linear Optimal Control Problems","display_name":"Asymptotic Convergence of\u00a0Phase Trajectories in\u00a0Linear Optimal Control Problems","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7147530285","doi":"https://doi.org/10.1007/978-3-032-15791-1_3"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-032-15791-1_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-032-15791-1_3","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5132715542","display_name":"Anatoly Antipin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210147539","display_name":"S.I. Vavilov Institute for the History of Science and Technology","ror":"https://ror.org/04kybmr51","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210147539"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Anatoly Antipin","raw_affiliation_strings":["FRC \u00abComputer Science and Control\u00bbof RAS, Vavilov 40, 119333, Moscow, Russia"],"raw_orcid":"https://orcid.org/0000-0003-1771-8580","affiliations":[{"raw_affiliation_string":"FRC \u00abComputer Science and Control\u00bbof RAS, Vavilov 40, 119333, Moscow, Russia","institution_ids":["https://openalex.org/I4210147539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5132676659","display_name":"Elena Khoroshilova","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Elena Khoroshilova","raw_affiliation_strings":["Lomonosov MSU, CMC Faculty, Leninskiye Gory, 119991, Moscow, Russia"],"raw_orcid":"https://orcid.org/0000-0002-5978-1564","affiliations":[{"raw_affiliation_string":"Lomonosov MSU, CMC Faculty, Leninskiye Gory, 119991, Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5132715542"],"corresponding_institution_ids":["https://openalex.org/I4210147539"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.81149425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"35","last_page":"49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7106000185012817,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7106000185012817,"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"}},{"id":"https://openalex.org/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.1145000010728836,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.07890000194311142,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/saddle-point","display_name":"Saddle point","score":0.7347999811172485},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.692300021648407},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5465999841690063},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.44839999079704285},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4447000026702881},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.42419999837875366},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42239999771118164},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.40860000252723694},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4011000096797943},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.39800000190734863}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7347999811172485},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.692300021648407},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5465999841690063},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5307999849319458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49000000953674316},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.44839999079704285},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4447000026702881},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.42419999837875366},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42239999771118164},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.40860000252723694},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4011000096797943},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.39800000190734863},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36419999599456787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3569999933242798},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.30640000104904175},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.30000001192092896},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.2815000116825104},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2624000012874603}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-032-15791-1_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-032-15791-1_3","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W2012823404","https://openalex.org/W2108244675","https://openalex.org/W2175692770","https://openalex.org/W2269513191","https://openalex.org/W2275525867","https://openalex.org/W2344328683","https://openalex.org/W2768291446","https://openalex.org/W2911370043","https://openalex.org/W2912161497","https://openalex.org/W3005032556","https://openalex.org/W3214264362","https://openalex.org/W4313407148","https://openalex.org/W4404126029","https://openalex.org/W4409732212"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-02T13:53:19.096889","created_date":"2026-04-02T00:00:00"}
