{"id":"https://openalex.org/W1529289765","doi":"https://doi.org/10.1109/acc.2015.7171167","title":"Piecewise polynomial policy iterations for synthesis of optimal control laws in input-saturated systems","display_name":"Piecewise polynomial policy iterations for synthesis of optimal control laws in input-saturated systems","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1529289765","doi":"https://doi.org/10.1109/acc.2015.7171167","mag":"1529289765"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2015.7171167","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171167","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","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/A5055979973","display_name":"Simone Baldi","orcid":"https://orcid.org/0000-0001-9752-8925"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Simone Baldi","raw_affiliation_strings":["Technische Universiteit Delft, Delft, Zuid-Holland, NL","Delft Center for Systems and Control, Delft University of Technology, 2628CD, the Netherlands"],"affiliations":[{"raw_affiliation_string":"Technische Universiteit Delft, Delft, Zuid-Holland, NL","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, 2628CD, the Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066966226","display_name":"Gi\u00f3rgio Valm\u00f3rbida","orcid":"https://orcid.org/0000-0002-1710-8590"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Giorgio Valmorbida","raw_affiliation_strings":["University of Oxford, Oxford, Oxfordshire, GB","Department of Engineering Science, Control Group, University of Oxford, Parks Road, OX1 3PJ, U.K"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, Oxfordshire, GB","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Department of Engineering Science, Control Group, University of Oxford, Parks Road, OX1 3PJ, U.K","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053811056","display_name":"Antonis Papachristodoulou","orcid":"https://orcid.org/0000-0002-3565-8967"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Antonis Papachristodoulou","raw_affiliation_strings":["University of Oxford, Oxford, Oxfordshire, GB","Department of Engineering Science, Control Group, University of Oxford, Parks Road, OX1 3PJ, U.K"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, Oxfordshire, GB","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Department of Engineering Science, Control Group, University of Oxford, Parks Road, OX1 3PJ, U.K","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071596476","display_name":"Elias B. Kosmatopoulos","orcid":"https://orcid.org/0000-0002-3735-4238"},"institutions":[{"id":"https://openalex.org/I147962203","display_name":"Democritus University of Thrace","ror":"https://ror.org/03bfqnx40","country_code":"GR","type":"education","lineage":["https://openalex.org/I147962203"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Elias B. Kosmatopoulos","raw_affiliation_strings":["Democritus University of Thrace, Komotini, GR","Dept. of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi 67100, Greece and Informatics & Telematics Institute, Center for Research and Technology Hellas (ITICERTH), Thessaloniki 57001, Greece"],"affiliations":[{"raw_affiliation_string":"Democritus University of Thrace, Komotini, GR","institution_ids":["https://openalex.org/I147962203"]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi 67100, Greece and Informatics & Telematics Institute, Center for Research and Technology Hellas (ITICERTH), Thessaloniki 57001, Greece","institution_ids":["https://openalex.org/I147962203"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055979973"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":null,"apc_paid":null,"fwci":0.701,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71411625,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"2850","last_page":"2855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9994999766349792,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9994999766349792,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9908999800682068,"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/T10675","display_name":"Mechanical Circulatory Support Devices","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/piecewise","display_name":"Piecewise","score":0.722199559211731},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6283162832260132},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.5699134469032288},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.491868257522583},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4697668254375458},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4568330943584442},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4357580244541168},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.4315722584724426},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4145810306072235},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.41087979078292847},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3850480914115906},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3566698431968689},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3360550105571747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20818081498146057},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.13410243391990662},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11281770467758179},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10691386461257935}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.722199559211731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6283162832260132},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.5699134469032288},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.491868257522583},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4697668254375458},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4568330943584442},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4357580244541168},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.4315722584724426},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4145810306072235},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.41087979078292847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3850480914115906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3566698431968689},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3360550105571747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20818081498146057},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.13410243391990662},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11281770467758179},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10691386461257935},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2015.7171167","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171167","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8029175688","display_name":null,"funder_award_id":"EP/J010537/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1574514837","https://openalex.org/W1576452626","https://openalex.org/W1601081659","https://openalex.org/W1964730816","https://openalex.org/W1974183644","https://openalex.org/W1979098741","https://openalex.org/W1995337553","https://openalex.org/W1999724422","https://openalex.org/W1999781429","https://openalex.org/W1999913571","https://openalex.org/W2002007892","https://openalex.org/W2016416286","https://openalex.org/W2028717619","https://openalex.org/W2083283377","https://openalex.org/W2097061644","https://openalex.org/W2103116581","https://openalex.org/W2112562680","https://openalex.org/W2113632300","https://openalex.org/W2147183770","https://openalex.org/W2150355110","https://openalex.org/W2160561608","https://openalex.org/W2165726932","https://openalex.org/W2341171179","https://openalex.org/W3103456419","https://openalex.org/W4237203567","https://openalex.org/W4246000934","https://openalex.org/W4250589301","https://openalex.org/W4285719527","https://openalex.org/W4307347247","https://openalex.org/W6634528131","https://openalex.org/W6673283935","https://openalex.org/W6704298589","https://openalex.org/W6785992799"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W1983756092","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W2381295697","https://openalex.org/W3009543351"],"abstract_inverted_index":{"This":[0,29],"work":[1],"proposes":[2],"a":[3,54,90],"policy":[4,50,85,93,102,113,144],"iteration":[5,51,86,110],"procedure":[6],"for":[7,17],"the":[8,36,70,73,77,84,99,109,111,118,132,143],"synthesis":[9],"of":[10,56,76,83,98,108,120,142],"optimal":[11],"and":[12,66,72,117],"globally":[13,115],"stabilizing":[14,116],"control":[15,92],"policies":[16],"Linear":[18],"Time":[19],"Invariant":[20],"(LTI)":[21],"Asymptotically":[22],"Null-controllable":[23],"with":[24,33,44,158],"Bounded":[25],"Inputs":[26],"(ANCBI)":[27],"systems.":[28],"class":[30,55],"includes":[31],"systems":[32],"eigenvalues":[34],"on":[35,53,89],"imaginary":[37],"axis":[38],"(possibly":[39],"repeated)":[40],"but":[41,64],"no":[42],"pole":[43],"positive":[45],"real":[46],"part.":[47],"The":[48,80,129],"proposed":[49,100],"relies":[52],"piecewise":[57,91,101],"quadratic":[58],"Lyapunov":[59],"functions":[60,75],"which":[61,134],"is":[62,87,103,114,125,135,146],"non-differentiable,":[63],"continuous,":[65],"polynomial":[67],"in":[68],"both":[69],"state":[71],"deadzone":[74],"input":[78],"signals.":[79],"second":[81],"step":[82,107,141],"based":[88],"improvement.":[94],"An":[95],"important":[96],"aspect":[97],"that":[104,153],"at":[105,139],"each":[106,140],"computed":[112],"existence":[119],"an":[121],"improving":[122],"value":[123],"function":[124],"guaranteed":[126],"as":[127],"well.":[128],"solution":[130],"to":[131,137],"inequalities":[133],"required":[136],"hold":[138],"iteration,":[145],"obtained":[147],"by":[148],"solving":[149],"Sum-of-Squares":[150],"Programs":[151],"(SOSP)":[152],"can":[154],"be":[155],"efficiently":[156],"implemented":[157],"semidefinite":[159],"programming":[160],"(SDP)":[161],"solvers.":[162]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}