{"id":"https://openalex.org/W4416452331","doi":"https://doi.org/10.1016/j.amc.2025.129849","title":"A learning-based value iteration scheme for singularly perturbed systems and its application in RC ladder circuit","display_name":"A learning-based value iteration scheme for singularly perturbed systems and its application in RC ladder circuit","publication_year":2025,"publication_date":"2025-11-21","ids":{"openalex":"https://openalex.org/W4416452331","doi":"https://doi.org/10.1016/j.amc.2025.129849"},"language":"en","primary_location":{"id":"doi:10.1016/j.amc.2025.129849","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.amc.2025.129849","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.amc.2025.129849","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zihan Wang","orcid":"https://orcid.org/0009-0002-1600-4308"},"institutions":[{"id":"https://openalex.org/I92178344","display_name":"Anhui University of Technology","ror":"https://ror.org/02qdtrq21","country_code":"CN","type":"education","lineage":["https://openalex.org/I92178344"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zihan Wang","raw_affiliation_strings":["School of Electrical and Information Engineering, Anhui University of Technology, Ma\u2019anshan 243002, China"],"raw_orcid":"https://orcid.org/0009-0002-1600-4308","affiliations":[{"raw_affiliation_string":"School of Electrical and Information Engineering, Anhui University of Technology, Ma\u2019anshan 243002, China","institution_ids":["https://openalex.org/I92178344"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Qing Yang","orcid":"https://orcid.org/0009-0009-6457-6328"},"institutions":[{"id":"https://openalex.org/I92178344","display_name":"Anhui University of Technology","ror":"https://ror.org/02qdtrq21","country_code":"CN","type":"education","lineage":["https://openalex.org/I92178344"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qing Yang","raw_affiliation_strings":["School of Electrical and Information Engineering, Anhui University of Technology, Ma\u2019anshan 243002, China"],"raw_orcid":"https://orcid.org/0009-0009-6457-6328","affiliations":[{"raw_affiliation_string":"School of Electrical and Information Engineering, Anhui University of Technology, Ma\u2019anshan 243002, China","institution_ids":["https://openalex.org/I92178344"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113368482","display_name":"Hao Shen","orcid":"https://orcid.org/0000-0001-7024-6573"},"institutions":[{"id":"https://openalex.org/I92178344","display_name":"Anhui University of Technology","ror":"https://ror.org/02qdtrq21","country_code":"CN","type":"education","lineage":["https://openalex.org/I92178344"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hao Shen","raw_affiliation_strings":["School of Electrical and Information Engineering, Anhui University of Technology, Ma\u2019anshan 243002, China"],"raw_orcid":"https://orcid.org/0000-0001-7024-6573","affiliations":[{"raw_affiliation_string":"School of Electrical and Information Engineering, Anhui University of Technology, Ma\u2019anshan 243002, China","institution_ids":["https://openalex.org/I92178344"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5113368482"],"corresponding_institution_ids":["https://openalex.org/I92178344"],"apc_list":{"value":3470,"currency":"USD","value_usd":3470},"apc_paid":{"value":3470,"currency":"USD","value_usd":3470},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27764158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"515","issue":null,"first_page":"129849","last_page":"129849"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9129999876022339,"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":0.9129999876022339,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.023000000044703484,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.01549999974668026,"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/convergence","display_name":"Convergence (economics)","score":0.7243000268936157},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5838000178337097},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5547999739646912},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5134000182151794},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5081999897956848},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.4180000126361847},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4133000075817108},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4011000096797943},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.39329999685287476}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7243000268936157},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5838000178337097},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5547999739646912},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5223000049591064},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5134000182151794},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5081999897956848},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.4180000126361847},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4068000018596649},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4011000096797943},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.39329999685287476},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.367000013589859},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.358599990606308},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3580000102519989},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.34929999709129333},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3474000096321106},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.33250001072883606},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2985000014305115},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.2712000012397766},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.2556999921798706}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.amc.2025.129849","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.amc.2025.129849","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.amc.2025.129849","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.amc.2025.129849","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1322164634","display_name":null,"funder_award_id":"62173001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1738785113","display_name":null,"funder_award_id":"2508085J044","funder_id":"https://openalex.org/F4320317137","funder_display_name":"Natural Science Foundation for Distinguished Young Scholars of Anhui Province"},{"id":"https://openalex.org/G258277902","display_name":null,"funder_award_id":"62573004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G328788861","display_name":null,"funder_award_id":"2022AH020034","funder_id":"https://openalex.org/F4320317137","funder_display_name":"Natural Science Foundation for Distinguished Young Scholars of Anhui Province"},{"id":"https://openalex.org/G3460663202","display_name":null,"funder_award_id":"62273006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4975918011","display_name":null,"funder_award_id":"2022AH030049","funder_id":"https://openalex.org/F4320317137","funder_display_name":"Natural Science Foundation for Distinguished Young Scholars of Anhui Province"},{"id":"https://openalex.org/G7883358773","display_name":null,"funder_award_id":"BWPU2023ZY02","funder_id":"https://openalex.org/F4320321408","funder_display_name":"Ministry of Education"}],"funders":[{"id":"https://openalex.org/F4320317137","display_name":"Natural Science Foundation for Distinguished Young Scholars of Anhui Province","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321408","display_name":"Ministry of Education","ror":"https://ror.org/01p262204"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1997603681","https://openalex.org/W2000111160","https://openalex.org/W2005437559","https://openalex.org/W2019338681","https://openalex.org/W2024303516","https://openalex.org/W2035003264","https://openalex.org/W2040085632","https://openalex.org/W2099775999","https://openalex.org/W2139416664","https://openalex.org/W2148439597","https://openalex.org/W2173749656","https://openalex.org/W2189990206","https://openalex.org/W2299109138","https://openalex.org/W2467518411","https://openalex.org/W2521856433","https://openalex.org/W2559988195","https://openalex.org/W2772589676","https://openalex.org/W2807477133","https://openalex.org/W2921869787","https://openalex.org/W2983464671","https://openalex.org/W3003569500","https://openalex.org/W3177891984","https://openalex.org/W4205172873","https://openalex.org/W4210556448","https://openalex.org/W4310258352","https://openalex.org/W4312247820","https://openalex.org/W4312714074","https://openalex.org/W4313435464","https://openalex.org/W4386766493","https://openalex.org/W4388579564","https://openalex.org/W4390576246","https://openalex.org/W4390776948","https://openalex.org/W4394909995","https://openalex.org/W4401717454","https://openalex.org/W4401879498","https://openalex.org/W4403863253","https://openalex.org/W4410808427"],"related_works":[],"abstract_inverted_index":{"In":[0,46],"this":[1,52],"paper,":[2],"a":[3,31,73],"value":[4],"iteration":[5],"(VI)":[6],"scheme":[7],"considering":[8],"the":[9,41,56,65,92,109,140,143],"guaranteed":[10,74],"state":[11,57,101,126],"convergence":[12,58,127],"rate":[13,59],"(GSCR)":[14],"is":[15,35,69,88,122,128,136,146],"proposed":[16,110,144],"for":[17,37],"multi-input":[18],"singularly":[19],"perturbed":[20],"systems":[21],"(MISPSs)":[22],"with":[23],"unknown":[24],"system":[25,134],"dynamics.":[26],"Unlike":[27],"traditional":[28],"reduced-order":[29],"methods,":[30],"full-order":[32],"modeling":[33],"approach":[34],"adopted":[36],"MISPSs,":[38],"thereby":[39],"avoiding":[40],"suboptimality":[42],"of":[43,142],"reduction":[44],"techniques.":[45],"contrast":[47],"to":[48,94,106],"classical":[49],"differential":[50],"games,":[51],"work":[53],"explicitly":[54],"considers":[55],"under":[60],"multiple":[61],"interacting":[62],"inputs.":[63],"Specifically,":[64],"control":[66,120],"policy":[67],"design":[68],"formulated":[70],"as":[71],"solving":[72],"game":[75],"algebraic":[76],"Riccati":[77],"equation":[78],"(GGARE).":[79],"To":[80],"solve":[81],"GGARE,":[82],"an":[83,149],"online":[84],"model-free":[85],"VI":[86],"algorithm":[87,111],"developed,":[89],"which":[90],"obtains":[91],"solutions":[93],"Nash":[95],"equilibrium":[96],"in":[97],"real-time":[98],"using":[99],"measured":[100],"and":[102],"input":[103],"data.":[104],"Compared":[105],"existing":[107],"algorithms,":[108],"offers":[112],"three":[113],"key":[114],"advantages:":[115],"i)":[116],"No":[117],"initial":[118],"stable":[119],"gain":[121],"needed;":[123],"ii)":[124],"Rapid":[125],"achieved;":[129],"iii)":[130],"The":[131],"information":[132],"on":[133],"dynamics":[135],"not":[137],"required.":[138],"Finally,":[139],"effectiveness":[141],"method":[145],"validated":[147],"through":[148],"RC":[150],"ladder":[151],"circuit":[152],"example.":[153]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-11-23T00:00:00"}