{"id":"https://openalex.org/W2039799007","doi":"https://doi.org/10.1109/tcst.2011.2141134","title":"Flexible Piecewise Function Evaluation Methods Based on Truncated Binary Search Trees and Lattice Representation in Explicit MPC","display_name":"Flexible Piecewise Function Evaluation Methods Based on Truncated Binary Search Trees and Lattice Representation in Explicit MPC","publication_year":2011,"publication_date":"2011-05-10","ids":{"openalex":"https://openalex.org/W2039799007","doi":"https://doi.org/10.1109/tcst.2011.2141134","mag":"2039799007"},"language":"en","primary_location":{"id":"doi:10.1109/tcst.2011.2141134","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2011.2141134","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control Systems Technology","raw_type":"journal-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/A5008156705","display_name":"Farhad Bayat","orcid":"https://orcid.org/0000-0001-5131-3419"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]},{"id":"https://openalex.org/I99861883","display_name":"University of Zanjan","ror":"https://ror.org/05e34ej29","country_code":"IR","type":"education","lineage":["https://openalex.org/I99861883"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Farhad Bayat","raw_affiliation_strings":["Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran","Zanjan University, Zanjan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]},{"raw_affiliation_string":"Zanjan University, Zanjan, Iran","institution_ids":["https://openalex.org/I99861883"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012692888","display_name":"Tor Arne Johansen","orcid":"https://orcid.org/0000-0001-9440-5989"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Tor Arne Johansen","raw_affiliation_strings":["Department of Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113789284","display_name":"Ali Jalali","orcid":null},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ali Akbar Jalali","raw_affiliation_strings":["Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.5084,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.96300522,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"3","first_page":"632","last_page":"640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":1.0,"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/T10791","display_name":"Advanced Control Systems Optimization","score":1.0,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9980000257492065,"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/T11053","display_name":"Process Optimization and Integration","score":0.9868999719619751,"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/algorithm","display_name":"Algorithm","score":0.5559164881706238},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5259606838226318},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5070741176605225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5062279105186462},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.487973153591156},{"id":"https://openalex.org/keywords/memory-footprint","display_name":"Memory footprint","score":0.4684581756591797},{"id":"https://openalex.org/keywords/binary-search-algorithm","display_name":"Binary search algorithm","score":0.4614061415195465},{"id":"https://openalex.org/keywords/binary-search-tree","display_name":"Binary search tree","score":0.45680731534957886},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.44975629448890686},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.42416274547576904},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40284237265586853},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.39774101972579956},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37013471126556396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3367665410041809},{"id":"https://openalex.org/keywords/search-algorithm","display_name":"Search algorithm","score":0.30750036239624023},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10071456432342529},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09876707196235657}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5559164881706238},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5259606838226318},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5070741176605225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5062279105186462},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.487973153591156},{"id":"https://openalex.org/C74912251","wikidata":"https://www.wikidata.org/wiki/Q6815727","display_name":"Memory footprint","level":2,"score":0.4684581756591797},{"id":"https://openalex.org/C121610932","wikidata":"https://www.wikidata.org/wiki/Q243754","display_name":"Binary search algorithm","level":3,"score":0.4614061415195465},{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.45680731534957886},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.44975629448890686},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.42416274547576904},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40284237265586853},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.39774101972579956},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37013471126556396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3367665410041809},{"id":"https://openalex.org/C125583679","wikidata":"https://www.wikidata.org/wiki/Q755673","display_name":"Search algorithm","level":2,"score":0.30750036239624023},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10071456432342529},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09876707196235657},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcst.2011.2141134","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2011.2141134","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control Systems Technology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.75}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1488542424","https://openalex.org/W1511213320","https://openalex.org/W1527567078","https://openalex.org/W1576823098","https://openalex.org/W1975662200","https://openalex.org/W1983864916","https://openalex.org/W1993170675","https://openalex.org/W1996497804","https://openalex.org/W1999780595","https://openalex.org/W2010566422","https://openalex.org/W2031280071","https://openalex.org/W2039322622","https://openalex.org/W2065787176","https://openalex.org/W2068820478","https://openalex.org/W2074168837","https://openalex.org/W2114501365","https://openalex.org/W2117568889","https://openalex.org/W2118132161","https://openalex.org/W2122893862","https://openalex.org/W2138962679","https://openalex.org/W2144884795","https://openalex.org/W2156963939","https://openalex.org/W2158647064","https://openalex.org/W2169117596","https://openalex.org/W2297159073","https://openalex.org/W2476491145","https://openalex.org/W3146603598","https://openalex.org/W4247323185","https://openalex.org/W6631607901","https://openalex.org/W6644037508","https://openalex.org/W6653203330","https://openalex.org/W6658367186","https://openalex.org/W6668772885","https://openalex.org/W6682899202","https://openalex.org/W6697341876"],"related_works":["https://openalex.org/W2363556447","https://openalex.org/W2539085113","https://openalex.org/W2384179084","https://openalex.org/W2092988444","https://openalex.org/W2354443135","https://openalex.org/W2582091787","https://openalex.org/W1499707946","https://openalex.org/W2374641630","https://openalex.org/W2016420340","https://openalex.org/W2107129281"],"abstract_inverted_index":{"Efficient":[0],"methods":[1,107,160],"for":[2,59,88,210],"evaluation":[3,144],"of":[4,57,68,98,145,157,196,213,215],"piecewise":[5,29],"functions":[6,90],"defined":[7],"over":[8],"convex":[9],"polyhedral":[10],"partitions":[11],"are":[12,179],"proposed.":[13],"As":[14],"an":[15,78],"important":[16],"application,":[17],"the":[18,61,96,109,137,150,158,163,200,224,239,249],"explicit":[19,151],"model":[20],"predictive":[21],"control":[22,32],"problem":[23],"is":[24,46,139,161,192,203,221],"considered":[25],"which":[26,60],"requires":[27],"a":[28,54,92,186,206,229],"affine":[30],"(PWA)":[31],"law":[33],"to":[34,48,51,111,128,149,228,238,248],"be":[35,49,126,167],"evaluated":[36],"online.":[37],"The":[38,74,122,154,177],"widely":[39],"used":[40],"binary":[41,81],"search":[42,82],"tree":[43,83],"(BST)":[44],"method":[45,63,76],"modified":[47],"able":[50],"deal":[52],"with":[53,169,205],"wider":[55],"class":[56],"problems":[58],"BST":[62,241],"becomes":[64],"prohibitive":[65],"in":[66,91],"terms":[67],"preprocessing":[69,114,232],"time":[70,175,233,246],"or":[71],"memory":[72,235],"requirements.":[73],"proposed":[75,159,225],"combines":[77],"orthogonal":[79],"truncated":[80],"(OTBST)":[84],"and":[85,103,118,134,199,234,242],"lattice":[86,251],"representation":[87],"PWA":[89,146],"unified":[93],"structure":[94],"enjoying":[95],"advantages":[97],"both":[99],"approaches.":[100],"Both":[101],"OTBST":[102,105,123],"Lattice-based":[104],"(LOTBST)":[106],"enable":[108],"designer":[110],"tradeoff":[112],"between":[113],"time,":[115],"storage":[116],"requirement,":[117],"online":[119,173,201,244],"computation":[120,174,245],"time.":[121],"approach":[124],"can":[125,166],"applied":[127],"more":[129,142],"general":[130],"partitions,":[131],"e.g.,":[132],"discontinues":[133],"overlapping,":[135],"while":[136],"LOTBST":[138,226],"directed":[140],"towards":[141],"efficient":[143],"functions,":[147],"associated":[148],"MPC":[152],"solutions.":[153],"key":[155],"feature":[156],"that":[162,223],"exact":[164],"solution":[165],"computed":[168],"predefined":[170],"worst":[171],"case":[172],"guarantees.":[176],"computations":[178],"readily":[180],"implementable":[181],"using":[182],"fixed-point":[183],"arithmetic":[184],"on":[185],"low":[187],"cost":[188],"microcontroller":[189],"since":[190],"there":[191],"no":[193],"recursive":[194],"accumulation":[195],"round-off":[197],"errors,":[198],"algorithm":[202],"simple":[204],"small":[207],"footprint":[208],"suitable":[209],"formal":[211],"verification":[212],"correctness":[214],"implementation.":[216],"Using":[217],"several":[218],"examples":[219],"it":[220],"shown":[222],"leads":[227],"considerably":[230],"less":[231,243],"requirement":[236],"comparing":[237,247],"pure":[240,250],"representation.":[252]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}