{"id":"https://openalex.org/W2165106672","doi":"https://doi.org/10.1109/cdc.2009.5400697","title":"A set-valued filter for discrete time polynomial systems using sum of squares programming","display_name":"A set-valued filter for discrete time polynomial systems using sum of squares programming","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2165106672","doi":"https://doi.org/10.1109/cdc.2009.5400697","mag":"2165106672"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2009.5400697","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400697","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","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/A5019000613","display_name":"Christoph Maier","orcid":"https://orcid.org/0000-0002-2379-729X"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christoph Maier","raw_affiliation_strings":["Institute for Systems Theory and Automatic Control (IST), University of Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Systems Theory and Automatic Control (IST), University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001090900","display_name":"Frank Allg\u00f6wer","orcid":"https://orcid.org/0000-0002-3702-3658"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank Allgower","raw_affiliation_strings":["Institute for Systems Theory and Automatic Control (IST), University of Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Systems Theory and Automatic Control (IST), University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019000613"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.13354236,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"95","issue":null,"first_page":"223","last_page":"228"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9994000196456909,"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/T11236","display_name":"Control Systems and Identification","score":0.9994000196456909,"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":0.9987999796867371,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9977999925613403,"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/ellipsoid","display_name":"Ellipsoid","score":0.6922491788864136},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5984944105148315},{"id":"https://openalex.org/keywords/ellipsoid-method","display_name":"Ellipsoid method","score":0.5438814759254456},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.5318942070007324},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.5154843926429749},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5056354999542236},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4994978904724121},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.4955211877822876},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.47917190194129944},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47295328974723816},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.451445996761322},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4501955509185791},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.428687185049057},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.4284036457538605},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4220788776874542},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41127273440361023},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3700595498085022},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.33149290084838867},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.22738391160964966}],"concepts":[{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.6922491788864136},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5984944105148315},{"id":"https://openalex.org/C205451395","wikidata":"https://www.wikidata.org/wiki/Q378574","display_name":"Ellipsoid method","level":5,"score":0.5438814759254456},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.5318942070007324},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.5154843926429749},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5056354999542236},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4994978904724121},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4955211877822876},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.47917190194129944},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47295328974723816},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.451445996761322},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4501955509185791},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.428687185049057},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.4284036457538605},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4220788776874542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41127273440361023},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3700595498085022},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.33149290084838867},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.22738391160964966},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2009.5400697","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400697","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W48760935","https://openalex.org/W126279018","https://openalex.org/W578614108","https://openalex.org/W940085979","https://openalex.org/W1536111662","https://openalex.org/W1536651105","https://openalex.org/W1539838732","https://openalex.org/W1572031236","https://openalex.org/W1632601927","https://openalex.org/W1967073510","https://openalex.org/W1971025315","https://openalex.org/W2026578200","https://openalex.org/W2065053468","https://openalex.org/W2066268967","https://openalex.org/W2066459185","https://openalex.org/W2101676748","https://openalex.org/W2106850246","https://openalex.org/W2106869700","https://openalex.org/W2112015490","https://openalex.org/W2116232320","https://openalex.org/W2124316064","https://openalex.org/W2124826205","https://openalex.org/W2127520982","https://openalex.org/W2133404041","https://openalex.org/W2149371065","https://openalex.org/W2154683459","https://openalex.org/W2161362637","https://openalex.org/W2163216828","https://openalex.org/W2164484193","https://openalex.org/W2164658917","https://openalex.org/W2293807537","https://openalex.org/W2536620281","https://openalex.org/W2912522929","https://openalex.org/W3210839039","https://openalex.org/W4233252806","https://openalex.org/W4239870056","https://openalex.org/W4285719527","https://openalex.org/W4299599836","https://openalex.org/W6601983264","https://openalex.org/W6605086722","https://openalex.org/W6676202895","https://openalex.org/W6676352161","https://openalex.org/W6678792611","https://openalex.org/W6684061903"],"related_works":["https://openalex.org/W2031732959","https://openalex.org/W2235431948","https://openalex.org/W2167422950","https://openalex.org/W2128588724","https://openalex.org/W7739709","https://openalex.org/W4292072222","https://openalex.org/W2562629174","https://openalex.org/W4253545527","https://openalex.org/W2016090484","https://openalex.org/W1500330311"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"a":[5,50,61,111],"novel":[6],"approach":[7,77],"for":[8],"robust":[9,93],"state":[10,32,44,86],"reconstruction":[11],"of":[12,24,49,60,67,84,100,110],"multi-output":[13],"discrete-time":[14],"systems":[15],"with":[16,54],"polynomial":[17],"nonlinear":[18],"dynamics":[19],"and":[20,33,47,98],"measurements":[21],"in":[22,81,107],"presence":[23],"unknown":[25],"but":[26],"bounded":[27],"disturbances":[28],"corrupting":[29],"both":[30],"the":[31,58,79,82,85,101],"measurement":[34],"equations.":[35],"The":[36,75,96],"proposed":[37],"recursive":[38],"algorithm":[39,103],"is":[40,104],"based":[41],"on":[42],"ellipsoidal":[43],"bounding":[45,87],"techniques":[46],"consists":[48],"two-step":[51],"prediction-correction":[52],"procedure,":[53],"each":[55],"step":[56],"requiring":[57],"solution":[59],"convex":[62],"optimization":[63],"problem":[64],"under":[65],"sum":[66],"squares":[68],"rather":[69],"than":[70],"linear":[71],"matrix":[72],"inequality":[73],"constraints.":[74],"presented":[76],"reduces":[78],"conservatism":[80],"calculation":[83],"ellipsoid":[88],"when":[89],"compared":[90],"to":[91],"existing":[92],"filtering":[94],"approaches.":[95],"applicability":[97],"effectiveness":[99],"new":[102],"exemplarily":[105],"shown":[106],"numerical":[108],"simulations":[109],"benchmark":[112],"system.":[113]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
