{"id":"https://openalex.org/W2572801168","doi":"https://doi.org/10.1109/ecc.2016.7810630","title":"Stability of Gaussian process state space models","display_name":"Stability of Gaussian process state space models","publication_year":2016,"publication_date":"2016-06-01","ids":{"openalex":"https://openalex.org/W2572801168","doi":"https://doi.org/10.1109/ecc.2016.7810630","mag":"2572801168"},"language":"en","primary_location":{"id":"doi:10.1109/ecc.2016.7810630","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2016.7810630","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1811.06646","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087890782","display_name":"Thomas Beckers","orcid":"https://orcid.org/0000-0003-1718-0338"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Beckers","raw_affiliation_strings":["Chair of Information-oriented Control (ITR), Technical University of Munich, Munich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Information-oriented Control (ITR), Technical University of Munich, Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024376647","display_name":"Sandra Hirche","orcid":"https://orcid.org/0000-0001-7819-5926"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sandra Hirche","raw_affiliation_strings":["Chair of Information-oriented Control (ITR), Technical University of Munich, Munich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Information-oriented Control (ITR), Technical University of Munich, Munich","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":2.3288,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.91663374,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"2275","last_page":"2281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11236","display_name":"Control Systems and Identification","score":0.9926999807357788,"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":0.9787999987602234,"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/gaussian-process","display_name":"Gaussian process","score":0.6717416644096375},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6613861322402954},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.6401028037071228},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.606474757194519},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.601517915725708},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5768418312072754},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5758011341094971},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4916148781776428},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4821555018424988},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46775054931640625},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.46742576360702515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.448030024766922},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43214109539985657},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38285866379737854},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34873610734939575},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1880125105381012},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11760318279266357},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09689804911613464}],"concepts":[{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.6717416644096375},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6613861322402954},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.6401028037071228},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.606474757194519},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.601517915725708},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5768418312072754},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5758011341094971},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4916148781776428},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4821555018424988},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46775054931640625},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46742576360702515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.448030024766922},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43214109539985657},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38285866379737854},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34873610734939575},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1880125105381012},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11760318279266357},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09689804911613464},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/ecc.2016.7810630","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2016.7810630","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1811.06646","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1811.06646","pdf_url":"https://arxiv.org/pdf/1811.06646","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1295931","is_oa":true,"landing_page_url":"http://mediatum.ub.tum.de/node?id=1295931","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1811.06646","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1811.06646","pdf_url":"https://arxiv.org/pdf/1811.06646","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3207356259","display_name":null,"funder_award_id":"2007\u20132013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G393177772","display_name":null,"funder_award_id":"FP7 2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5702163051","display_name":null,"funder_award_id":"FP7/2007","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2572801168.pdf","grobid_xml":"https://content.openalex.org/works/W2572801168.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W51652903","https://openalex.org/W1519859729","https://openalex.org/W1527620910","https://openalex.org/W1545374208","https://openalex.org/W1601795611","https://openalex.org/W1663973292","https://openalex.org/W1746819321","https://openalex.org/W1968749873","https://openalex.org/W2034013221","https://openalex.org/W2052551665","https://openalex.org/W2088407732","https://openalex.org/W2119702195","https://openalex.org/W2124609748","https://openalex.org/W2126877537","https://openalex.org/W2129202194","https://openalex.org/W2154575165","https://openalex.org/W2161083632","https://openalex.org/W2166063021","https://openalex.org/W2313806658","https://openalex.org/W2480512873","https://openalex.org/W2962837602","https://openalex.org/W4211049957","https://openalex.org/W4235601388","https://openalex.org/W4285719527","https://openalex.org/W6602145669","https://openalex.org/W6631830761","https://openalex.org/W6682906688","https://openalex.org/W6684451488"],"related_works":["https://openalex.org/W2386803684","https://openalex.org/W3178402891","https://openalex.org/W651058035","https://openalex.org/W143964308","https://openalex.org/W2073389045","https://openalex.org/W2046078371","https://openalex.org/W4315750325","https://openalex.org/W1971337326","https://openalex.org/W2060696366","https://openalex.org/W4213259725"],"abstract_inverted_index":{"Gaussian":[0],"Process":[1],"State":[2],"Space":[3],"Models":[4],"(GP-SSMs)":[5],"are":[6,30,46],"a":[7,33,66],"non-parametric":[8],"model":[9],"class":[10],"suitable":[11],"to":[12,103],"represent":[13],"nonlinear":[14,96],"dynamics.":[15],"They":[16],"become":[17],"increasingly":[18],"popular":[19],"in":[20,74],"data-driven":[21],"modeling":[22],"approaches,":[23],"i.e.":[24],"when":[25],"no":[26],"first-order":[27],"physics-based":[28],"models":[29],"available.":[31],"Although":[32],"GP-SSM":[34,59,108],"produces":[35],"well-behaved":[36],"approximations":[37],"and":[38,109],"gains":[39],"increasing":[40],"popularity,":[41],"the":[42,58,75,82,90,104],"fundamental":[43],"system":[44],"dynamics":[45],"just":[47],"sparsely":[48],"researched.":[49],"In":[50],"this":[51],"paper,":[52],"we":[53],"present":[54],"stability":[55],"results":[56],"for":[57,95,113],"depending":[60],"on":[61,81],"selected":[62],"covariance":[63,93],"function":[64,85],"employing":[65],"deterministic":[67],"point":[68],"of":[69,89,107],"view":[70],"as":[71],"widely":[72],"done":[73],"literature.":[76],"The":[77],"focus":[78],"is":[79,87],"set":[80],"squared":[83],"exponential":[84],"which":[86],"one":[88],"most":[91],"used":[92],"functions":[94],"regression.":[97],"We":[98],"start":[99],"with":[100,111],"calculations":[101],"according":[102],"equilibrium":[105],"points":[106],"continue":[110],"conditions":[112],"stability.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
