{"doi":"10.1515/amcs-2016-0057","title":"Set-membership identifiability of nonlinear models and related parameter estimation properties","abstract":"<jats:title>Abstract</jats:title>\n               <jats:p> Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.</jats:p>","journal":"International Journal of Applied Mathematics and Computer Science","year":2016,"id":20747,"datarank":0.5749742310820275,"base_score":1.9459101490553132,"endowment":1.9459101490553132,"self_citation_contribution":0.29188652235829704,"citation_network_contribution":0.28308770872373046,"self_endowment_contribution":0.29188652235829704,"citer_contribution":0.28308770872373046,"corpus_percentile":null,"corpus_rank":null,"citation_count":6,"citer_count":4,"citers_with_citation_signal":4,"citers_with_endowment":4,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":136085,"name":"Louise Travé-MassuyèEs","orcid":null,"position":1,"is_corresponding":false},{"id":136086,"name":"Nathalie Verdière","orcid":null,"position":2,"is_corresponding":false},{"id":136084,"name":"Carine Jauberthie","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":1.9459101490553132,"endowment":1.9459101490553132,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21071399","pmcid":null,"openalex_id":"https://openalex.org/W2573470972","authors":[],"funders":[],"total_grants":0,"fwci":0.81,"citation_percentile":0.77192455,"influential_citations":0,"citation_trend":[{"year":2017,"count":1},{"year":2018,"count":2},{"year":2021,"count":2},{"year":2022,"count":1}],"oa_status":"gold","license":"cc-by-nc-nd","oa_locations":[{"url":"https://content.sciendo.com/downloadpdf/journals/amcs/26/4/article-p803.pdf","host_type":"journal"},{"url":"https://content.sciendo.com/downloadpdf/journals/amcs/26/4/article-p803.pdf","host_type":"GOLD"},{"url":"https://content.sciendo.com/downloadpdf/journals/amcs/26/4/article-p803.pdf","host_type":"publisher"},{"url":"http://content.sciendo.com/view/journals/amcs/26/4/article-p803.xml","host_type":"publisher"},{"url":"https://www.sciendo.com/article/10.1515/amcs-2016-0057","host_type":"publisher"},{"url":"https://doi.org/10.1515/amcs-2016-0057","host_type":"journal"},{"url":"https://hal.science/hal-01701564","host_type":"repository"},{"url":"https://hal.archives-ouvertes.fr/hal-01739551","host_type":"repository"},{"url":"https://doaj.org/article/e98aefe703094e5f989de72bcb5d992b","host_type":"repository"}],"fields_of_study":["Control Systems and Identification","Advanced Control Systems Optimization","Fault Detection and Control Systems","Mathematics","Computer Science","Engineering"],"mesh_terms":[],"keywords":["Identifiability","Soundness","Mathematics","Consistency (knowledge bases)","Applied mathematics","Estimation theory","Set (abstract data type)","Nonlinear system","Differential algebra","Mathematical optimization","Computer science","Algorithm","Statistics","Discrete mathematics","Pure mathematics"],"sdg_mappings":[{"sdg_number":0,"sdg_label":"Reduced inequalities"}],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-06T10:18:31.532499Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}