{"title":"Identifiable specializations for ODE models","authors":"Alexey Ovchinnikov , Anand Pillay , Gleb Pogudin , Thomas Scanlon","doi":"10.1016/j.sysconle.2025.106226","DOIUrl":null,"url":null,"abstract":"<div><div>The parameter identifiability problem for a dynamical system is to determine whether the parameters of the system can be found from data for the outputs of the system. Verifying whether the parameters are identifiable is a necessary first step before a meaningful parameter estimation can take place. Non-identifiability occurs in practical models. To reparametrize a model to achieve identifiability is a challenge. The existing approaches have been shown to be useful for many important examples. However, these approaches are either limited to linear models and scaling parametrizations or are not guaranteed to find a reparametrization even if it exists. In the present paper, we prove that there always exists a locally identifiable model with the same input–output behavior as the original one obtained from a given one by a partial specialization of the parameters. Our result applies to parametric rational ODE models with or without input, and our algorithm can find non-scaling reparametrizations. As an extra feature of our approach, the resulting (at least) locally identifiable reparametrization has the same shape: the monomials in the new state variables in the new model are formed in the same way as in the original model. Furthermore, we give a sufficient observability condition for the existence of a state space transformation from the original model to the new one. Our proof is constructive and can be translated to an algorithm, which we illustrate by several examples, with and without inputs.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"204 ","pages":"Article 106226"},"PeriodicalIF":2.5000,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691125002087","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The parameter identifiability problem for a dynamical system is to determine whether the parameters of the system can be found from data for the outputs of the system. Verifying whether the parameters are identifiable is a necessary first step before a meaningful parameter estimation can take place. Non-identifiability occurs in practical models. To reparametrize a model to achieve identifiability is a challenge. The existing approaches have been shown to be useful for many important examples. However, these approaches are either limited to linear models and scaling parametrizations or are not guaranteed to find a reparametrization even if it exists. In the present paper, we prove that there always exists a locally identifiable model with the same input–output behavior as the original one obtained from a given one by a partial specialization of the parameters. Our result applies to parametric rational ODE models with or without input, and our algorithm can find non-scaling reparametrizations. As an extra feature of our approach, the resulting (at least) locally identifiable reparametrization has the same shape: the monomials in the new state variables in the new model are formed in the same way as in the original model. Furthermore, we give a sufficient observability condition for the existence of a state space transformation from the original model to the new one. Our proof is constructive and can be translated to an algorithm, which we illustrate by several examples, with and without inputs.
期刊介绍:
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.