{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T06:06:46Z","timestamp":1783490806987,"version":"3.55.0"},"reference-count":138,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2024,7,27]],"date-time":"2024-07-27T00:00:00Z","timestamp":1722038400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62103218"],"award-info":[{"award-number":["62103218"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p>This paper mainly discussed the highly efficient iterative identification methods for bilinear systems with autoregressive moving average noise. Firstly, the input-output representation of the bilinear systems is derived through eliminating the unknown state variables in the model. Then based on the maximum-likelihood principle, a maximum-likelihood gradient-based iterative (ML-GI) algorithm is proposed to identify the parameters of the bilinear systems with colored noises. For improving the computational efficiency, the original identification model is divided into three sub-identification models with smaller dimensions and fewer parameters, and a hierarchical maximum-likelihood gradient-based iterative (H-ML-GI) algorithm is derived by using the hierarchical identification principle. A gradient-based iterative (GI) algorithm is given for comparison. Finally, the algorithms are verified by a simulation example and a practical continuous stirred tank reactor (CSTR) example. The results show that the proposed algorithms are effective for identifying bilinear systems with colored noises and the H-ML-GI algorithm has a higher computational efficiency and a faster convergence rate than the ML-GI algorithm and the GI algorithm.<\/jats:p>","DOI":"10.1177\/09596518241256145","type":"journal-article","created":{"date-parts":[[2024,7,27]],"date-time":"2024-07-27T05:21:11Z","timestamp":1722057671000},"page":"1763-1784","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":23,"title":["Highly efficient maximum-likelihood identification methods for bilinear systems with colored noises"],"prefix":"10.1177","volume":"238","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3007-8944","authenticated-orcid":false,"given":"Meihang","family":"Li","sequence":"first","affiliation":[{"name":"College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ximei","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yamin","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Electronic Information Engineering, Taiyuan University of Science and Technology, Taiyuan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feng","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Internet of Things Engineering, Jiangnan University, Wuxi, China"},{"name":"School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2024,7,27]]},"reference":[{"key":"bibr1-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2022.3207415"},{"key":"bibr2-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-020-0619-y"},{"key":"bibr3-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-021-1028-6"},{"key":"bibr4-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-021-1018-8"},{"key":"bibr5-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-021-0845-y"},{"key":"bibr6-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-022-0253-y"},{"key":"bibr7-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2015.1195"},{"key":"bibr8-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.6657"},{"issue":"1","key":"bibr9-09596518241256145","first-page":"206","volume":"70","author":"Ji Y","year":"2023","journal-title":"IEEE Trans Circuits Syst II Express Briefs"},{"key":"bibr10-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1177\/09596518231207417"},{"key":"bibr11-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2022.3151587"},{"key":"bibr12-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1177\/09596518231171226"},{"key":"bibr13-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2016.02.013"},{"key":"bibr14-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1177\/09596518211054921"},{"key":"bibr15-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2018.12.015"},{"key":"bibr16-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2022.110365"},{"key":"bibr17-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/9.769370"},{"key":"bibr18-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1049\/ip-d.1989.0018"},{"key":"bibr19-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3607"},{"key":"bibr20-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2022.114794"},{"key":"bibr21-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2024.01.035"},{"key":"bibr22-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1080\/00207178708933743"},{"key":"bibr23-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3655"},{"key":"bibr24-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-016-2035-z"},{"key":"bibr25-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3203"},{"key":"bibr26-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3308"},{"key":"bibr27-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2016.04.026"},{"key":"bibr28-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2023.05.006"},{"key":"bibr29-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.856664"},{"key":"bibr30-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3657"},{"key":"bibr31-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-019-0191-5"},{"key":"bibr32-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2023.115107"},{"key":"bibr33-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-021-0923-1"},{"key":"bibr34-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.5450"},{"key":"bibr35-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2019.0112"},{"key":"bibr36-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1049\/iet-spr.2019.0481"},{"key":"bibr37-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-019-0140-3"},{"key":"bibr38-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2014.10.126"},{"key":"bibr39-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.7014"},{"key":"bibr40-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2024.100942"},{"key":"bibr41-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.6227"},{"key":"bibr42-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3420"},{"key":"bibr43-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3029"},{"key":"bibr44-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-021-0367-7"},{"key":"bibr45-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.4961"},{"key":"bibr46-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2023.100909"},{"key":"bibr47-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2021.11.002"},{"key":"bibr48-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2020.3026286"},{"key":"bibr49-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3753"},{"key":"bibr50-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-021-0448-7"},{"key":"bibr51-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3669"},{"key":"bibr52-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.5084"},{"key":"bibr53-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2022.04.011"},{"key":"bibr54-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2023.03.003"},{"key":"bibr55-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2022.02.001"},{"key":"bibr56-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2022.04.012"},{"key":"bibr57-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2022.10.001"},{"key":"bibr58-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2023.03.009"},{"key":"bibr59-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2023.03.004"},{"key":"bibr60-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.6796"},{"key":"bibr61-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s00034-023-02477-1"},{"key":"bibr62-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/oca.2813"},{"key":"bibr63-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2022.01.032"},{"key":"bibr64-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3354"},{"key":"bibr65-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.5675"},{"key":"bibr66-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.109034"},{"key":"bibr67-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2022.3183104"},{"key":"bibr68-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2019.2924421"},{"key":"bibr69-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2022.3193879"},{"key":"bibr70-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2022.3153814"},{"key":"bibr71-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2020.3016254"},{"key":"bibr72-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2021.3137600"},{"key":"bibr73-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s42835-022-01130-2"},{"key":"bibr74-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-022-0189-2"},{"key":"bibr75-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s00034-024-02627-z"},{"key":"bibr76-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2020.2991609"},{"key":"bibr77-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.109184"},{"key":"bibr78-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2023.115104"},{"key":"bibr79-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2021.04.006"},{"key":"bibr80-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3699"},{"key":"bibr81-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3602"},{"key":"bibr82-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3550"},{"key":"bibr83-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3604"},{"key":"bibr84-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2019.2907505"},{"key":"bibr85-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2019.1704093"},{"key":"bibr86-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3519"},{"key":"bibr87-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.6101"},{"key":"bibr88-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3712"},{"key":"bibr89-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.5718"},{"key":"bibr90-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3367"},{"key":"bibr91-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2023.103007"},{"key":"bibr92-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2023.115297"},{"key":"bibr93-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TVT.2019.2925903"},{"key":"bibr94-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TAES.2022.3215946"},{"key":"bibr95-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1049\/cje.2017.08.024"},{"key":"bibr96-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TVT.2022.3158436"},{"key":"bibr97-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2021.3127677"},{"key":"bibr98-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2020.3026999"},{"key":"bibr99-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2023.2178864"},{"key":"bibr100-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2023.10.038"},{"key":"bibr101-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2014.2387216"},{"key":"bibr102-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2024.105762"},{"key":"bibr103-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1142\/S0219519424500040"},{"key":"bibr104-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s11760-023-02951-y"},{"key":"bibr105-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s11517-024-03046-7"},{"key":"bibr106-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X22400990"},{"key":"bibr107-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2020.12.010"},{"key":"bibr108-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2019.2939358"},{"key":"bibr109-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.aap.2022.106764"},{"key":"bibr110-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1049\/cje.2021.00.241"},{"key":"bibr111-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2022.3170950"},{"key":"bibr112-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2022.3155628"},{"key":"bibr113-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2021.3109632"},{"key":"bibr114-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/TVT.2019.2914936"},{"key":"bibr115-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2024.105774"},{"key":"bibr116-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1080\/15435075.2024.2332331"},{"issue":"3","key":"bibr117-09596518241256145","first-page":"2677","volume":"77","author":"Shu J","year":"2023","journal-title":"Comput Mat Contin"},{"key":"bibr118-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2022.03.006"},{"key":"bibr119-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2018.04.013"},{"key":"bibr120-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1109\/MITS.2022.3174238"},{"key":"bibr121-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2021.11.011"},{"key":"bibr122-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.est.2023.110240"},{"key":"bibr123-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1115\/1.4063847"},{"key":"bibr124-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/acs.3593"},{"key":"bibr125-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.6951"},{"key":"bibr126-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.5323"},{"key":"bibr127-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2019.0731"},{"key":"bibr128-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-019-0940-5"},{"key":"bibr129-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.5850"},{"key":"bibr130-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s00034-018-1015-1"},{"key":"bibr131-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-022-0053-4"},{"key":"bibr132-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s00034-018-1014-2"},{"key":"bibr133-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-023-0003-9"},{"key":"bibr134-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2023.126998"},{"key":"bibr135-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2024.111329"},{"key":"bibr136-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.7344"},{"key":"bibr137-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1002\/oca.3158"},{"key":"bibr138-09596518241256145","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2023.115724"}],"container-title":["Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/09596518241256145","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/09596518241256145","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/09596518241256145","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:46:38Z","timestamp":1777675598000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/09596518241256145"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,27]]},"references-count":138,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["10.1177\/09596518241256145"],"URL":"https:\/\/doi.org\/10.1177\/09596518241256145","relation":{},"ISSN":["0959-6518","2041-3041"],"issn-type":[{"value":"0959-6518","type":"print"},{"value":"2041-3041","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,27]]}}}