{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:13Z","timestamp":1760242513965,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,7,31]],"date-time":"2017-07-31T00:00:00Z","timestamp":1501459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61403166"],"award-info":[{"award-number":["61403166"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["China; BK20140164"],"award-info":[{"award-number":["China; BK20140164"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["JUSRP11561, JUSRP51510"],"award-info":[{"award-number":["JUSRP11561, JUSRP51510"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the structure of the lifted models using the traditional lifting technique. Furthermore, an auxiliary model-based multi-innovation stochastic gradient algorithm is presented to estimate the parameters involved in the linear and nonlinear blocks. The simulation results confirm that the proposed algorithm is effective and can achieve a high estimation performance.<\/jats:p>","DOI":"10.3390\/a10030084","type":"journal-article","created":{"date-parts":[[2017,8,1]],"date-time":"2017-08-01T03:30:06Z","timestamp":1501558206000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Auxiliary Model Based Multi-Innovation Stochastic Gradient Identification Algorithm for Periodically Non-Uniformly Sampled-Data Hammerstein Systems"],"prefix":"10.3390","volume":"10","author":[{"given":"Li","family":"Xie","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China"},{"name":"School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huizhong","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China"},{"name":"School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.jprocont.2009.08.003","article-title":"Selective recursive kernel learning for online identification of nonlinear systems with NARX form","volume":"20","author":"Liu","year":"2010","journal-title":"J. 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