{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:24:22Z","timestamp":1760243062974,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,6,24]],"date-time":"2015-06-24T00:00:00Z","timestamp":1435104000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The identification difficulties for a dual-rate Hammerstein system lie in two aspects. First, the identification model of the system contains the products of the parameters of the nonlinear block and the linear block, and a standard least squares method cannot be directly applied to the model; second, the traditional single-rate discrete-time Hammerstein model cannot be used as the identification model for the dual-rate sampled system. In order to solve these problems, by combining the polynomial transformation technique with the key variable separation technique, this paper converts the Hammerstein system into a dual-rate linear regression model about all parameters (linear-in-parameter model) and proposes a recursive least squares algorithm to estimate the parameters of the dual-rate system. The simulation results verify the effectiveness of the proposed algorithm.<\/jats:p>","DOI":"10.3390\/a8030366","type":"journal-article","created":{"date-parts":[[2015,6,24]],"date-time":"2015-06-24T11:05:12Z","timestamp":1435143912000},"page":"366-379","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Identification of Dual-Rate Sampled Hammerstein Systems with a Piecewise-Linear Nonlinearity Using the Key Variable Separation Technique"],"prefix":"10.3390","volume":"8","author":[{"given":"Ying-Ying","family":"Wang","sequence":"first","affiliation":[{"name":"College of Automation Engineering, Qingdao University, 308 Ningxia Road, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiang-Dong","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Engineering, Ocean University of China, 238 Songling Road, Qingdao 266100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong-Qing","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Automation Engineering, Qingdao University, 308 Ningxia Road, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.na.2013.11.015","article-title":"Discrete collapsing sandpile model","volume":"99","author":"Igbida","year":"2014","journal-title":"Nonlinear Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.na.2014.01.002","article-title":"Stability of a turnpike phenomenon for approximate solutions of nonautonomous discrete-time optimal control systems","volume":"100","author":"Zaslavski","year":"2014","journal-title":"Nonlinear Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.aml.2012.04.007","article-title":"Multi-innovation stochastic gradient algorithms for dual-rate sampled systems with preload nonlinearity","volume":"26","author":"Chen","year":"2013","journal-title":"Appl. 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