{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:16:09Z","timestamp":1760148969788,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T00:00:00Z","timestamp":1687219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2022YFC3803700","2022YFE0123400","2022JQ-667"],"award-info":[{"award-number":["2022YFC3803700","2022YFE0123400","2022JQ-667"]}]},{"name":"Key R&amp;D Project of the Ministry of Science and Technology of China","award":["2022YFC3803700","2022YFE0123400","2022JQ-667"],"award-info":[{"award-number":["2022YFC3803700","2022YFE0123400","2022JQ-667"]}]},{"name":"Natural Science Foundation of Shaanxi Province","award":["2022YFC3803700","2022YFE0123400","2022JQ-667"],"award-info":[{"award-number":["2022YFC3803700","2022YFE0123400","2022JQ-667"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A novel optimal control problem is considered for multiple input multiple output (MIMO) stochastic systems with mixed parameter drift, external disturbance and observation noise. The proposed controller can not only track and identify the drift parameters in finite time but, furthermore, drive the system to move towards the desired trajectory. However, there is a conflict between control and estimation, which makes the analytic solution unattainable in most situations. A dual control algorithm based on weight factor and innovation is, therefore, proposed. First, the innovation is added to the control goal by the appropriate weight and the Kalman filter is introduced to estimate and track the transformed drift parameters. The weight factor is used to adjust the degree of drift parameter estimation in order to achieve a balance between control and estimation. Then, the optimal control is derived by solving the modified optimization problem. In this strategy, the analytic solution of the control law can be obtained. The control law obtained in this paper is optimal because the estimation of drift parameters is integrated into the objective function rather than the suboptimal control law, which includes two parts of control and estimation in other studies. The proposed algorithm can achieve the best compromise between optimization and estatimation. Finally, the effectiveness of the algorithm is verified by numerical experiments in two different cases.<\/jats:p>","DOI":"10.3390\/s23125743","type":"journal-article","created":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T02:30:51Z","timestamp":1687314651000},"page":"5743","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimal Control Algorithm for Stochastic Systems with Parameter Drift"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5347-1787","authenticated-orcid":false,"given":"Xiaoyan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Song","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaobo","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaoru","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Electronic Information Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1718","DOI":"10.1016\/j.automatica.2007.10.029","article-title":"Optimal and suboptimal smoothing algorithms for identification of time-varying systems with randomly drifting parameters","volume":"44","author":"Maciej","year":"2008","journal-title":"Automatica"},{"key":"ref_2","unstructured":"Nakamura, S. 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