{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:57:19Z","timestamp":1760147839663,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T00:00:00Z","timestamp":1678233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundations of china","award":["62173267","62273269","61573276","62173266","U1809202","2019JM-111","2020JC-05"],"award-info":[{"award-number":["62173267","62273269","61573276","62173266","U1809202","2019JM-111","2020JC-05"]}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["62173267","62273269","61573276","62173266","U1809202","2019JM-111","2020JC-05"],"award-info":[{"award-number":["62173267","62273269","61573276","62173266","U1809202","2019JM-111","2020JC-05"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A significant challenge in robust model predictive control (MPC) is the online computational complexity. This paper proposes a learning-based approach to accelerate online calculations by combining recent advances in deep learning with robust MPC. The use of soft constraint variables addresses feasibility issues in the robust MPC design, while the employment of a symmetrical structure deep neural network (DNN) approximates the robust MPC control law. The symmetry of the network structure facilitates the training process. The use of soft constraints expands the feasible region and also increases the complexity of the training data, making the network difficult to train. To overcome this issue, a dataset construction method is employed. The performance of the proposed method is demonstrated through simulated examples, and the proposed algorithm can be applied to control systems in various fields such as aerospace, three-dimensional printing, optical imaging, and chemical production.<\/jats:p>","DOI":"10.3390\/sym15030676","type":"journal-article","created":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T03:29:05Z","timestamp":1678246145000},"page":"676","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Offline Computation of the Explicit Robust Model Predictive Control Law Based on Deep Neural Networks"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3059-5186","authenticated-orcid":false,"given":"Chaoqun","family":"Ma","sequence":"first","affiliation":[{"name":"Ministry of Education Key Laboratory of Intelligent and Network Security, School of Electronics and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"given":"Xiaoyu","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Information Communication, Army Academy of Armored Forces, Beijing 100072, China"}]},{"given":"Pei","family":"Li","sequence":"additional","affiliation":[{"name":"Research Institute of Tsinghua University in Shenzhen, Shenzhen 518000, China"}]},{"given":"Jing","family":"Liu","sequence":"additional","affiliation":[{"name":"Ministry of Education Key Laboratory of Intelligent and Network Security, School of Electronics and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1016\/0005-1098(96)00063-5","article-title":"Robust constrained model predictive control using linear matrix inequalities","volume":"32","author":"Kothare","year":"1996","journal-title":"Automatica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1109\/9.871769","article-title":"Efficient robust predictive control","volume":"45","author":"Kouvaritakis","year":"2000","journal-title":"IEEE Trans. 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