{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:34:37Z","timestamp":1777455277807,"version":"3.51.4"},"reference-count":28,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62221004"],"award-info":[{"award-number":["62221004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U24A20264"],"award-info":[{"award-number":["U24A20264"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62533013"],"award-info":[{"award-number":["62533013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62303226"],"award-info":[{"award-number":["62303226"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100017534","name":"Project 333 of Jiangsu Province","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100017534","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002553","name":"Seoul National University of Science and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002553","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20230921"],"award-info":[{"award-number":["BK20230921"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Automatica"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.automatica.2026.112956","type":"journal-article","created":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T14:10:20Z","timestamp":1774707020000},"page":"112956","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Asymptotic tracking control of dynamic reference over homomorphically encrypted data with finite modulus"],"prefix":"10.1016","volume":"188","author":[{"given":"Shuai","family":"Feng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junsoo","family":"Kim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.automatica.2026.112956_b1","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1016\/j.automatica.2007.06.030","article-title":"Performance limitations in reference tracking and path following for nonlinear systems","volume":"44","author":"Aguiar","year":"2008","journal-title":"Automatica"},{"issue":"5","key":"10.1016\/j.automatica.2026.112956_b2","doi-asserted-by":"crossref","first-page":"2357","DOI":"10.1109\/TAC.2020.3005920","article-title":"Cloud-based quadratic optimization with partially homomorphic encryption","volume":"66","author":"Alexandru","year":"2020","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"7","key":"10.1016\/j.automatica.2026.112956_b3","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.1109\/9.867021","article-title":"Quantized feedback stabilization of linear systems","volume":"45","author":"Brockett","year":"2000","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112956_b4","doi-asserted-by":"crossref","unstructured":"Cheon,\u00a0J. H., Han,\u00a0K., Kim,\u00a0H., Kim,\u00a0J., & Shim,\u00a0H. (2018). Need for controllers having integer coefficients in homomorphically encrypted dynamic system. In IEEE Conference on Decision and Control (pp. 5020\u20135025).","DOI":"10.1109\/CDC.2018.8619600"},{"issue":"3","key":"10.1016\/j.automatica.2026.112956_b5","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/MCS.2021.3062956","article-title":"Encrypted control for networked systems: An illustrative introduction and current challenges","volume":"41","author":"Darup","year":"2021","journal-title":"IEEE Control Systems Magazine"},{"issue":"2","key":"10.1016\/j.automatica.2026.112956_b6","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1109\/LCSYS.2017.2779473","article-title":"Towards encrypted MPC for linear constrained systems","volume":"2","author":"Darup","year":"2017","journal-title":"IEEE Control Systems Letters"},{"issue":"4","key":"10.1016\/j.automatica.2026.112956_b7","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/TIT.1985.1057074","article-title":"A public key cryptosystem and a signature scheme based on discrete logarithms","volume":"31","author":"ElGamal","year":"1985","journal-title":"Institute of Electrical and Electronics Engineers. Transactions on Information Theory"},{"key":"10.1016\/j.automatica.2026.112956_b8","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.conengprac.2017.07.004","article-title":"Secure and private control using semi-homomorphic encryption","volume":"67","author":"Farokhi","year":"2017","journal-title":"Control Engineering Practice"},{"issue":"1","key":"10.1016\/j.automatica.2026.112956_b9","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1109\/TAC.2020.2981083","article-title":"Networked control under DoS attacks: Tradeoffs between resilience and data rate","volume":"66","author":"Feng","year":"2021","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112956_b10","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2023.111424","article-title":"The bottleneck and ceiling effects in quantized tracking control of heterogeneous multi-agent systems under DoS attacks","volume":"160","author":"Feng","year":"2024","journal-title":"Automatica"},{"issue":"3","key":"10.1016\/j.automatica.2026.112956_b11","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1137\/0315033","article-title":"The linear multivariable regulator problem","volume":"15","author":"Francis","year":"1977","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"5","key":"10.1016\/j.automatica.2026.112956_b12","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/0005-1098(76)90006-6","article-title":"The internal model principle of control theory","volume":"12","author":"Francis","year":"1976","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112956_b13","series-title":"Matrix analysis","author":"Horn","year":"2012"},{"key":"10.1016\/j.automatica.2026.112956_b14","doi-asserted-by":"crossref","unstructured":"Kim,\u00a0J., Darup,\u00a0M. S., Sandberg,\u00a0H., & Johansson,\u00a0K. H. (2022). Asymptotic Stabilization over Encrypted Data with Limited Controller Capacity and Time-varying Quantizer. In IEEE Conference on Decision and Control (pp. 7762\u20137767).","DOI":"10.1109\/CDC51059.2022.9993215"},{"key":"10.1016\/j.automatica.2026.112956_b15","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.arcontrol.2022.10.002","article-title":"Comparison of encrypted control approaches and tutorial on dynamic systems using learning with errors-based homomorphic encryption","volume":"54","author":"Kim","year":"2022","journal-title":"Annual Reviews in Control"},{"issue":"2","key":"10.1016\/j.automatica.2026.112956_b16","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/TAC.2022.3142124","article-title":"Dynamic controller that operates over homomorphically encrypted data for infinite time horizon","volume":"68","author":"Kim","year":"2022","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112956_b17","doi-asserted-by":"crossref","unstructured":"Kogiso,\u00a0K., & Fujita,\u00a0T. (2015). Cyber-security enhancement of networked control systems using homomorphic encryption. In IEEE Conference on Decision and Control (pp. 6836\u20136843).","DOI":"10.1109\/CDC.2015.7403296"},{"issue":"2","key":"10.1016\/j.automatica.2026.112956_b18","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1109\/TAC.2002.808487","article-title":"On stabilization of linear systems with limited information","volume":"48","author":"Liberzon","year":"2003","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"5","key":"10.1016\/j.automatica.2026.112956_b19","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1109\/TAC.2007.895850","article-title":"Input-to-state stabilization of linear systems with quantized state measurements","volume":"52","author":"Liberzon","year":"2007","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112956_b20","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1109\/LCSYS.2022.3188944","article-title":"Secure formation control via edge computing enabled by fully homomorphic encryption and mixed uniform-logarithmic quantization","volume":"7","author":"Marcantoni","year":"2022","journal-title":"IEEE Control Systems Letters"},{"issue":"9","key":"10.1016\/j.automatica.2026.112956_b21","doi-asserted-by":"crossref","first-page":"3950","DOI":"10.1109\/TAC.2020.2992445","article-title":"Secure and private implementation of dynamic controllers using semihomomorphic encryption","volume":"65","author":"Murguia","year":"2020","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112956_b22","doi-asserted-by":"crossref","unstructured":"Paillier,\u00a0P. (1999). Public-key cryptosystems based on composite degree residuosity classes. In Proceedings of the international conference on theory and application of cryptographic techniques (pp. 223\u2013238).","DOI":"10.1007\/3-540-48910-X_16"},{"issue":"10","key":"10.1016\/j.automatica.2026.112956_b23","doi-asserted-by":"crossref","first-page":"4035","DOI":"10.1109\/TAC.2019.2890887","article-title":"Secure and privacy-preserving consensus","volume":"64","author":"Ruan","year":"2019","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112956_b24","doi-asserted-by":"crossref","DOI":"10.1016\/j.arcontrol.2023.100913","article-title":"A brief survey on encrypted control: From the first to the second generation and beyond","author":"Schl\u00fcter","year":"2023","journal-title":"Annual Reviews in Control"},{"issue":"10","key":"10.1016\/j.automatica.2026.112956_b25","doi-asserted-by":"crossref","first-page":"5610","DOI":"10.1109\/TAC.2021.3131126","article-title":"On the stability of linear dynamic controllers with integer coefficients","volume":"67","author":"Schl\u00fcter","year":"2021","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"6","key":"10.1016\/j.automatica.2026.112956_b26","doi-asserted-by":"crossref","first-page":"2163","DOI":"10.1109\/TCST.2025.3577536","article-title":"Cyber-secure teleoperation with encrypted four-channel bilateral control","volume":"33","author":"Takanashi","year":"2025","journal-title":"IEEE Transactions on Control Systems Technology"},{"key":"10.1016\/j.automatica.2026.112956_b27","doi-asserted-by":"crossref","unstructured":"Teranishi,\u00a0K., Shimada,\u00a0N., & Kogiso,\u00a0K. (2019). Stability analysis and dynamic quantizer for controller encryption. In IEEE Conference on Decision and Control (pp. 7184\u20137189).","DOI":"10.1109\/CDC40024.2019.9029356"},{"issue":"4","key":"10.1016\/j.automatica.2026.112956_b28","doi-asserted-by":"crossref","first-page":"1704","DOI":"10.1109\/TCST.2020.3019501","article-title":"Secure state estimation using hybrid homomorphic encryption scheme","volume":"29","author":"Zhang","year":"2020","journal-title":"IEEE Transactions on Control Systems Technology"}],"container-title":["Automatica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0005109826001408?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0005109826001408?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:58:42Z","timestamp":1777381122000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0005109826001408"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":28,"alternative-id":["S0005109826001408"],"URL":"https:\/\/doi.org\/10.1016\/j.automatica.2026.112956","relation":{},"ISSN":["0005-1098"],"issn-type":[{"value":"0005-1098","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Asymptotic tracking control of dynamic reference over homomorphically encrypted data with finite modulus","name":"articletitle","label":"Article Title"},{"value":"Automatica","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.automatica.2026.112956","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"112956"}}