{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T16:09:05Z","timestamp":1777910945586,"version":"3.51.4"},"reference-count":40,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T00:00:00Z","timestamp":1717718400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:p>This article introduces a method for the adaptive control of a six-dimensional (6D) hyperchaotic system using a multi-input multi-output (MIMO) approach, leveraging the deep deterministic policy gradient (DDPG) algorithm. The states and tracking errors of the hyperchaotic system are amalgamated to form an input image signal. This signal is then processed by a deep convolutional neural network (CNN) to extract profound features. Subsequently, the DDPG determines the coefficients of the proportional\u2013integral\u2013derivative (PID) controller based on the features discerned from the CNN. The proposed approach exhibits robustness to uncertainties and varying initial conditions, attributed to the DDPG\u2019s ability to learn from the input image signal and adaptively adjust control policies and PID coefficients. The results demonstrate that the proposed adaptive PID controller, integrated with DDPG and CNN, surpasses conventional controllers in terms of synchronization accuracy and response speed. The paper presents the following: a 6D hyperchaotic system\u2019s dynamic model, a CNN-based DDPG\u2019s structure, and how it performs and compares to traditional methods. Then, it summarizes the main findings.<\/jats:p>","DOI":"10.1177\/01423312241253639","type":"journal-article","created":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T03:50:16Z","timestamp":1717732216000},"page":"572-584","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Adaptive PID controller using deep deterministic policy gradient for a 6D hyperchaotic system"],"prefix":"10.1177","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9124-4139","authenticated-orcid":false,"given":"Mohammad Ali","family":"Labbaf Khaniki","sequence":"first","affiliation":[{"name":"Department of Control Engineering, Faculty of Electrical Engineering, K.N. Toosi University of Technology, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amirhossein","family":"Samii","sequence":"additional","affiliation":[{"name":"Department of Electrical & Computer Engineering, School of Electrical and Computer Engineering, Technical University of Crete, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6851-1614","authenticated-orcid":false,"given":"Mahsan","family":"Tavakoli-Kakhki","sequence":"additional","affiliation":[{"name":"Department of Control Engineering, Faculty of Electrical Engineering, K.N. Toosi University of Technology, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,6,7]]},"reference":[{"key":"bibr1-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2013.796068"},{"key":"bibr2-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2021.08.005"},{"key":"bibr3-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2017.2743240"},{"key":"bibr4-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1007\/s11235-021-00790-1"},{"key":"bibr5-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6579\/ad1459"},{"key":"bibr6-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1177\/10775463221101935"},{"key":"bibr7-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2020.02.017"},{"key":"bibr8-01423312241253639","doi-asserted-by":"publisher","DOI":"10.3390\/min13040472"},{"key":"bibr9-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1177\/01423312231152936"},{"key":"bibr10-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2018.1532607"},{"key":"bibr11-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2020.2979561"},{"key":"bibr12-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1109\/TETCI.2023.3301793"},{"key":"bibr13-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1002\/asjc.2653"},{"key":"bibr14-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1109\/ICCKE50421.2020.9303634"},{"issue":"6","key":"bibr15-01423312241253639","first-page":"171","volume":"20","author":"Labbaf Khaniki MA","year":"2023","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"bibr16-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1177\/01423312221087578"},{"key":"bibr17-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1109\/LCOMM.2018.2825444"},{"key":"bibr18-01423312241253639","volume-title":"Proceedings of the 4th international conference on learning representations (ICLR\u20192016)","author":"Lillicrap TP","year":"2016"},{"key":"bibr19-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1016\/j.tre.2019.09.013"},{"key":"bibr20-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0249993"},{"key":"bibr21-01423312241253639","unstructured":"McCarthy PX, Rizoiu M-A, Eghbal S, et al. (2020) Long-term trends of diversity online. Available at: https:\/\/arxiv.org\/abs\/2003.07049v1"},{"key":"bibr22-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1109\/PESGM52003.2023.10252920"},{"key":"bibr23-01423312241253639","doi-asserted-by":"publisher","DOI":"10.3390\/s24082585"},{"key":"bibr24-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1109\/ICRoM48714.2019.9071803"},{"key":"bibr25-01423312241253639","unstructured":"Rabiee P, Safari A (2023) Safe exploration in reinforcement learning: Training backup control barrier functions with zero training time safety violations. Available at: https:\/\/arxiv.org\/abs\/2312.07828"},{"key":"bibr26-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1080\/09540091.2020.1723491"},{"key":"bibr27-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1115\/IMECE2022-96034"},{"key":"bibr28-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1115\/IMECE2022-95145"},{"key":"bibr29-01423312241253639","doi-asserted-by":"crossref","unstructured":"Safari K, Khalfalla S, Imani F. (n.d.) Physics-guided deep learning for discovering and monitoring melt pool dynamics in additive manufacturing. DOI: 10.2139\/ssrn.4280300","DOI":"10.2139\/ssrn.4280300"},{"key":"bibr30-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2020.03.063"},{"key":"bibr31-01423312241253639","volume-title":"Reinforcement Learning: An Introduction","author":"Sutton RS","year":"2018"},{"key":"bibr32-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1186\/s40638-016-0055-x"},{"key":"bibr33-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1007\/s12652-020-01768-8"},{"key":"bibr34-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1109\/ICDABI51230.2020.9325622"},{"key":"bibr35-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-020-0809-7"},{"key":"bibr36-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1002\/cta.2617"},{"key":"bibr37-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1177\/01423312221114694"},{"key":"bibr38-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1177\/0142331218778324"},{"key":"bibr39-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/6683284"},{"key":"bibr40-01423312241253639","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2021.102193"}],"container-title":["Transactions of the Institute of Measurement and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/01423312241253639","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/01423312241253639","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/01423312241253639","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T15:10:47Z","timestamp":1777648247000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/01423312241253639"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,7]]},"references-count":40,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["10.1177\/01423312241253639"],"URL":"https:\/\/doi.org\/10.1177\/01423312241253639","relation":{},"ISSN":["0142-3312","1477-0369"],"issn-type":[{"value":"0142-3312","type":"print"},{"value":"1477-0369","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,7]]}}}