{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T12:41:03Z","timestamp":1760704863343,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:00:00Z","timestamp":1760400000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Intelligent networked Robotic Research Center","award":["602531004PQ"],"award-info":[{"award-number":["602531004PQ"]}]},{"name":"Guangdong Provincial Department of Education research project","award":["2023ZDZX3077"],"award-info":[{"award-number":["2023ZDZX3077"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>This paper investigates the data-driven event-triggering control of discrete time-delay systems. When there is enough data available, the system parameters can be determined by identified methods, and the model-based controller design can be implemented. However, with little data, this method does not result in an accurate system. The data-driven control method is introduced to address this issue. This paper classifies discrete-time systems with time delays into those with known delays and those with unknown delays. Controllers for systems with known delays and unknown delays are designed based on limited data, and stability is ensured by constructing improved Lyapunov functions. Two analyses are introduced: For the known delay condition, the lifting model method is presented to raise order and change the time-delay system to a delay-free system. Further, the stabilization criterion is presented. For the unknown time-delay system, according to the basic data-driven assumption, the data-driven stabilization criterion is presented. Also, the introduction of a dynamic event-triggering scheme and the discussion in this paper on how its parameters can be chosen can save more computational resources. Based on the two methods, the Lyapunov function is constructed separately, and the controller is derived through Linear Matrix Inequality. Finally, a discrete time-delay system is used as an example to show the effectiveness of these two methods. In addition, the dynamic event-triggering scheme proposed in this paper is compared with other articles to show that the parameter selection method proposed in this paper has better performance.<\/jats:p>","DOI":"10.3390\/info16100893","type":"journal-article","created":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T11:39:34Z","timestamp":1760701174000},"page":"893","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Data-Driven Event-Triggering Control of Discrete Time-Delay Systems"],"prefix":"10.3390","volume":"16","author":[{"given":"Yifan","family":"Gong","sequence":"first","affiliation":[{"name":"School of Information and Communication Technology, Shenzhen City Ploytechinic, Shenzhen 518116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhicheng","family":"Li","sequence":"additional","affiliation":[{"name":"IoT Research Institute, Shenzhen Polytechnic University, Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Wang","sequence":"additional","affiliation":[{"name":"IoT Research Institute, Shenzhen Polytechnic University, Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Van Overschee, P., and De Moor, B. (1996). Subspace Identification for Linear Systems: Theory, Implementation, Applications, Springer Science & Business Media.","DOI":"10.1007\/978-1-4613-0465-4"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1115\/1.4019264","article-title":"Optimum settings for automatic controllers","volume":"64","author":"Ziegler","year":"1942","journal-title":"Trans. Am. Soc. Mech. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.sysconle.2004.09.003","article-title":"A note on persistency of excitation","volume":"54","author":"Willems","year":"2005","journal-title":"Syst. Control Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1946","DOI":"10.1080\/00207170801942170","article-title":"Data-driven simulation and control","volume":"81","author":"Markovsky","year":"2008","journal-title":"Int. J. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1016\/j.automatica.2008.12.012","article-title":"Stability analysis and control design of lti discrete-time systems by the direct use of time series data","volume":"45","author":"Park","year":"2009","journal-title":"Automatica"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.sysconle.2016.04.006","article-title":"Data-driven control: A behavioral approach","volume":"101","author":"Maupong","year":"2017","journal-title":"Syst. Control Lett."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Safonov, M.G., and Tsao, T.-C. (1995). The unfalsified control concept: A direct path from experiment to controller. Feedback Control, Nonlinear Systems, and Complexity, Springer.","DOI":"10.1007\/BFb0027678"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/37.710876","article-title":"Iterative feedback tuning: Theory and applications","volume":"18","author":"Hjalmarsson","year":"1998","journal-title":"IEEE Control Syst. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2173","DOI":"10.1109\/TNN.2011.2176141","article-title":"Data-driven model-free adaptive control for a class of mimo nonlinear discrete-time systems","volume":"22","author":"Shangtai","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3069","DOI":"10.1080\/00207721.2024.2364897","article-title":"Data-driven adaptive optimal control for discrete-time linear time-invariant systems","volume":"55","author":"Wu","year":"2024","journal-title":"Int. J. Syst. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1016\/j.automatica.2010.02.018","article-title":"Online actor\u2013critic algorithm to solve the continuous-time infinite horizon optimal control problem","volume":"46","author":"Vamvoudakis","year":"2010","journal-title":"Automatica"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2699","DOI":"10.1016\/j.automatica.2012.06.096","article-title":"Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics","volume":"48","author":"Jiang","year":"2012","journal-title":"Automatica"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.ifacol.2018.11.059","article-title":"Data-based predictive control via direct weight optimization","volume":"51","author":"Salvador","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, Z., Liu, K., Wang, X., Yuan, X., and Wang, Y. (2024). Efficient data-driven event-triggered predictive control for cyber-physical systems. J. Control Decis., 1\u201310.","DOI":"10.1080\/23307706.2024.2346950"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Dai, T., and Sznaier, M. (2018, January 17\u201319). A moments based approach to designing mimo data driven controllers for switched systems. Proceedings of the 2018 IEEE Conference on Decision and Control (CDC), Miami, FL, USA.","DOI":"10.1109\/CDC.2018.8619361"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1680","DOI":"10.1109\/TAC.2007.904277","article-title":"Event-triggered real-time scheduling of stabilizing control tasks","volume":"52","author":"Tabuada","year":"2007","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.1109\/TAC.2014.2366855","article-title":"Dynamic triggering mechanisms for event-triggered control","volume":"60","author":"Girard","year":"2014","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3300","DOI":"10.1109\/TAC.2018.2874703","article-title":"Dynamic event-triggered and self-triggered control for multi-agent systems","volume":"64","author":"Yi","year":"2018","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2334304","DOI":"10.1080\/21642583.2024.2334304","article-title":"Dynamic event-triggered state estimation for discrete-time delayed switched neural networks with constrained bit rate","volume":"12","author":"Zhang","year":"2024","journal-title":"Syst. Sci. Control. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.1109\/TCYB.2018.2818941","article-title":"Synchronization control for a class of discrete time-delay complex dynamical networks: A dynamic event-triggered approach","volume":"49","author":"Li","year":"2018","journal-title":"IEEE Trans. Cybern."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3322","DOI":"10.1080\/00207721.2024.2371959","article-title":"Fixed time cluster consensus for nonlinear multiagent systems by double dynamic event-triggered mechanisms","volume":"55","author":"Wu","year":"2024","journal-title":"Int. J. Syst. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6066","DOI":"10.1109\/TCYB.2023.3272216","article-title":"Model-based and data-driven control of event-and self-triggered discrete-time linear systems","volume":"53","author":"Wang","year":"2023","journal-title":"IEEE Trans. Cybern."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/10\/893\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T12:04:39Z","timestamp":1760702679000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/10\/893"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,14]]},"references-count":22,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["info16100893"],"URL":"https:\/\/doi.org\/10.3390\/info16100893","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,14]]}}}