{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:04:39Z","timestamp":1760234679927,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T00:00:00Z","timestamp":1622764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Cyber\u2013physical systems (CPS) have been widely employed as wireless control networks. There is a special type of CPS which is developed from the wireless networked control systems (WNCS). They usually include two communication links: Uplink transmission and downlink transmission. Those two links form a closed-loop. When such CPS are deployed for time-sensitive applications such as remote control, the uplink and downlink propagation delay are non-negligible. However, existing studies on CPS\/WNCS usually ignore the propagation delay of the uplink and downlink channels. In order to achieve the best balance between uplink and downlink transmissions under such circumstances, we propose a heuristic framework to obtain the optimal scheduling strategy that can minimize the long-term average control cost. We model the optimization problem as a Markov decision process (MDP), and then give the sufficient conditions for the existence of the optimal scheduling strategy. We propose the semi-predictive framework to eliminate the impact of the coupling characteristic between the uplink and downlink data packets. Then we obtain the lookup table-based optimal offline strategy and the neural network-based suboptimal online strategy. Numerical simulation shows that the scheduling strategies obtained by this framework can bring significant performance improvements over the existing strategies.<\/jats:p>","DOI":"10.3390\/e23060714","type":"journal-article","created":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T11:12:13Z","timestamp":1622805133000},"page":"714","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Scheduling Strategy Design Framework for Cyber\u2013Physical System with Non-Negligible Propagation Delay"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3404-0636","authenticated-orcid":false,"given":"Zuoyu","family":"An","sequence":"first","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6950-0594","authenticated-orcid":false,"given":"Shaohua","family":"Wu","sequence":"additional","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9835-8200","authenticated-orcid":false,"given":"Tiange","family":"Liu","sequence":"additional","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7988-9820","authenticated-orcid":false,"given":"Jian","family":"Jiao","sequence":"additional","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JAS.2019.1911651","article-title":"Networked control systems: A survey of trends and techniques","volume":"7","author":"Zhang","year":"2020","journal-title":"IEEE\/CAA J. 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