{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:08:09Z","timestamp":1770898089142,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,1]],"date-time":"2020-02-01T00:00:00Z","timestamp":1580515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005047","name":"Natural Science Foundation of Liaoning Province","doi-asserted-by":"publisher","award":["20180551003"],"award-info":[{"award-number":["20180551003"]}],"id":[{"id":"10.13039\/501100005047","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper proposes a non-singular fast terminal sliding mode control strategy based on the self-organizing radial basis function neural network (RBFNN) approximation for the train key network system to realize the safe and reliable operation of the train. In order to improve the RBFNN approximation performance and speed, an improved multi-strategy particle swarm optimization (IMPSO) algorithm, which utilizes multi-strategy evolution ways with a nonlinear deceasing inertia weight to improve the global optimizing performance of particle swarm, is proposed to optimize the structure and parameters for better mapping the highly nonlinear characteristics of train traction braking. In addition, the IMPSO is also introduced into a non-singular fast terminal sliding mode (NFTSM) controller to obtain the most appropriate tuning parameters of the controller and suppresses the chattering phenomenon from sliding mode controller. The stability characteristic of the system under the proposed NFTSM controller is studied based on the Lyapunov theory. Further combined with effective delay prediction and delay compensation methods, the NFTSM high-precision control of the train key nonlinear network system is implemented. The simulation results show that the proposed method has more efficient and robust tracking performance and real-time performance compared with other control methods, which can provide effective means for realizing the symmetrical bus control by automatic train operation (ATO) at both ends of the train, with the safe operation of the train under every complex motion condition.<\/jats:p>","DOI":"10.3390\/sym12020205","type":"journal-article","created":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T01:25:51Z","timestamp":1580693151000},"page":"205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Non-Singular Fast Terminal Sliding Mode Control of High-Speed Train Network System Based on Improved Particle Swarm Optimization Algorithm"],"prefix":"10.3390","volume":"12","author":[{"given":"Xiangyu","family":"Kong","sequence":"first","affiliation":[{"name":"College of Electrical and Information Engineering, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Tong","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,1]]},"reference":[{"key":"ref_1","first-page":"93","article-title":"Real-Time Control Method for Communication Network of High-Speed EMU Based on T-S Fuzzy Model","volume":"39","author":"Zhang","year":"2018","journal-title":"China Railw. 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