{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T15:19:29Z","timestamp":1772637569647,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T00:00:00Z","timestamp":1719100800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003052","name":"Ministry of Trade, Industry &amp; Energy (MOTIE, Korea)","doi-asserted-by":"publisher","award":["20015831"],"award-info":[{"award-number":["20015831"]}],"id":[{"id":"10.13039\/501100003052","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003052","name":"Ministry of Trade, Industry &amp; Energy (MOTIE, Korea)","doi-asserted-by":"publisher","award":["2021RIS-003"],"award-info":[{"award-number":["2021RIS-003"]}],"id":[{"id":"10.13039\/501100003052","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministry of Education (MOE)","award":["20015831"],"award-info":[{"award-number":["20015831"]}]},{"name":"Ministry of Education (MOE)","award":["2021RIS-003"],"award-info":[{"award-number":["2021RIS-003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Given the increased significance of electric vehicles in recent years, this study aimed to develop a novel form of direct yaw-moment control (DYC) to enhance the driving stability of four-wheel independent drive (4WID) electric vehicles. Specifically, this study developed an innovative non-singular fast terminal sliding mode control (NFTSMC) method that integrates NFTSM and a fast-reaching control law. Moreover, this study employed a radial basis function neural network (RBFNN) to approximate both the entire system model and uncertain components, thereby reducing the computational load associated with a complex system model and augmenting the overall control performance. Using the aforementioned factors, the optimal additional yaw moment to ensure the lateral stability of a vehicle is determined. To generate the additional yaw moment, we introduce a real-time optimal torque distribution method based on the vertical load ratio. The stability of the proposed approach is comprehensively verified using the Lyapunov theory. Lastly, the validity of the proposed DYC system is confirmed by simulation tests involving step and sinusoidal inputs conducted using Matlab\/Simulink and CarSim software. Compared to conventional sliding mode control (SMC) and NFTSMC methods, the proposed approach showed improvements in yaw rate tracking accuracy for all scenarios, along with a significant reduction in the chattering phenomenon in control torques.<\/jats:p>","DOI":"10.3390\/s24134079","type":"journal-article","created":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T06:59:58Z","timestamp":1719212398000},"page":"4079","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Improving Direct Yaw-Moment Control via Neural-Network-Based Non-Singular Fast Terminal Sliding Mode Control for Electric Vehicles"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8322-8999","authenticated-orcid":false,"given":"Jung Eun","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Electrical, Electronic and Computer Engineering, University of Ulsan, Ulsan 44610, Republic of Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5945-5497","authenticated-orcid":false,"given":"Byeong Woo","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronic and Computer Engineering, University of Ulsan, Ulsan 44610, Republic of Korea"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3400","DOI":"10.1109\/TSMC.2022.3228314","article-title":"Parallel vision for intelligent transportation systems in metaverse: Challenges, solutions, and potential applications","volume":"53","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Syst. Man. Cybern. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TVT.2020.3046052","article-title":"Holistic adaptive multi-model predictive control for the path following of 4WID autonomous vehicles","volume":"70","author":"Liang","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1792","DOI":"10.1177\/0954407019880427","article-title":"Coordinated control of stability and economy based on torque distribution of distributed drive electric vehicle","volume":"234","author":"Zhao","year":"2020","journal-title":"Proc. Inst. Mech. Eng. D J. Automob. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"12807","DOI":"10.1109\/TVT.2020.3030863","article-title":"Evaluating model predictive path following and yaw stability controllers for over-actuated autonomous electric vehicles","volume":"69","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","first-page":"559","article-title":"Comparison of path tracking and torque-vectoring controllers for autonomous electric vehicles","volume":"3","author":"Chatzikomis","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2696","DOI":"10.1109\/TITS.2017.2754140","article-title":"Improving vehicle handling stability based on combined AFS and DYC system via robust Takagi-Sugeno fuzzy control","volume":"19","author":"Jin","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1742","DOI":"10.1080\/00423114.2021.1879390","article-title":"Driver assistant yaw stability control via integration of AFS and DYC","volume":"60","author":"Ahmadian","year":"2022","journal-title":"Veh. Syst. Dyn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"11030","DOI":"10.1109\/TITS.2023.3276699","article-title":"DYC Design for Autonomous Distributed Drive Electric Vehicle Considering Tire Nonlinear Mechanical Characteristics in the PWA Form","volume":"24","author":"Sun","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"105947","DOI":"10.1016\/j.conengprac.2024.105947","article-title":"A direct yaw moment control frame through model predictive control considering vehicle trajectory tracking performance and handling stability for autonomous driving","volume":"148","author":"Jin","year":"2024","journal-title":"Control Eng. Pract."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2046","DOI":"10.1109\/TIV.2023.3284220","article-title":"A novel event-triggered torque vectoring control for improving lateral stability and communication resource consumption of electric vehicles","volume":"9","author":"Wong","year":"2023","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"32769","DOI":"10.1109\/ACCESS.2018.2834565","article-title":"Automotive ABS\/DYC coordinated control under complex driving conditions","volume":"6","author":"Wang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1109\/TMECH.2014.2322629","article-title":"An ABS control strategy for commercial vehicle","volume":"20","author":"Wei","year":"2014","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1016\/j.conengprac.2011.08.005","article-title":"Nested PID steering control for lane keeping in autonomous vehicles","volume":"19","author":"Marino","year":"2011","journal-title":"Control Eng. Pract."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1080\/10584587.2018.1457370","article-title":"Research on path tracking of intelligent vehicle based on optimal deviation control","volume":"191","author":"Zhang","year":"2018","journal-title":"Integr. Ferroelectr."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2482","DOI":"10.1109\/TITS.2017.2749416","article-title":"An adaptive hierarchical trajectory following control approach of autonomous four-wheel independent drive electric vehicles","volume":"19","author":"Guo","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1080\/00423114.2015.1025082","article-title":"A novel vehicle dynamics stability control algorithm based on the hierarchical strategy with constrain of nonlinear tyre forces","volume":"53","author":"Li","year":"2015","journal-title":"Veh. Syst. Dyn."},{"key":"ref_17","first-page":"175","article-title":"Model predictive control system based on direct yaw moment control for 4WID self-steering agriculture vehicle","volume":"14","author":"Liu","year":"2021","journal-title":"Int. J. Agric. Biol. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1109\/JAS.2023.123111","article-title":"Resilient event-triggered model predictive control for adaptive cruise control under sensor attacks","volume":"10","author":"Hu","year":"2023","journal-title":"IEEE-CAA J. Autom. Sin."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2488","DOI":"10.1109\/TMECH.2019.2946895","article-title":"Resilient control design for lateral motion regulation of intelligent vehicle","volume":"24","author":"Chang","year":"2019","journal-title":"IEEE-ASME Trans. Mechatron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1016\/j.ifacol.2023.10.1709","article-title":"Security Enhancement for Longitudinal Vehicle Platooning under Denial-of-Service Attacks: From Resilient Controller Design Perspective","volume":"56","author":"Hu","year":"2023","journal-title":"IFAC-PapersOnLine"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.automatica.2016.07.038","article-title":"Second-order sliding mode controller design subject to mismatched term","volume":"77","author":"Ding","year":"2017","journal-title":"Automatica"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"17141","DOI":"10.1007\/s11071-023-08760-9","article-title":"Direct yaw-moment control design for in-wheel electric vehicle with composite terminal sliding mode","volume":"111","author":"Ma","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1109\/TAC.2011.2174676","article-title":"Chattering-free digital sliding-mode control with state observer and disturbance rejection","volume":"57","author":"Acary","year":"2011","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"57854","DOI":"10.1109\/ACCESS.2023.3284686","article-title":"Design and experimental analysis of an adaptive second-order fast non-singular terminal sliding mode controller for electronic throttle with disturbance","volume":"11","author":"Long","year":"2023","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"126896","DOI":"10.1016\/j.neucom.2023.126896","article-title":"Neural network-based sliding mode controllers applied to robot manipulators: A review","volume":"562","author":"Truong","year":"2023","journal-title":"Neurocomputing"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhu, H., Zhang, F., Zhang, Y., Su, L., and Gong, G. (2022). Yaw Stability Research of the Distributed Drive Electric Bus by Adaptive Nonsingular Fast Terminal Sliding Mode Control. Machines, 10.","DOI":"10.3390\/machines10110969"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Han, G., Fu, W., Wang, W., and Wu, Z. (2017). The lateral tracking control for the intelligent vehicle based on adaptive PID neural network. Sensors, 17.","DOI":"10.3390\/s17061244"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3210","DOI":"10.1109\/TFUZZ.2023.3247693","article-title":"Adaptive fuzzy fault tolerant control for robot manipulators with fixed-time convergence","volume":"31","author":"Van","year":"2023","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"8637","DOI":"10.1109\/TAES.2023.3308552","article-title":"Observer-based adaptive fuzzy finite-time attitude control for quadrotor UAVs","volume":"59","author":"Liu","year":"2023","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Swain, S.K., Rath, J.J., and Veluvolu, K.C. (2021). Neural network based robust lateral control for an autonomous vehicle. Electronics, 10.","DOI":"10.3390\/electronics10040510"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Nguyen Truong, T., Tuan Vo, A., Kang, H.J., and Le, T.D. (2021, January 12\u201315). A neural terminal sliding mode control for tracking control of robotic manipulators in uncertain dynamical environments. Proceedings of the International Conference on Intelligent Computing, Shenzhen, China.","DOI":"10.1007\/978-3-030-84529-2_18"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Lee, J.E., and Kim, B.W. (2023, January 11\u201313). Research on Direct Yaw Moment Control Based on Neural Sliding Mode Control for Four-Wheel Actuated Electric Vehicles. Proceedings of the 2023 IEEE 6th International Conference on Knowledge Innovation and Invention (ICKII), Sapporo, Japan.","DOI":"10.1109\/ICKII58656.2023.10332604"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"108668","DOI":"10.1016\/j.ast.2023.108668","article-title":"Antisaturation fixed-time attitude tracking control based low-computation learning for uncertain quadrotor UAVs with external disturbances","volume":"142","author":"Liu","year":"2023","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_34","first-page":"7502516","article-title":"Observer-based Adaptive Finite-Time Neural Control for Constrained Nonlinear Systems With Actuator Saturation Compensation","volume":"73","author":"Liu","year":"2024","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Lin, J., Zou, T., Zhang, F., and Zhang, Y. (2022). Yaw stability research of the distributed drive electric bus by adaptive fuzzy sliding mode control. Energies, 15.","DOI":"10.3390\/en15041280"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2568","DOI":"10.1109\/TTE.2022.3212171","article-title":"Nonsingular terminal sliding mode based direct yaw moment control for four-wheel independently actuated autonomous vehicles","volume":"9","author":"Sun","year":"2022","journal-title":"IEEE Trans. Transp. Electrif."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Wang, H., Han, J., and Zhang, H. (2022). Lateral stability analysis of 4WID electric vehicle based on sliding mode control and optimal distribution torque strategy. Actuators, 11.","DOI":"10.3390\/act11090244"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1049\/iet-cta.2014.0202","article-title":"Non-singular fixed-time terminal sliding mode control of non-linear systems","volume":"9","author":"Zuo","year":"2015","journal-title":"IET Control Theory Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1109\/JAS.2019.1911729","article-title":"Four wheel independent drive electric vehicle lateral stability control strategy","volume":"7","author":"Tian","year":"2020","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1007\/s12239-021-0104-5","article-title":"Hierarchical control of yaw stability and energy efficiency for distributed drive electric vehicles","volume":"22","author":"Jing","year":"2021","journal-title":"Int. J. Automot. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"6752","DOI":"10.1109\/TIE.2017.2682024","article-title":"Sliding mode direct yaw-moment control design for in-wheel electric vehicles","volume":"64","author":"Ding","year":"2017","journal-title":"IEEE Trans. Ind. Electron."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/13\/4079\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:03:13Z","timestamp":1760108593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/13\/4079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,23]]},"references-count":41,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["s24134079"],"URL":"https:\/\/doi.org\/10.3390\/s24134079","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,23]]}}}