{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:03:42Z","timestamp":1760151822390,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T00:00:00Z","timestamp":1650499200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Gansu Provincial Department of Education: Excellent Postgraduate &quot;Innovation Star&quot; Project","award":["2021CXZX-552"],"award-info":[{"award-number":["2021CXZX-552"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper studies the distributed adaptive cooperative control of multiple urban rail trains with position output constraints and uncertain parameters. Based on an ordered set of trains running on the route, a dynamic multiple trains movement model is constructed to capture the dynamic evolution of the trains in actual operation. Aiming at the position constraints and uncertainties in the system, different distributed adaptive control algorithms are designed for all trains by using the local information about the position, speed and acceleration of the train operation, so that each train can dynamically adjust its speed through communicating with its neighboring trains. This control algorithm for each train is designed to track the desired position and speed curve, and the headway distance between any two neighboring trains is stable within a preset safety range, which guarantee the safety of tracking operation of multiple urban rail trains. Finally, the effectiveness of the designed scheme is verified by numerical examples.<\/jats:p>","DOI":"10.3390\/a15050138","type":"journal-article","created":{"date-parts":[[2022,4,22]],"date-time":"2022-04-22T05:07:22Z","timestamp":1650604042000},"page":"138","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive Cooperative Control of Multiple Urban Rail Trains with Position Output Constraints"],"prefix":"10.3390","volume":"15","author":[{"given":"Junxia","family":"Yang","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Automation, Lanzhou Jiaotong University, Lanzhou 730070, China"}]},{"given":"Youpeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Lanzhou Jiaotong University, Lanzhou 730070, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1016\/j.trc.2017.09.009","article-title":"Research and development of automatic train operation for railway transportation systems: A survey","volume":"85","author":"Yin","year":"2017","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s00521-011-0681-8","article-title":"Extended fuzzy logic controller for high speed train","volume":"22","author":"Dong","year":"2013","journal-title":"Neural Comput. Appl."},{"key":"ref_3","first-page":"1","article-title":"Driving curve algorithm for heavy haul train based on improved BP Neural Network","volume":"25","author":"Tan","year":"2016","journal-title":"Railw. Comput. Appl."},{"key":"ref_4","first-page":"72","article-title":"Research on automatic train operation based on model-free adaptive control","volume":"38","author":"Shi","year":"2016","journal-title":"J. China Railw. Soc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"14135","DOI":"10.1007\/s10586-018-2258-0","article-title":"Application of fuzzy predictive control technology in automatic train operation","volume":"22","author":"Cao","year":"2018","journal-title":"Clust. Comput."},{"key":"ref_6","first-page":"69","article-title":"Automatic train operation algorithm based on adaptive iterative learning control theory","volume":"20","author":"He","year":"2020","journal-title":"J. Transp. Syst. Eng. Inf. Technol."},{"key":"ref_7","first-page":"61","article-title":"Combined sliding model and PID control of automatic train operation system","volume":"36","author":"Yang","year":"2014","journal-title":"J. China Railw. Soc."},{"key":"ref_8","first-page":"56","article-title":"Precise automatic train stop control of algorithm based on adaptive terminal sliding mode control","volume":"38","author":"Wang","year":"2016","journal-title":"J. China Railw. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.knosys.2015.10.016","article-title":"Smart train operation algorithms based on expert knowledge and ensemble CART for the electric locomotive","volume":"92","author":"Yin","year":"2016","journal-title":"Knowl. Based Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1177\/0954406214532908","article-title":"Stability analysis of bidirectional adaptive cruise control with asymmetric information flow","volume":"229","author":"Ghasemi","year":"2015","journal-title":"ARCHIVE Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3072","DOI":"10.1016\/j.automatica.2013.07.008","article-title":"Energy-efficient train control: From local convexity to global optimization and uniqueness","volume":"49","author":"Albrecht","year":"2013","journal-title":"Automatica"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.trc.2014.06.004","article-title":"Robust sampled-data cruise control scheduling of high speed train","volume":"46","author":"Li","year":"2014","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.trc.2012.02.001","article-title":"Control of metro-trains equipped with onboard super capacitors for energy saving and reduction of power peak demand","volume":"24","author":"Ciccarelli","year":"2012","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.trc.2015.04.016","article-title":"Coordinated cruise control for high-speed train movements based on a multi-agent model","volume":"56","author":"Li","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2157","DOI":"10.1007\/s11071-015-2472-8","article-title":"Adaptive coordinated control of multiple high-speed trains with input saturation","volume":"83","author":"Li","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2740","DOI":"10.1109\/TITS.2018.2877171","article-title":"Cooperative Prescribed Performance Tracking Control for Multiple High-Speed Trains in Moving Block Signaling System","volume":"20","author":"Gao","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"108646","DOI":"10.1016\/j.automatica.2019.108646","article-title":"Distributed optimal control for multiple high-speed train movement: An alternating direction method of multipliers","volume":"112","author":"Li","year":"2020","journal-title":"Automatica"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1109\/TASE.2014.2371816","article-title":"Adaptive Iterative Learning Control for High-Speed Trains with Unknown Speed Delays and Input Saturations","volume":"13","author":"Ji","year":"2015","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_19","first-page":"3657","article-title":"Distributed Consensus of second-order multiagent systems with nonconvex input constraints","volume":"11","author":"Li","year":"2018","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"129437","DOI":"10.1109\/ACCESS.2019.2939953","article-title":"Cooperative H\u221e Control of Multiple High-Speed Trains with Saturation Constraints","volume":"7","author":"Xiang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5788","DOI":"10.1109\/TAC.2016.2637005","article-title":"Distributed Velocity-Constrained Consensus of Discrete-Time Multi-Agent Systems with Nonconvex Constraints, Switching Topologies, and Delays","volume":"62","author":"Lin","year":"2017","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1109\/TAC.2017.2742140","article-title":"Distributed Consensus of Second-Order Multiagent Systems with Nonconvex Velocity and Control Input Constraints","volume":"63","author":"Lin","year":"2018","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1016\/j.automatica.2008.11.017","article-title":"Barrier Lyapunov Functions for the control of output-constrained nonlinear systems","volume":"45","author":"Tee","year":"2009","journal-title":"Automatica"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1109\/TNN.2010.2047115","article-title":"Adaptive Neural Control for Output Feedback Nonlinear Systems Using a Barrier Lyapunov Function","volume":"21","author":"Ren","year":"2010","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1109\/TCYB.2013.2262935","article-title":"Fuzzy Neural Network-Based Adaptive Control for a Class of Uncertain Nonlinear Stochastic Systems","volume":"44","author":"Chen","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yang, J., Zhang, Y., and Jin, Y. (2021). Fully Automatic Operation Algorithm of Urban Rail Train Based on RBFNN Position Output Constrained Robust Adaptive Control. Algorithms, 14.","DOI":"10.3390\/a14090264"},{"key":"ref_27","first-page":"89","article-title":"Some issues on iterative learning control based high speed train operation control","volume":"6","author":"Li","year":"2016","journal-title":"Beijing Jiaotong Univ."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/5\/138\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:58:34Z","timestamp":1760137114000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/5\/138"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,21]]},"references-count":27,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["a15050138"],"URL":"https:\/\/doi.org\/10.3390\/a15050138","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,4,21]]}}}