{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T12:24:40Z","timestamp":1783772680063,"version":"3.55.0"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T00:00:00Z","timestamp":1757116800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Shanghai","award":["25ZR1401118"],"award-info":[{"award-number":["25ZR1401118"]}]},{"name":"Natural Science Foundation of Shanghai","award":["2023CSJGG0900"],"award-info":[{"award-number":["2023CSJGG0900"]}]},{"name":"Key Research and Development Program of China Yangtze River Delta","award":["25ZR1401118"],"award-info":[{"award-number":["25ZR1401118"]}]},{"name":"Key Research and Development Program of China Yangtze River Delta","award":["2023CSJGG0900"],"award-info":[{"award-number":["2023CSJGG0900"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the concept of symmetry is utilized to design active fault tolerant trajectory-tracking control of autonomous distributed-drive electric vehicles\u2014that is, the construction and the solution of active fault tolerant trajectory-tracking controllers are symmetrical. This paper presents a hierarchical fault tolerant control strategy for improving the trajectory-tracking performance of autonomous distributed-drive electric vehicles (ADDEVs) under steer-by-wire (SBW) system failures. Since ADDEV trajectory dynamics are inherently affected by complex traffic conditions, various driving maneuvers, and other road environments, the main control objective is to deal with the ADDEV trajectory-tracking control challenges of system uncertainties, SBW failures, and external disturbance. First, the differential steering dynamics model incorporating a 3-DOF coupled system and stability criteria based on the phase\u2013plane method is established to characterize autonomous vehicle motion during SBW failures. Then, by integrating cascade active disturbance rejection control (ADRC) with Karush\u2013Kuhn\u2013Tucker (KKT)-based torque allocation, the active fault tolerant control framework of trajectory tracking and lateral stability challenges caused by SBW actuator malfunctions and steering lockup is addressed. The upper-layer ADRC employs an extended state observer (ESO) to estimate and compensate against uncertainties and disturbances, while the lower-layer utilizes KKT conditions to optimize four-wheel torque distribution to compensate for SBW failures. Simulations validate the effectiveness of the controller with serpentine and double-lane-change maneuvers in the co-simulation platform MATLAB\/Simulink-Carsim\u00ae (2019).<\/jats:p>","DOI":"10.3390\/sym17091471","type":"journal-article","created":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T08:06:32Z","timestamp":1757318792000},"page":"1471","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Active Fault Tolerant Trajectory-Tracking Control of Autonomous Distributed-Drive Electric Vehicles Considering Steer-by-Wire Failure"],"prefix":"10.3390","volume":"17","author":[{"given":"Xianjian","family":"Jin","sequence":"first","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China"},{"name":"Shanghai Key Laboratory of Intelligent Manufacturing and Robotics, Shanghai University, Shanghai 200072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huaizhen","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yinchen","family":"Tao","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianning","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianbo","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nonsly Valerienne","family":"Opinat Ikiela","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1109\/TMECH.2022.3233705","article-title":"Fault tolerant predictive control with deep-reinforcement-learning-based torque distribution for four in-wheel motor drive","volume":"28","author":"Deng","year":"2023","journal-title":"IEEE\/ASME Trans. 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