{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T03:39:36Z","timestamp":1770521976904,"version":"3.49.0"},"reference-count":18,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T00:00:00Z","timestamp":1690243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science and Technology Program Foundation of Weifang","award":["2015GX007"],"award-info":[{"award-number":["2015GX007"]}]},{"name":"Science and Technology Program Foundation of Weifang","award":["2021RALKFKT008"],"award-info":[{"award-number":["2021RALKFKT008"]}]},{"name":"Open Research Fund from the State Key Laboratory of Rolling and Automation, Northeastern University","award":["2015GX007"],"award-info":[{"award-number":["2015GX007"]}]},{"name":"Open Research Fund from the State Key Laboratory of Rolling and Automation, Northeastern University","award":["2021RALKFKT008"],"award-info":[{"award-number":["2021RALKFKT008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate tracking of a given path is one of the primary factors in the maneuverability of a vehicle and is also an important topic in autonomous vehicle research. To solve the problem of vehicle path tracking, the problem must first be transformed into an optimal control problem. Then, a symplectic pseudospectral method (SPM) based on the third-generation function of symplectic theory and pseudospectral discretization is proposed to efficiently solve the nonlinear optimal control problems. Finally, the results obtained by the proposed algorithm are compared with those obtained by the Gauss pseudospectral method (GPM). The simulation results show that the proposed method can effectively solve the vehicle path tracking problem. Furthermore, the vehicle can track the given path controlled by the proposed algorithm with higher accuracy and greater applicability than other methods.<\/jats:p>","DOI":"10.3390\/s23156673","type":"journal-article","created":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T01:09:01Z","timestamp":1690333741000},"page":"6673","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Optimum Control for Path Tracking Problem of Vehicle Handling Inverse Dynamics"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8615-7372","authenticated-orcid":false,"given":"Yingjie","family":"Liu","sequence":"first","affiliation":[{"name":"School of Machinery and Automation, Weifang University, Weifang 261061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dawei","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Machinery and Automation, Weifang University, Weifang 261061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen","family":"Peng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"936","DOI":"10.21595\/jve.2022.22356","article-title":"Vehicle state and parameter estimation based on double cubature Kalman filter algorithm","volume":"24","author":"Liu","year":"2022","journal-title":"J. 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