{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T20:15:45Z","timestamp":1783109745446,"version":"3.54.6"},"reference-count":36,"publisher":"Elsevier BV","issue":"9","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/100016510","name":"Center for Autonomous Systems and Technologies","doi-asserted-by":"publisher","award":["YESS20240112"],"award-info":[{"award-number":["YESS20240112"]}],"id":[{"id":"10.13039\/100016510","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62403166"],"award-info":[{"award-number":["62403166"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62473110"],"award-info":[{"award-number":["62473110"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62573167"],"award-info":[{"award-number":["62573167"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of the Franklin Institute"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.jfranklin.2026.108696","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T14:58:07Z","timestamp":1777993087000},"page":"108696","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"title":["Majorant-based control for trajectory tracking of quadrotor UAVs under external disturbances"],"prefix":"10.1016","volume":"363","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6150-3646","authenticated-orcid":false,"given":"Yanning","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7711-1436","authenticated-orcid":false,"given":"Guangtao","family":"Ran","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sihong","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chuanjiang","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"8","key":"10.1016\/j.jfranklin.2026.108696_bib0001","doi-asserted-by":"crossref","first-page":"3409","DOI":"10.1109\/TITS.2019.2927838","article-title":"Development of UAV-based target tracking and recognition systems","volume":"21","author":"Wang","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"issue":"16","key":"10.1016\/j.jfranklin.2026.108696_bib0002","doi-asserted-by":"crossref","first-page":"17608","DOI":"10.1109\/JSEN.2021.3049471","article-title":"Unmanned aerial vehicles in smart agriculture: applications, requirements, and challenges","volume":"21","author":"Maddikunta","year":"2021","journal-title":"IEEE Sens. J."},{"issue":"16","key":"10.1016\/j.jfranklin.2026.108696_bib0003","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfranklin.2025.108082","article-title":"An enhanced anti-disturbance of quadrotor UAV via the adaptive reduced-order GPEBO","volume":"362","author":"Chen","year":"2025","journal-title":"J. Frankl. Inst."},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108696_bib0004","doi-asserted-by":"crossref","first-page":"7251","DOI":"10.1109\/TVT.2025.3526360","article-title":"Performance-optimize adaptive robust tracking control for USV-UAV heterogeneous systems with uncertainty","volume":"74","author":"Chen","year":"2025","journal-title":"IEEE Trans. Veh. Technol."},{"issue":"16","key":"10.1016\/j.jfranklin.2026.108696_bib0005","doi-asserted-by":"crossref","first-page":"3337","DOI":"10.1080\/00207721.2024.2367719","article-title":"Attitude-position obstacle avoidance of trajectory tracking control for a quadrotor UAV using barrier functions","volume":"55","author":"Fu","year":"2024","journal-title":"Int. J. Syst. Sci."},{"key":"10.1016\/j.jfranklin.2026.108696_bib0006","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TAES.2026.3707080","article-title":"Fixed-time prescribed performance formation control for heterogeneous UAV-UGV systems with velocity estimation and dynamic event-triggering","author":"Huang","year":"2026","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"10.1016\/j.jfranklin.2026.108696_bib0007","doi-asserted-by":"crossref","first-page":"4490","DOI":"10.1109\/TASE.2024.3355225","article-title":"Robust adaptive tracking control for aerial transporting a cable-suspended payload using backstepping sliding mode techniques","volume":"22","author":"Liang","year":"2024","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108696_bib0008","doi-asserted-by":"crossref","first-page":"3885","DOI":"10.1109\/TCE.2024.3355061","article-title":"AI-enabled trajectory optimization of logistics UAVs with wind impacts in smart cities","volume":"70","author":"Du","year":"2024","journal-title":"IEEE Trans. Consum. Electron."},{"issue":"7","key":"10.1016\/j.jfranklin.2026.108696_bib0009","doi-asserted-by":"crossref","first-page":"2389","DOI":"10.1109\/TFUZZ.2022.3225672","article-title":"Dissipative tracking control of nonlinear Markov jump systems with incomplete transition probabilities: a multiple-event-triggered approach","volume":"31","author":"Ran","year":"2023","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"8","key":"10.1016\/j.jfranklin.2026.108696_bib0010","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6501\/ad4627","article-title":"Fixed-time trajectory tracking control of a quadrotor UAV under time-varying wind disturbances: theory and experimental validation","volume":"35","author":"Cai","year":"2024","journal-title":"Meas. Sci. Technol."},{"key":"10.1016\/j.jfranklin.2026.108696_bib0011","article-title":"Trajectory optimization under uncertainty: a convex optimization approach with polynomial chaos-based uncertainty quantification","author":"Kun","year":"2025","journal-title":"Chin. J. Aeronaut."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108696_bib0012","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1016\/j.jfranklin.2022.10.042","article-title":"Command filter-based adaptive fuzzy integral backstepping control for quadrotor UAV with input saturation","volume":"360","author":"Liu","year":"2023","journal-title":"J. Frankl. Inst."},{"key":"10.1016\/j.jfranklin.2026.108696_bib0013","doi-asserted-by":"crossref","DOI":"10.1016\/j.ast.2023.108803","article-title":"Optimized intelligent tracking control for a quadrotor unmanned aerial vehicle with actuator failures","volume":"144","author":"Li","year":"2024","journal-title":"Aerosp. Sci. Technol."},{"issue":"11","key":"10.1016\/j.jfranklin.2026.108696_bib0014","doi-asserted-by":"crossref","first-page":"4658","DOI":"10.1002\/rnc.7932","article-title":"RBFNN-based parameter adaptive sliding mode control for an uncertain TQUAV with time-varying mass","volume":"35","author":"Xiong","year":"2025","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"6","key":"10.1016\/j.jfranklin.2026.108696_bib0015","doi-asserted-by":"crossref","first-page":"3737","DOI":"10.1002\/rnc.6001","article-title":"Fault-tolerant attitude tracking control with practical finite time convergence for unmanned aerial vehicles under actuation faults","volume":"32","author":"Yu","year":"2022","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"4","key":"10.1016\/j.jfranklin.2026.108696_bib0016","doi-asserted-by":"crossref","first-page":"2265","DOI":"10.1109\/TAES.2021.3053109","article-title":"Adaptive fractional-order nonsingular fast terminal sliding mode based robust tracking control of quadrotor UAV with Gaussian random disturbances and uncertainties","volume":"57","author":"Labbadi","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"issue":"16","key":"10.1016\/j.jfranklin.2026.108696_bib0017","doi-asserted-by":"crossref","first-page":"8454","DOI":"10.1016\/j.jfranklin.2022.09.008","article-title":"On novel trajectory tracking control of quadrotor UAV: a finite-time guaranteed performance approach","volume":"359","author":"Cao","year":"2022","journal-title":"J. Frankl. Inst."},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108696_bib0018","doi-asserted-by":"crossref","first-page":"11267","DOI":"10.1109\/TAES.2025.3567280","article-title":"Predefined-time attitude tracking control for liquid-filled spacecraft under angular velocity and torque constraints","volume":"61","author":"Zhang","year":"2025","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108696_bib0019","first-page":"73","article-title":"Fixed-time consensus tracking control for nonlinear multi-agent systems: a dynamic edge\/self-triggered approach","volume":"73","author":"Liu","year":"2026","journal-title":"IEEE Trans. Circuits Syst. II: Express Br."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108696_bib0020","doi-asserted-by":"crossref","first-page":"1782","DOI":"10.1109\/TCE.2025.3643924","article-title":"Fast fixed-time-synchronized time-varying formation tracking control of quadrotor UAVs under external disturbances","volume":"72","author":"Gao","year":"2026","journal-title":"IEEE Trans. Consum. Electron."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108696_bib0021","doi-asserted-by":"crossref","first-page":"2363","DOI":"10.1007\/s11071-021-07080-0","article-title":"Fixed-time disturbance observer-based robust fault-tolerant tracking control for uncertain quadrotor UAV subject to input delay","volume":"107","author":"Liu","year":"2022","journal-title":"Nonlinear Dyn."},{"issue":"16","key":"10.1016\/j.jfranklin.2026.108696_bib0022","doi-asserted-by":"crossref","first-page":"3009","DOI":"10.3390\/math10163009","article-title":"Adaptive barrier fast terminal sliding mode actuator fault tolerant control approach for quadrotor UAVs","volume":"10","author":"Najafi","year":"2022","journal-title":"Mathematics"},{"issue":"8","key":"10.1016\/j.jfranklin.2026.108696_bib0023","doi-asserted-by":"crossref","first-page":"3756","DOI":"10.1007\/s40815-022-01361-5","article-title":"Fuzzy approximation-based adaptive finite-time tracking control for a quadrotor UAV with actuator faults","volume":"24","author":"Yang","year":"2022","journal-title":"Int. J. Fuzzy Syst."},{"issue":"11","key":"10.1016\/j.jfranklin.2026.108696_bib0024","doi-asserted-by":"crossref","first-page":"13225","DOI":"10.1007\/s11071-024-10826-1","article-title":"Singularity-free predefined time tracking control for quadrotor UAV with input saturation and error constraints","volume":"113","author":"Li","year":"2025","journal-title":"Nonlinear Dyn."},{"key":"10.1016\/j.jfranklin.2026.108696_bib0025","doi-asserted-by":"crossref","first-page":"157916","DOI":"10.1109\/ACCESS.2021.3126123","article-title":"Majorant-based control methodology for mechatronic and transportation processes","volume":"9","author":"Celentano","year":"2021","journal-title":"IEEE Access"},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108696_bib0026","doi-asserted-by":"crossref","first-page":"2021","DOI":"10.1109\/TIE.2019.2905811","article-title":"Path-following control of a quadrotor UAV with a cable-suspended payload under wind disturbances","volume":"67","author":"Qian","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108696_bib0027","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.1109\/TII.2023.3274234","article-title":"UDE-based distributed formation control for MSVs with collision avoidance and connectivity preservation","volume":"20","author":"He","year":"2024","journal-title":"IEEE Trans. Ind. Inform."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108696_bib0028","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1007\/s12555-016-0771-6","article-title":"Wind-gust compensation algorithm based on high-gain residual observer to control a quadrotor aircraft: real-time verification task at fixed point","volume":"16","author":"Rodr\u00edguez-Mata","year":"2018","journal-title":"Int. J. Control Autom. Syst."},{"key":"10.1016\/j.jfranklin.2026.108696_bib0029","series-title":"2022 American Control Conference (ACC)","first-page":"4050","article-title":"Filtered high-gain observer design for a class of nonlinear systems subject to delayed measurements: application to a quadrotor UAV","author":"Dam","year":"2022"},{"key":"10.1016\/j.jfranklin.2026.108696_bib0030","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.ast.2019.04.003","article-title":"High-order ESO based output feedback dynamic surface control for quadrotors under position constraints and uncertainties","volume":"89","author":"Shao","year":"2019","journal-title":"Aerosp. Sci. Technol."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108696_bib0031","first-page":"207","article-title":"Fixed-time prescribed performance fault-tolerant control for quadrotor UAV based on ESO","volume":"14","author":"Liu","year":"2023","journal-title":"Int. J. Syst. Control Commun."},{"issue":"4","key":"10.1016\/j.jfranklin.2026.108696_bib0032","first-page":"2263","article-title":"Robust three-loop trajectory tracking control for quadrotors with multiple uncertainties","volume":"63","author":"Liu","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"10","key":"10.1016\/j.jfranklin.2026.108696_bib0033","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1049\/iet-cta.2018.0101","article-title":"New results on robust stability analysis and synthesis for MIMO uncertain systems","volume":"12","author":"Celentano","year":"2018","journal-title":"IET Control Theory Appl."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108696_bib0034","first-page":"637","article-title":"Adaptive neural fixed-time control for uncertain nonlinear systems","volume":"71","author":"Liu","year":"2024","journal-title":"IEEE Trans. Circuits Syst. II: Express Br."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108696_bib0035","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1109\/TIV.2024.3420939","article-title":"Fast finite-time formation control of UAVs with multiple loops and external disturbances","volume":"10","author":"Huang","year":"2025","journal-title":"IEEE Trans. Intell. Veh."},{"issue":"11","key":"10.1016\/j.jfranklin.2026.108696_bib0036","doi-asserted-by":"crossref","first-page":"2236","DOI":"10.3390\/app8112236","article-title":"A unified approach to design robust controllers for nonlinear uncertain engineering systems","volume":"8","author":"Celentano","year":"2018","journal-title":"Appl. Sci."}],"container-title":["Journal of the Franklin Institute"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0016003226002966?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0016003226002966?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T19:23:46Z","timestamp":1783106626000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0016003226002966"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":36,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["S0016003226002966"],"URL":"https:\/\/doi.org\/10.1016\/j.jfranklin.2026.108696","relation":{},"ISSN":["0016-0032"],"issn-type":[{"value":"0016-0032","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Majorant-based control for trajectory tracking of quadrotor UAVs under external disturbances","name":"articletitle","label":"Article Title"},{"value":"Journal of the Franklin Institute","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jfranklin.2026.108696","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Franklin Institute. Published by Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"108696"}}