{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T20:40:29Z","timestamp":1771620029648,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,20]],"date-time":"2021-02-20T00:00:00Z","timestamp":1613779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61833001"],"award-info":[{"award-number":["61833001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The adaptive trajectory and attitude control is essential for the four-dimensional (4D) trajectory operation of civil aircraft in symmetric thrust flight. In this work, an integrated trajectory and attitude control scheme is proposed based on the =multi-input multi-output (MIMO) model free adaptive control (MFAC) method. First, the full-form dynamic linearization technique is adopted to build the equivalent data model of aircraft. Also, the MIMO MFAC scheme with saturation constraint is designed to achieve an accurate tracking control for a given 4D trajectory and attitude. Besides, the performance limitations of aircraft are taken into consideration, and the MIMO MFAC scheme with hard constraints is designed. In addition, to improve the simulation efficiency, a control scheme with mixed constraints, i.e., saturation and hard constraints, is further proposed. It can be seen from the simulation results that the proposed method can perform an integrated control of the aircraft 4D trajectory and attitude without precise modeling, and the control performance is better than that of the model-based control method in terms of flight altitude and yaw angle control. The integrated data-driven control scheme proposed in this paper provides a theoretical solution for the precise operation of aircraft under 4D trajectory.<\/jats:p>","DOI":"10.3390\/sym13020347","type":"journal-article","created":{"date-parts":[[2021,2,21]],"date-time":"2021-02-21T21:15:01Z","timestamp":1613942101000},"page":"347","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Model Free Adaptive Scheme for Integrated Control of Civil Aircraft Trajectory and Attitude"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8478-0619","authenticated-orcid":false,"given":"Gaoyang","family":"Jiang","sequence":"first","affiliation":[{"name":"Institute of Advanced Control System, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7855-5909","authenticated-orcid":false,"given":"Genfeng","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Advanced Control System, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3577-4607","authenticated-orcid":false,"given":"Hansong","family":"Yu","sequence":"additional","affiliation":[{"name":"Institute of Advanced Control System, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,20]]},"reference":[{"key":"ref_1","unstructured":"FAA (2018). NextGen Implementation Plan, Technical Report."},{"key":"ref_2","unstructured":"SESAR (2019). SESAR Solutions Catalogue 2019, SESAR Joint Undertaking. [3rd ed.]. Technical Report."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"26","DOI":"10.2514\/2.4871","article-title":"Aggressive longitudinal aircraft trajectory tracking using nonlinear control","volume":"25","author":"McClamroch","year":"2002","journal-title":"J. Guid. Control Dyn."},{"key":"ref_4","unstructured":"Bouadi, H. (2014). Contribution to Flight Control Law Design and Aircraft Trajectory Tracking. [Ph.D. Thesis, INSA de Toulouse]."},{"key":"ref_5","unstructured":"Nu\u00f1ez, H.E. (2018). Contribution To Flight Guidance In High Density Traffic. [Ph.D. Thesis, National School of Civil Aviation]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.sna.2014.03.011","article-title":"High-performance trajectory tracking control of a quadrotor with disturbance observer","volume":"211","author":"Dong","year":"2014","journal-title":"Sens. Actuators A Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ast.2016.07.001","article-title":"A robust back-stepping based trajectory tracking controller for the tanker with strict posture constraints under unknown flow perturbations","volume":"56","author":"Su","year":"2016","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"666","DOI":"10.2514\/1.C034477","article-title":"Modeling and adaptive flight control for quadrotor trajectory tracking","volume":"55","author":"Bouadi","year":"2018","journal-title":"J. Aircr."},{"key":"ref_9","first-page":"105","article-title":"4D trajectory generation and tracking for waypoint-based aerial navigation","volume":"8","author":"Bousson","year":"2013","journal-title":"WSEAS Trans. Syst. Control"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Stastny, T., Dash, A., and Siegwart, R. (2017). Nonlinear MPC for fixed-wing UAV trajectory tracking: Implementation and flight experiments. AIAA Guidance, Navigation, and Control Conference, AIAA.","DOI":"10.2514\/6.2017-1512"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1049\/iet-cta.2017.1048","article-title":"Adaptive model predictive control-based attitude and trajectory tracking of a VTOL aircraft","volume":"12","author":"Emami","year":"2018","journal-title":"IET Control Theory Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.1049\/iet-cta.2017.0942","article-title":"Synchronised trajectory tracking for a network of MIMO non-minimum phase systems with application to aircraft control","volume":"12","author":"Zhu","year":"2018","journal-title":"IET Control Theory Appl."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wang, X., Sang, Y., and Zhou, G. (2020). Combining stable inversion and H-infinity synthesis for trajectory tracking and disturbance rejection control of civil aircraft autolanding. Appl. Sci., 10.","DOI":"10.3390\/app10041224"},{"key":"ref_14","unstructured":"Buelta, A., Olivares, A., and Staffetti, E. (2019). Iterative learning control for precise aircraft trajectory tracking in continuous climb operations, Thirteenth USA\/Europe Air Traffic Management Research and Development Seminar."},{"key":"ref_15","unstructured":"Buelta, A., Olivares, A., and Universidad, E.S. (2019, January 1\u20134). Iterative learning control for precise aircraft trajectory tracking in continuous descent approaches. Proceedings of the 8th European Conference for Aeronautics and Aerospace Sciences, EUCASS Association, Madrid, Spain."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s10846-018-0880-y","article-title":"Robust trajectory tracking for unmanned aircraft systems using a nonsingular terminal modified super-twisting sliding mode controller","volume":"93","author":"Munoz","year":"2019","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2020","DOI":"10.1109\/TCST.2017.2753162","article-title":"Closing gaps for aircraft attitude higher order sliding mode control certification via practical stability margins identification","volume":"26","author":"Panathula","year":"2018","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.ast.2016.06.006","article-title":"Full-altitude attitude angles envelope and model predictive control-based attitude angles protection for civil aircraft","volume":"55","author":"Dong","year":"2016","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1109\/JAS.2017.7510679","article-title":"A novel robust attitude control for quadrotor aircraft subject to actuator faults and wind gusts","volume":"5","author":"Guo","year":"2018","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"171359","DOI":"10.1109\/ACCESS.2020.3024793","article-title":"Active disturbance rejection attitude control for a bird-like flapping wing micro air vehicle during automatic landing","volume":"8","author":"Liang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zhang, S., Han, W., and Zhang, Y. (2020). Finite time convergence incremental nonlinear dynamic inversion-based attitude control for flying-wing aircraft with actuator faults. Actuators, 9.","DOI":"10.3390\/act9030070"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1109\/TCST.2017.2709274","article-title":"Gain scheduled attitude control of fixed-wing UAV with automatic controller tuning","volume":"26","author":"Poksawat","year":"2018","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"54106","DOI":"10.1109\/ACCESS.2019.2912902","article-title":"Data-driven model-free adaptive attitude control approach for launch vehicle with virtual reference feedback parameters dining method","volume":"7","author":"Duan","year":"2019","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"37910","DOI":"10.1109\/ACCESS.2018.2853145","article-title":"Attitude control of aircraft using only synthetic jet actuators when stall occurs","volume":"6","author":"Li","year":"2018","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"199931","DOI":"10.1109\/ACCESS.2020.3035436","article-title":"Reconfigurable nonlinear dynamic inversion for attitude control of a structurally damaged aircraft","volume":"8","author":"He","year":"2020","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"17006","DOI":"10.1109\/ACCESS.2017.2743059","article-title":"Dynamic modeling and active morphing trajectory-attitude separation control approach for gull-wing aircraft","volume":"5","author":"Guo","year":"2017","journal-title":"IEEE Access"},{"key":"ref_27","first-page":"522437","article-title":"Integrated 4D trajectory and attitude adaptive controller for civil aircraft","volume":"40","author":"Fan","year":"2019","journal-title":"Acta Aeronaut. Et Astronaut. Sin."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"650","DOI":"10.3724\/SP.J.1004.2009.00650","article-title":"On data-driven control theory: The state of the art and perspective","volume":"35","author":"Hou","year":"2009","journal-title":"Acta Autom. Sin."},{"key":"ref_29","unstructured":"Hou, Z. (1994). Parameter Identification, Adaptive Control and Model-Free Learning Adaptive Control. [Ph.D. Thesis, Northeastern University]."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Hou, Z., and Jin, S. (2013). Model Free Adaptive Control: Theory and Applications, CRC Press.","DOI":"10.1201\/b15752"},{"key":"ref_31","unstructured":"Jin, S. (2008). On Model Free Learning Adaptive Control and Applications. [Ph.D. Thesis, Beijing Jiaotong University]."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.ins.2012.07.014","article-title":"From model-based control to data-driven control: Survey, classification and perspective","volume":"235","author":"Hou","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4076","DOI":"10.1109\/TIE.2016.2636126","article-title":"An overview of dynamic-linearization-based data-driven control and applications","volume":"64","author":"Hou","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4070","DOI":"10.1109\/TIE.2017.2653767","article-title":"Data-driven control and learning systems","volume":"64","author":"Hou","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1177\/0142331212444664","article-title":"A new model- free adaptive controller versus non-linear H-infinity controller for levitation of an electromagnetic system","volume":"35","author":"Javadi","year":"2013","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Bai, L., Feng, Y.W., Li, N., Xue, X.F., and Cao, Y. (2019). Data-driven adaptive iterative learning method for active vibration control based on imprecise probability. Symmetry, 11.","DOI":"10.3390\/sym11060746"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1109\/TCST.2010.2093136","article-title":"A novel data-driven control approach for a class of discrete-time nonlinear systems","volume":"19","author":"Hou","year":"2011","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3145","DOI":"10.1177\/0142331218818653","article-title":"Data-driven multi-inverter cooperative control for voltage tracking and current sharing in islanded AC microgrids","volume":"41","author":"Meng","year":"2019","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2894","DOI":"10.1109\/TITS.2019.2921381","article-title":"Data-driven model free adaptive perimeter control for multi-region urban traffic networks with route choice","volume":"21","author":"Lei","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2166","DOI":"10.1177\/0142331220909004","article-title":"A data-driven approach for trajectory-based aircraft operation with controlled time of arrival and along-track wind effects","volume":"42","author":"Jiang","year":"2020","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"8196","DOI":"10.1016\/j.ifacol.2017.08.1268","article-title":"Towards 4D trajectory tracking for transport aircraft","volume":"50","author":"Camino","year":"2017","journal-title":"IFAC-PapersOnLine"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/347\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:26:48Z","timestamp":1760160408000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/347"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,20]]},"references-count":41,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["sym13020347"],"URL":"https:\/\/doi.org\/10.3390\/sym13020347","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,20]]}}}