{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T19:46:36Z","timestamp":1771703196514,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T00:00:00Z","timestamp":1692316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Grants Council of the President of the Russian Federation","award":["MD-1787.2022.4"],"award-info":[{"award-number":["MD-1787.2022.4"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>A quadrotor trajectory tracking problem is addressed via the design of a model reference adaptive control (MRAC) system. As for real-world applications, the entire quadrotor dynamics is typically unknown. To take that into account, we consider a plant model, which contains uncertain nonlinear terms resulting from aerodynamic friction, blade flapping, and the fact that the mass and inertia moments of the quadrotor may change from their nominal values. Unlike many known studies, the explicit equations of the parameter uncertainty for the position control loop are derived in two different ways using the differential flatness approach: the control signals are (i) used and (ii) not used in the parametric uncertainty parameterization. After analysis, the neural network (NN) is chosen for both cases as a compensator of such uncertainty, and the set of NN input signals is justified for each of them. Unlike many known MRAC systems with NN for quadrotors, in this study, we use the kxx+krr baseline controller, which follows from the control system derivation, with both time-invariant (parameterization (i)) and adjustable (parameterization (ii)) parameters instead of an arbitrarily chosen non-tunable PI\/PD\/PID-like one. Adaptive laws are derived to adjust the parameters of NN uncertainty compensator for both parameterizations. As a result, the position controller ensures the asymptotic stability of the tracking error for both cases under the assumption of perfect attitude loop tracking, which is ensured in the system previously developed by the authors. The results of the numerical experiments support the theoretical conclusions and provide a comparison of the effectiveness of the derived parameterizations. They also allow us to make conclusions on the necessity of the baseline controller adjustment.<\/jats:p>","DOI":"10.3390\/computation11080163","type":"journal-article","created":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T10:28:48Z","timestamp":1692354528000},"page":"163","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Quadrotor Trajectory Tracking Using Model Reference Adaptive Control, Neural Network-Based Parameter Uncertainty Compensator, and Different Plant Parameterizations"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6948-9807","authenticated-orcid":false,"given":"Anton","family":"Glushchenko","sequence":"first","affiliation":[{"name":"V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1409-0401","authenticated-orcid":false,"given":"Konstantin","family":"Lastochkin","sequence":"additional","affiliation":[{"name":"V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Glushchenko, A., and Lastochkin, K. (2022, January 9\u201311). Neural Network Based Parameter Uncertainty Compensation to Solve Quadrotor Trajectory Tracking Problem. Proceedings of the 2022 4th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), Lipetsk, Russia.","DOI":"10.1109\/SUMMA57301.2022.9974070"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.arcontrol.2019.08.004","article-title":"Position and attitude control of multi-rotor aerial vehicles: A survey","volume":"48","author":"Nascimento","year":"2019","journal-title":"Annu. Rev. Control"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Fan, F., Lin, M., Ding, R., Zheng, Z., and Liu, Y. (2016, January 12\u201315). Augmented-MRAC for quadrotor UAVs with parameter change. Proceedings of the 2016 IEEE International Conference on Advanced Intelligent Mechatronics (AIM), Banff, AB, Canada.","DOI":"10.1109\/AIM.2016.7576817"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Glushchenko, A., and Lastochkin, K. (2022, January 1\u20133). 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Inst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2365","DOI":"10.1007\/s12555-018-0720-7","article-title":"Neural network-based robust adaptive certainty equivalent controller for quadrotor UAV with unknown disturbances","volume":"17","author":"Doukhi","year":"2019","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Choutri, K., Lagha, M., Dala, L., and Lipatov, M. (2017, January 4\u20136). Quadrotors trajectory tracking using a differential flatness-quaternion based approach. 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Robust Nonlinear Control"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/8\/163\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:37:11Z","timestamp":1760128631000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/8\/163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,18]]},"references-count":20,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["computation11080163"],"URL":"https:\/\/doi.org\/10.3390\/computation11080163","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,18]]}}}