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To address this issue, the present paper investigates a fault-tolerant control scheme based on the adaptive dynamic programming (ADP) method and fault observer. The whole closed-loop system is composed of a position loop and an attitude loop. An ADP-based position-tracking controller is established with an improved cost function that can simultaneously represent actuator faults, control inputs, and tracking errors. In addition, a single-layer critic neural network is constructed to estimate the cost function and approximate control inputs. In the process of adjusting the weights of the neural network, a unique adjustment method combining policy gradient and prioritized experience replay is adopted to improve the data usage efficiency and speed up the weight convergence. Furthermore, a sliding mode\u2013based attitude controller is utilized for the inner-loop attitude subsystem. The significant feature of this scheme is that it has the ability to self-learn and self-adapt. A Lyapunov stability analysis is performed to verify whether the signals are uniformly ultimately bounded. Finally, simulation experiments are conducted to demonstrate the effectiveness of the proposed scheme.<\/jats:p>","DOI":"10.1177\/01423312241264070","type":"journal-article","created":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T02:10:39Z","timestamp":1726625439000},"page":"1893-1905","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Adaptive dynamic programming\u2013based fault-tolerant control of multi-UAV formation system"],"prefix":"10.1177","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5309-6147","authenticated-orcid":false,"given":"Yifan","family":"Tang","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, China"}]},{"given":"Liqian","family":"Dou","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, China"}]},{"given":"Ruilong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Aerospace Automatic Control Institute, China"}]},{"given":"Xiuyun","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, China"}]},{"given":"Siyuan","family":"Cai","sequence":"additional","affiliation":[{"name":"AVIC Xi\u2019an Flight Automatic Control Research Institute, China"}]}],"member":"179","published-online":{"date-parts":[[2024,9,17]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2018.2850701"},{"key":"e_1_3_2_3_1","first-page":"1","article-title":"LSTM-based output-constrained adaptive fault-tolerant control for fixed-wing UAV with high dynamic disturbances and actuator faults","volume":"4","author":"Chang X","year":"2021","unstructured":"Chang X, Rong L, Chen K, et al. 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