{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T06:42:46Z","timestamp":1760424166847,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T00:00:00Z","timestamp":1760313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Dezhou Industrial Robot System Integration Engineering Research Center"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study proposes a sliding-mode-based adaptive control framework for symmetric quad-rotor altitude and attitude tracking under parametric uncertainties and mismatched disturbances. To address mismatched disturbances, a finite-time disturbance observer (DO) is integrated into a high-order terminal sliding mode manifold design. While conventional sliding mode control suffers from dependence on precise dynamic models that are unavailable in quad-rotor applications, we devise a fully connected double hidden layer recurrent neural network (FCDHRNN) with full interlayer feedback to approximate unmodeled dynamics. The structure uses double hidden layer connections to strengthen the approximation ability, and its double-layer structure achieves higher accuracy and generalization ability and uses fewer neurons than the single-hidden-layer network. Through Lyapunov stability analysis, weight adaptation laws are rigorously derived to guarantee finite-time convergence of both tracking errors and estimation residuals. Simulation results show that the proposed scheme has superior performance compared with the existing quad-rotor control scheme.<\/jats:p>","DOI":"10.3390\/sym17101720","type":"journal-article","created":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T05:48:21Z","timestamp":1760420901000},"page":"1720","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive Integral Sliding Mode Control for Symmetric UAV with Mismatched Disturbances Based on an Improved Recurrent Neural Network"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-6461-6388","authenticated-orcid":false,"given":"Shanping","family":"Wang","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Shandong Huayu University of Technology, Dezhou 253000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-3850-3347","authenticated-orcid":false,"given":"Haicheng","family":"Wan","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Shandong Huayu University of Technology, Dezhou 253000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1848-1565","authenticated-orcid":false,"given":"Ping","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Shandong Huayu University of Technology, Dezhou 253000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7178-800X","authenticated-orcid":false,"given":"Wendong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Shandong Huayu University of Technology, Dezhou 253000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103932","DOI":"10.1016\/j.jnca.2024.103932","article-title":"Blockchain applications in UAV industry: Review, opportunities, and challenges","volume":"230","author":"Hawashin","year":"2024","journal-title":"J. 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