{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:04:33Z","timestamp":1760241873389,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,10,26]],"date-time":"2018-10-26T00:00:00Z","timestamp":1540512000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A Fractional Order Sliding Mode Control (FOSMC) is proposed in this paper for an integer second order nonlinear system with an unknown additive perturbation term. A sufficient condition is given to assure the attractiveness to a given sliding surface where trajectory tracking is assured, despite the presence of the perturbation term. The control scheme is applied to the model of a quadrotor vehicle in order to have trajectory tracking in the space. Simulation results are presented to evaluate the performance of the control scheme.<\/jats:p>","DOI":"10.3390\/a11110168","type":"journal-article","created":{"date-parts":[[2018,10,26]],"date-time":"2018-10-26T10:51:01Z","timestamp":1540551061000},"page":"168","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Fractional Order Sliding Mode Control of a Class of Second Order Perturbed Nonlinear Systems: Application to the Trajectory Tracking of a Quadrotor"],"prefix":"10.3390","volume":"11","author":[{"given":"Arturo","family":"Govea-Vargas","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, CINVESTAV, Av. IPN 2508, Ciudad de M\u00e9xico 07360, M\u00e9xico"}]},{"given":"Rafael","family":"Castro-Linares","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, CINVESTAV, Av. IPN 2508, Ciudad de M\u00e9xico 07360, M\u00e9xico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2367-4553","authenticated-orcid":false,"given":"Manuel A.","family":"Duarte-Mermoud","sequence":"additional","affiliation":[{"name":"Advanced Mining Technology Center, University of Chile, Av. Tupper 2007, Santiago 8370451, Chile"},{"name":"Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago 8370451, Chile"}]},{"given":"Norelys","family":"Aguila-Camacho","sequence":"additional","affiliation":[{"name":"Departmento de Electricidad, Universidad Tecnol\u00f3gica Metropolitana, Av. Jos\u00e9 Pedro Alessandri 1242, Santiago 7800002, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5707-2967","authenticated-orcid":false,"given":"Gustavo E.","family":"Ceballos-Benavides","sequence":"additional","affiliation":[{"name":"Facultad de Negocios, Ingenier\u00eda y Artes Digitales, Universidad Gabriela Mistral, Av. Ricardo Lyon 1177, Providencia, Santiago 7510549, Chile"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Oustaloup, A. (2006). From Fractality to Non Integer Derivation: A Fundamental Idea for a New Process Control Strategy. Anal. Optim. Syst., 53\u201364.","DOI":"10.1007\/BFb0042201"},{"key":"ref_2","unstructured":"Podlubny, I., Dorcak, K., and Kostial, I. (1997, January 10\u201312). On fractional derivatives, fractional-order dynamic systems and PI\u03bbD\u03bc controllers. 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