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Using the backstepping technique and a disturbance observer method, a nonlinear control scheme has been designed and its closed loop system stability has been guaranteed. The parameters of the proposed controller have been optimized via a metaheuristic optimization algorithm called the firefly algorithm. In the optimization design, the modified Integral of the time-weighted absolute value of the error has been used as the cost function. To prove the effectiveness of the controller, the results are compared via simulation with the traditional backstepping controller on a model ship named Cybership II.<\/jats:p>","DOI":"10.1177\/0142331217695388","type":"journal-article","created":{"date-parts":[[2017,3,22]],"date-time":"2017-03-22T18:35:26Z","timestamp":1490207726000},"page":"1983-1998","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":12,"title":["Optimal backstepping control for a ship using firefly optimization algorithm and disturbance observer"],"prefix":"10.1177","volume":"40","author":[{"given":"Muhammad","family":"Ejaz","sequence":"first","affiliation":[{"name":"College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mou","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,3,22]]},"reference":[{"issue":"6","key":"bibr1-0142331217695388","first-page":"1311","volume":"11","author":"Atwell JA","year":"2001","journal-title":"Applied Mathematics And Computer Science"},{"key":"bibr2-0142331217695388","doi-asserted-by":"publisher","DOI":"10.2528\/PIERB11053108"},{"key":"bibr3-0142331217695388","volume-title":"Encyclopd\u00e6ia Britannica. 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