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Based on a nonlinear model of formation flying, two optimal tracking control laws are proposed to ensure the formation pattern converges to the predetermined configuration. The first optimal control law which combines Lyapunov optimizing control with a trajectory-following optimization technique is developed to solve the finite-time nonlinear optimal control problem. For the second controller, an extended [Formula: see text]-[Formula: see text] method is applied to design a closed-form feedback control scheme for nonlinear control problem of spacecraft formation flying with non-standard cost functions. By taking into account the flying safety, a repulsive control scheme is incorporated in the optimal controller to ensure collision avoidance and minimize the performance index. Finally, a numerical example is performed to demonstrate the effectiveness of the proposed approaches. <\/jats:p>","DOI":"10.1177\/0142331218773506","type":"journal-article","created":{"date-parts":[[2018,6,11]],"date-time":"2018-06-11T13:11:36Z","timestamp":1528722696000},"page":"889-899","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":12,"title":["Nonlinear optimal tracking control of spacecraft formation flying with collision avoidance"],"prefix":"10.1177","volume":"41","author":[{"given":"Ruixia","family":"Liu","sequence":"first","affiliation":[{"name":"Research Center of Satellite Technology, Harbin Institute of Technology, China"}]},{"given":"Ming","family":"Liu","sequence":"additional","affiliation":[{"name":"Research Center of Satellite Technology, Harbin Institute of Technology, China"}]},{"given":"Yuan","family":"Liu","sequence":"additional","affiliation":[{"name":"Research Center of Satellite Technology, 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