Distributed Finite-time Formation Coordinated Control For Formation Flying Satellite

Satellite Formation flying plays a more and more important role in the future space.As a new space technology, satellite formation can accomplish many tasks that singlesatellite is unable to finish, such as Spatial Interferometer，Synthetic Aperture Radar andso on. Moreover, compared with the traditional big satellites, consider modularizing thebig satellites, which has more advantage in many aspects such as design cycle, launchcost, reliability and so on. By researching the satellite formation flying technology, it iseasy to find out that it has wide application prospect and practical value in civil,scientific and military area. In the task of practical formation flying, it usually requireseach formation member to do the formation maneuver in special formation coordinationor in special configuration. The traditional controller can only guarantee that the closedloop system is gradually stabilizing, but it can not guarantee that it has the stability inlimited time. As the finite-time controller can make the system stable in limited time, itleads to more and more wide research. This paper aims at coordinated formation, whosedesign is based on finite-time controlling arithmetic of a terminal sliding mode, torealize the formation establishing or formation keeping in limited time.At first, the paper finds out that distributed cooperation strategy has the obviousadvantage in coordinated problems, and summarizes the theory knowledge of algebramap about describing the local information exchange of distributed cooperation.Through the dynamical equation of reference satellite and formation satellite, build therelative movement model of satellite formation, hypothesize the measure,communication and so on among formation members, and describe the satelliteformation cooperation problems in all aspects.Next, in order to realize the coordinated formation in limited time, design afinite-time controller, which is based on a terminal sliding mode. Through mathematic,it proves that the controller can realize the finite-time formation establishing, formationkeeping, and formation maneuvering and so on. Besides, it also introduces two kinds ofsaturation functions. Considering the fantastic possibilities of the terminal sliding modelcontrollers, it needs to further to design nonsingular terminal sliding model controller,and analyzes and compare some measures to improve cooperation function effects byintroducing consistent cooperation.Finally, in order to further improve the controlling effects, consider the basis ofnonsingular terminal sliding model, and introduce the higher-order terms of error toimprove the rapidity of the system. So, designing non-singular rapid terminal slidingcontroller，it proves in theory that the controller can realize the finite-time cooperationof the satellite formation and also proves the rapidity compared with nonsingular terminal sliding model. The emulator shows that the controller can meet the designrequirements and validate its rapidity. In order to increase the robustness, this paper isconsidering doing the adaptive identification to the perturbation, and designs anonsingular rapid terminal sliding model controller with perturbing adaptiveidentification. Both the theory and the emulator show that the controller can realize theaim of controlling.