Sliding Mode/Backstepping Coordinated Control Of Satellite Formation Based On Consensus Theory

Satellite formation flying has huge technological advantages and broad applicationprospects, and has received a lot of research interest in recent years. Based on consensustheory, this paper investigates the coordinated control of attitude and orbit of the satelliteformation using sliding mode and backstepping method.Considering attitude coordination control for satellite formation with matchedperturbations, a time-varying sliding mode control method is proposed to guarantee theoccurrence of the sliding mode at the very beginning. Thus, the reaching phase of slidingmode control is eliminated and the global robustness is realized. Moreover, the attitudes ofthe satellite formation converge to the desired trajectory with exponential speed, whilecoordinating with each other. Furthermore, the coordinated control of attitudes for satelliteformation in presence of matched perturbations and noises is studied. Firstly, a virtualsystem used to generate reference trajectory is designed, which has the second-orderproperty and improves the attitude coordination and the flexibility of control design. Then,the attitude coordination control law is proposed by using sliding mode and LMI method.Sliding mode method makes the satellites not sensitive to the matched perturbations andLMI method contributes to the H∞performance through adjusting the feedback from theneighbor satellites.Attitude coordination control of satellite formation is addressed in two cases. In thefirst case, attitude reference is constant and only available to a part of the satellites. Inanother case, attitude is time-varying and available to all of the satellites. For the first case,the virtual systems corresponding to each satellite is introduced, which includes thefeedback from the satellite formation system and thus avoid the too fast convergence of thevirtual systems. Based on this design, the coordination control law for the first case isproposed by combining the Lyapunov stability theory and the backstepping method. Foranother case, a virtual angular velocity control input is firstly designed, and thenLyapunov-Krasovski function and backstepping makes it possible to propose the controllaw for this case.Finally, the virtual systems idea and the backstepping method are used to design theorbit coordination control for the satellite formation. A acceleration input law is proposed torealize the orbit coordination control for the formation keeping and reconfiguration of the satellite formation in presence of multiple delays, moreover, the satellite formation isdescribed by HCW equation.