Noncertainty-Equivalence Spacecraft Adaptive Formation Control with Filtered Signals

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Journal of Aerospace Engineering






The paper develops a noncertainty-equivalence adaptive (NCEA) spacecraft formation control system, using filtered signals, based on the immersion and invariance methodology. It is assumed that a target spacecraft is in an elliptic orbit and a follower satellite is moving around it. It is also assumed that the mass of the follower satellite is not known, and its dynamics include time-varying periodic as well as random disturbance forces. The objective is to design an adaptive control system so that the follower spacecraft remains in a specified formation with respect to the target spacecraft. First, based on the immersion and invariance theory, a control system - consisting of an adaptive stabilizing law and a parameter identifier - is designed for the relative position control of the follower satellite, perturbed by time-varying periodic forces. The control system is synthesized using filtered signals. Unlike traditional certainty-equivalence adaptive laws, the parameter estimates include certain nonlinear algebraic functions, besides signals obtained by integral action. Based on the Lyapunov approach, it is shown that all the signals in the closed-loop system are bounded, and that the relative position trajectory error asymptotically converges to zero. A special feature of the control systems is that the trajectories of the closed-loop system eventually evolve on an attractive manifold in an extended state space. Furthermore, the parameter identifier has strong stability properties. Although the NCEA system is robust to disturbance inputs, σ modification is introduced in the update law for regulating the residual set, and global uniform ultimate boundedness of the trajectories is established. Simulation results are presented which show that the designed control system achieves precise formation control, despite parameter uncertainty and time-varying periodic and random disturbance forces. © 2017 American Society of Civil Engineers.



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