Tracking control of spacecraft formation flying with time delay and H2/H∞ constraints

In this paper, the tracking control of relative motion of two spacecraft in a leader-follower form is investigated. The time delay of signal transmission between the two spacecraft and external disturbances are explicitly considered. For time delay, we model the relative motion in a linear form and utilize the Lyapunov-Krasovskii functional combining with free-weighting matrix method to complete the stability analysis. The external disturbances are then attenuated in the H_∞ sense. Besides, we take the integral quadratic of the tracking error and control input as the tracking performance index, which is in the H₂ sense. A set of linear matrix inequalities (LMIs) is then derived incorporating all the design requirements and cone complementarity linearization technique is used to solve the LMIs. The theoretical analysis is completed based on the general motion model of circular reference orbit for leader spacecraft and numerical simulation results demonstrate the validity of the designed controller.