Robust control of a hub-spoke tethered formation system of microsatellites using Hamilton-Jacobi inequality

The problem of controlling a rotating hub-spoke tethered formation system in low Earth orbit is considered, in which microsatellites are located radially around the central spacecraft (hub) and connected to it by tethers (spokes). To analyze the dynamics of the tethered system, a mathematical model is developed in the orbital coordinate system by Lagrange method, in which the central spacecraft is regarded as a rigid body. In the proposed control scheme, the spin motion of the central body is regulated by the control moment, and tether deployment control law is proposed by robust approach, which is carried out by regulating the tether tensions and low thrusts acting on the microsatellites. The robustness and stability of the system are investigated using Lyapunov theory and Hamilton-Jacobi inequality, which is used to determine the robustness index of the control system. The results of numerical calculations are presented, which confirm that the proposed control scheme is effective when taking into account periodic gravitational perturbations, external perturbations and perturbations associated with uncertainty in the initial states of the system and with the rotation of the central body.