Suboptimal on Average Satellite Attitude Control in the Presence of Discrete Inaccurate Measurements

The problem of the active stabilization of the oscillations of an artificial satellite by thrusters is considered. The satellite moves in a circular orbit and oscillates around the center of mass in the plane of the orbit. Relay control is used to minimize fuel consumption. The state of the plant is not known with certainty, but it is refined by discrete inaccurate measurements. Therefore, the problem of the optimal on average control of a bundle of trajectories is investigated. The stability error is characterized by the average value of the energy integral. Taking into account the practical accuracy of executing the thruster firing and shutdown commands, the constrained minimization problem to be solved becomes discrete. The optimal control of one trajectory is used to control the bundle. This approach based on the principle of separation leads to the suboptimal control of the bundle, which, however, proves to be acceptable in practice.