Long-Term Linear-Quadratic Control of Satellite Constellations in Highly Elliptical Orbits

Abstract

A mathematical model is proposed for representing a multisatellite constellation as a tree graph for the purpose of maintaining its formation. The method of correction of the satellite constellation with transversal impulses using the classical linear-quadratic control is developed. The results of the long-term modeling of a satellite constellation (SC) of four spacecraft for different variants representing its formation as a graph are presented. Questions on the stability of the control laws and accuracy of maintaining the fformation are discussed; the necessary expenses of the characteristic velocity of the corrective impulses are listed. The choice of the control-law parameters reflects a compromise between the accuracy of maintaining the formation and the required fuel consumption. The method allows taking into account an additional requirement, which is typical for highly elliptical orbits: the restriction of the minimum altitude of the perigee. The modeling of the constellations involved using a highly accurate model to predict the spacecraft’s motion, which takes into account the noncentrality of the Earth’s gravitational field, the gravity of the Moon and Sun, and the pressure of solar radiation.