A Decomposition-Based Approach to Linear Time-Periodic Distributed Control of Satellite Formations

In this paper, we consider the problem of designing a distributed controller for a formation of spacecraft following a periodic orbit. Each satellite is controlled locally on the basis of information from only a subset of the others (the nearest ones). We describe the dynamics of each spacecraft by means of a linear time-periodic (LTP) approximation, and we cast the satellite formation into a state-space formulation that facilitates control synthesis. Our technique exploits a novel modal decomposition of the state-space model and uses linear matrix inequalities (LMIs) for suboptimal control design of distributed controllers with guaranteed H_∞ performance for formations of any size. The application of the method is shown in two case studies. The first example is inspired by a mission in a low, sun-synchronous Earth orbit, namely the new Dutch-Chinese Formation for Atmospheric Science and Technology demonstration mission (FAST), which is now in the preliminary design phase. The second example deals with a formation of spacecraft in a halo orbit.