An energy-matching optimal control method for consensus of spacecraft cluster flight

This paper presents an optimal control method for consensus of spacecraft cluster flight under a kind of energy matching condition. Firstly, the relationship between energy matching and spacecraft periodically bounded relative motion is analyzed, and the spacecraft energy matching principle is applied to configure the initial conditions. Then, the period-delayed errors are employed as state variables to establish the period-delayed errors dynamics model of a single spacecraft and the cluster. Next a novel spacecraft cluster feedback control law with coupling gain is designed, so that the spacecraft cluster periodically bounded relative motion consensus problem is transformed into a period-delayed errors state consensus problem. Based on the consensus region theory in the research of multi-agent system consensus issues, considering the spacecraft information cluster topology relationship as well, the coupling gain can be obtained to meet the consensus region. Linear quadratic regulator (LQR) based optimal control approach is used to determine the feedback control gain matrix. This method can realize the synchronization of spacecraft cluster period-delayed errors, leading to the semi-major axis (SMA) tending to be consistent and the energy-matching of spacecraft cluster. Then spacecraft can emerge the global coordination cluster behavior. Finally the feasibility and effectiveness of the present energy-matching optimal consensus for spacecraft cluster flight is verified through numerical simulations.