Optimal control for consensus of spacecrafts cluster flight

This paper presents an optimal control method for consensus of spacecrafts cluster flight based on linear quadratic regulation (LQR). Firstly, we employ period-delayed errors as states of cooperative control and derive period-delayed errors dynamics of single spacecraft and the cluster of spacecrafts. Then, we converts the control problem of spacecrafts cluster flight periodically bounded relative motion into the consensus of period-delayed errors. We devise a feedback control law with a positive scalar called coupling gain. The notion of consensus region used in the consensus problem of multi-agent systems and the graph theory are analyzed. Considering the communication topology, we can select a suitable coupling gain according to the consensus region. Employing LQR-based optimal method, we can design the feedback control gain. So that the period-delayed errors of the spacecrafts cluster and semi-major axis of each spacecraft tend to consensus, which result in spacecrafts cluster emerging the global coordination swarming-like behavior. Numerical simulations are conducted verifying the effectiveness of the proposed LQR-based optimal control method for consensus of spacecrafts cluster flight.