Resilient consensus-based satellite coordinate formation against Byzantine adversaries with noisy communication

This paper investigates the problem of resilient satellite coordinate formation control considering two issues: a) the network may contain some Byzantine satellites, which update controls abnormally and can send arbitrarily different information to neighbors; b) the inter-satellite communication contains unknown but bounded noise. The former can drive the motion of normal satellites arbitrarily and deteriorate formation performances or even destroy the formation. Moreover, communication noises may be coupled with the erroneous information sent by adversaries and make normal satellites difficult to suppress the Byzantines’ effects on formation control. Two formation scenarios are considered. In the first, each satellite can access its desired formation coordinate trajectory, while in the second, such information is only known by leaders and other satellites can access the desired relative positions with respect to neighbors. For each scenario, a novel consensus-based coordinate formation method is proposed guaranteeing that normal satellites are unaffected by the disruption of Byzantine satellites. By the proposed methods, normal satellites can communicate with neighbors periodically in discrete times and their states always evolve boundedly, and converge to be around the desired values. The conditions on the communication period and the graph connectivity that can ensure the achievement of resilient formations are characterized. The effectiveness of proposed methods are verified by numerical examples.