Coding Matrix based Detection of False Data Injection Attack for Coulomb Satellite Formation Systems with LQG Control

In this paper, parameters of Coulomb satellite formation process are derived based on two sets of coordinate systems, and the relative motion equations of the formation is obtained by substituting the energy function of the system into the Lagrange equation. A control scheme to stabilize the formation process of Coulomb satellites is designed by combining a Kalman filter with a LQG controller. At the same time, a signal is designed from the perspective of the attackers so that the residue related value captured by the detector can be maintained in a small range while a significant state estimation error is achieved. At the same time, a coding matrix scheme is proposed from the perspective of the defender to destroy the stealthiness of the attack by properly encoding/decoding the data transmitted/received, so that the attack can be successfully detected. Finally, stealthiness of the false data injection attack and the method of encryption matrix detection are verified through simulation.