Controlling Multispacecraft Formations Under Eavesdropping Constraints: A $\epsilon$-Nash Equilibrium Approach

Abstract

This article addresses the formation control problem for multispacecraft systems in the presence of eavesdroppers. The spacecrafts in the system transmit information through a distributed communication topology, and the eavesdropping rate is modeled as distance-dependence. To mitigate the impact of eavesdropping, we design a control strategy based on $\epsilon$-Nash equilibrium and the backstepping method, ensuring the spacecrafts achieve the desired formation while minimizing information leakage. Finally, we prove the stability of the proposed algorithm and the boundedness of $\epsilon$. The effectiveness of the proposed approach is demonstrated through simulations with satellite clusters and experimental validation using wheeled robots.