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

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula>-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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula>. The effectiveness of the proposed approach is demonstrated through simulations with satellite clusters and experimental validation using wheeled robots.