Privacy-Preserving Cooperative Control of Multi-Spacecraft with Encrypted Communication

Ensuring security in cooperative control is essential for multi-spacecraft systems, particularly given the escalating frequency of cyberattacks. Existing research predominantly addresses integrity attacks such as sensor spoofing, command injection, and false data injection, but confidentiality vulnerabilities, including eavesdropping and leakage of mission-critical data, remain challenging. To bridge this gap, this paper proposes a privacypreserving cooperative control scheme that integrates a Paillier-based encrypted communication protocol with a state-independent dynamic quantization strategy. By incorporating Paillier encryption and a stochastic confusion factor, the proposed protocol prevents unauthorized access and data leakage, defending against both external eavesdroppers and untrusted neighboring spacecraft within the formation. Building on the encrypted communication protocol, a privacy-preserving coordinated controller is developed to achieve the desired formation maintenance of multi-spacecraft systems. Furthermore, the time-varying quantization sensitivity design ensures progressively diminishing quantization errors over time, thereby guaranteeing asymptotic system convergence. This design outperforms both traditional fixed-step uniform quantization techniques and existing dynamic quantization approaches reliant on precise model knowledge or state-dependent adjustments. Numerical simulations validate the effectiveness of the proposed scheme in enhancing both data privacy and formation stability.